visual representation examples in science

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Teaching and Learning Science through Multiple Representations: Intuitions and Executive Functions

• Janice Hansen
• Lindsey Engle Richland

Director of Undergraduate Education, School of Education, University of California Irvine, Irvine, CA 92697

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*Address correspondence to: Lindsey Richland ( E-mail Address: [email protected] ; uciscienceoflearning.org).

Associate Professor of Education, School of Education, University of California Irvine, Irvine, CA 92697

Reasoning about visual representations in science requires the ability to control one’s attention, inhibit attention to irrelevant or incorrect information, and hold information in mind while manipulating it actively—all aspects of the limited-capacity cognitive system described as humans’ executive functions. This article describes pedagogical intuitions on best practices for how to sequence visual representations among pre-service teachers, adult undergraduates, and middle school children, with learning also tested in the middle school sample. Interestingly, at all ages, most people reported beliefs about teaching others that were different from beliefs about how they would learn. Teaching beliefs were most often that others would learn better from presenting representations one at a time, serially; while learning beliefs were that they themselves would learn best from simultaneous presentations. Students did learn best from simultaneously presented representations of mitosis and meiosis, but only when paired with self-explanation prompts to discuss the relationships between the graphics. These results provide new recommendations for helping students draw connections across visual representations, particularly mitosis and meiosis, and suggest that science educators would benefit from shifting their teaching beliefs to align with beliefs about their own learning from multiple visual representations.

INTRODUCTION

Science, even in a defined field of study such as biology, is not a set of discrete facts, but an interconnected system of complex concepts. The development of conceptually organized and integrated scientific knowledge is an overarching goal of science education, articulated at the K–12 level in the United States recently within the Next Generation Science Standards ( NGSS Lead States, 2013 ). One of the most common instructional supports that science teachers use to engage students in thinking about complex relationships is sequences of visual representations such as diagrams, pictures, or animations ( Roth et al. , 2006 ). Visualizations are central to the learning of science, the practice of science, and the communication of science, and both cognitive scientists and educators agree that they are a vitally important component of science teaching ( Ainsworth and Newton, 2014 ; Eilam and Gilbert, 2014 ; Matthewson, 1999 ). Multiple representations can help learners construct deeper understanding of scientific concepts or system structures than single representations used alone ( National Research Council, 2012 ; Ainsworth, 2014 ). These may be particularly useful when concepts are complex and interrelated, as is the case when one concept builds on another. As learners compare and contrast graphics, they are better able to construct deeper domain understanding ( Ainsworth, 2014 ).

At the same time, one representation is rarely adequate to capture the entirety of a science concept, and multiple representations are often used to describe related aspects of a system (e.g., a diagram of a heart and a diagram of a circulatory system; see Roth et al. , 2006 ). Concerns have been raised, however, about the potential of multiple representations to overly tax learners’ cognitive resources, leading them to not be able to fully process or reason on the basis of the information provided or notice and make inferences about the relationships between the representations ( Kirschner, 2002 ; Cho et al. , 2007 ). This is particularly problematic when the relationship between the representations is important, such as in the case of the model of a heart and a model of the human circulatory system with the heart at its center. Similarly, when two diagrams are intended to allow learners to compare and/or contrast aspects of systems, for example, comparing diagrams of cellular reproduction between those undergoing mitosis and meiosis, both visual representations capture important information that should be learned, but the differences between them are also illustrative and conceptually important.

Adding to the complexity of using multiple representations in classrooms are teacher and student beliefs about how people learn best from these tools. Teachers hold private beliefs about subject matter, teaching, and learning, and these influence their teaching practices ( National Academy of Sciences, 2000 ). Learners also have beliefs about how they learn best, though they are not always reliable judges of their own learning from different classroom practices. This is particularly true when individuals are required to put forth extra effort in learning ( Deslauriers et al. , 2019 ). Understanding these naïve belief systems and how they align with instructional outcomes may inform the development of more effective practices for using multiple representations in classrooms.

This article draws on the cognitive science literature to provide a novel lens for understanding the challenges inherent in learning biological science from the relationships between representations. Cognitive scientists have widely demonstrated that the human attentional system has limited resources, such that one can only meaningfully and actively process a limited set of information at once (see Baddeley and Hitch, 1974 ; Engle, 2002 ; Miyake and Friedman, 2012 ; Diamond, 2013 ). Generally, this system has been described as a system of executive functions (EFs), which are comprised of three broad components that enable a person to selectively allocate attention to information in the world and that are correlated but distinct processes ( Miyake et al. , 2000 ; Miyake and Friedman, 2012 ). Working memory (WM) is defined most broadly as the ability to hold information in mind and manipulate it (see Baddeley and Hitch, 1974 ; Engle, 2002 ; Miyake and Friedman, 2012 ). Working memory is not simply the ability to hold information in mind (e.g., a list of vocabulary words) but also to do cognitive work with that information (e.g., reorganizing new vocabulary words into a concept map). Inhibitory control (IC; see Diamond, 2013 ) is described as the integrated processes of inhibiting attention and prepotent actions based on irrelevant or misleading information (e.g., saying “night” when presented with a diagram of a sun, or expending effort to not consider the size of a textbook drawing of a cell to avoid misconceptions that cells are visible to the natural eye). Task switching refers to the processing involved in changing one’s goal-oriented task engagement and routines, for example, switching categorization criterion or switching from pointing to parts of a cell diagram to explaining how cells are part of a reproductive system (see Miyaki et al. , 2000). While separate processes, EFs are generally believed to share a limited set of resources, such that if someone is exerting all of their cognitive resources attempting to inhibit attention to something very salient but misleading, they will have less capacity to use WM to make inferences about the relationships between representations.

EFs are primarily controlled by the prefrontal cortex of the brain, an area that has been found to develop well into adolescence ( Diamond, 2013 ). Therefore, when reasoning about complex relationships between visual representations, which has a high requirement for EFs (see Waltz et al. , 2000 ; Simms et al. , 2018 ), children may need significant support for noticing key correspondences of visual representations and ignoring irrelevant or misleading features. This is particularly the case when reasoning about complex concepts such as scientific systems or solving complex problems (e.g., Gick and Holyoak, 1980 , 1983 ; Zook, 1991 ).

Though using diagrams, charts, pictures, and models is common classroom practice, careful consideration of the psychological processes of learning will aid educators in optimizing student learning from these visual representations. Theories of learning from multiple representations have generally focused on how to engage cognitive resources effectively and avoid high demand that is not intrinsic to the conceptual aspects of the intended task ( Sweller et al. , 1998 ; Mayer, 2019 ). Theories of multimedia learning build on this foundation to describe how learners make sense of text and pictures presented together. While well-designed instruction that includes text and media together may enhance learning, the processes whereby learners make sense of both textual and visual input within the cognitive architecture are complex (for a full discussion, see Mayer, 2019 ) and involve the coordination of more than one cognitive subsystem ( Schnotz and Bannert, 2003 ; Schnotz, 2019 ). Complementary representations, which are designed to highlight comparisons across diagrams, as in the case of the related processes of photosynthesis and respiration, may be particularly difficult for learners to process ( Ainsworth, 2014 ).

The Role of EFs in Making Sense of Visual Representations

Cognitive scientists broadly agree that the complexity and amount of information to be processed in visual representations can be cognitively demanding, particularly when the relationships between representations are meaningful and will lead the learner to build a broader understanding of the concept being represented ( Phillips et al. , 2010 ). The optimal way to reduce the burden on learners has been explored, yet not fully answered, and the relationship between research and practice remains complex ( Ainsworth and Newton, 2014 ).

One field of cognitive science focuses on relational and analogical reasoning, exploring how reasoners draw connections between representational systems (see Holyoak, 2012 ). Some have argued that the process of drawing structural (or conceptual) relationships between representations imposes a high burden on WM and IC of attention, particularly when the representations are not visible simultaneously (see Cho et al. , 2007 ; Krawczyk et al. , 2008 ; Begolli et al. , 2018 ).

One can compare the surface and structural elements of visual representations. Surface-level elements are those that are based in the appearance of the figures (e.g., the colors, shapes, and sizes of the objects). The structural or relational elements are the relationships between and among the visual forms, which are more typically the abstract scientific processes being explained (e.g., cell reproduction in a diagram of mitosis). As understood within the structure-mapping theory of analogical reasoning, reasoners make inferences by taking a mental model of the key structured relationships within one representation and aligning them with the key structures within a target problem, concept, or representation. They may notice the surface appearance of the visual representations, and sometimes those provide clues about how to align and recognize abstract relationships across the representations, but those surface features are typically not intended to be what was memorized. Instead, learners should map correspondences between those aligned representations to notice key abstract/conceptual similarities or differences and then draw inferences based on those alignments about the target context.

When the related representations are presented one at a time—serially—this alignment process is more effortful. When looking at the second figure, the reasoner must recall a prior visual representation and hold it in WM, while manipulating it to determine its relevance to the currently visible visual representation. The complexity involved in this mental processing is clear when considering related science concepts such as mitosis and meiosis, where a learner might align the structures of chromosomal replication, the process of cellular division, the characteristics of daughter cells, and so on, to construct an understanding of how the two types of cellular reproduction relate to each other. The learner may first notice that representations of mitosis and meiosis often both contain circles that show cells, and each cell has some wiggly lines (chromosomes) inside (i.e., the surface features of these representations), but this is not the key insight; rather, learners must go further to notice the relationships . They must see the changes from one cell to the next and the relative numbers of chromosomes in particular.

Importantly, the relational reasoning literature suggests that having visual information available should reduce the burden on reasoners’ cognitive processing by providing WM off-load, yet at the same time, this may not be enough to ensure that reasoners notice and map correspondences across representations ( Gick and Holyoak, 1983 ). Thus, reasoners may require additional support to draw their attention to link the representations actively. This may be especially important when the burden on EF for representing the information is high ( Richland and McDonough, 2010 ; Begolli and Richland, 2016 ). In a classroom context, children’s individual level of EF capacity predicted learning from a lesson in which visual representations were not visible simultaneously ( Begolli et al. , 2018 ), providing some evidence that, particularly for children with lower levels of EF available, ensuring that multiple representations are visible simultaneously and well supported might be important for improving learning.

In contrast, cognitive scientists within the field of multimodal learning, drawing on Baddeley and Hitch’s (1974) model of WM, as well as cognitive load theory (see Sweller et al. , 1998 ), have argued that simplifying representations is important to reducing cognitive overload and improving intended learning (for a comprehensive review of historical visual representation research, see Phillips et al. , 2010 ). In particular, Mayer’s cognitive theory of multimedia learning (see Mayer, 2019 ) suggests that, when a person processes a visual representation with text, he or she develops two mental representations of the material. One mental representation draws on resources within the verbal WM system based on the text, and the other draws on resources within a visual–spatial WM store, which Baddeley’s model of WM suggests draws on the same overall WM resources. So, if a visual representation has too much information of both types, a learner’s attentional resources might be overloaded, leaving little EF stores to inhibit irrelevant information (e.g., irrelevant colors and graphics to promote interest). More importantly to our current discussion, this might also impede processing of the relationships between representations. The theory does hypothesize that providing language and visual representations simultaneously can improve overall knowledge, but suggests that auditory narration is better than written text when possible. Thus, it is not clear how one would optimize learning from multiple representations when the instructional goal is to have students compare these, recognize correspondences, recognize differences, or otherwise relate them. The field of multimodal learning and cognitive load suggests that presenting two visual representations with accompanying text labels, all simultaneously, might be too high a burden for the EF system.

Thus, while science educators generally agree that guiding students toward an organized, complex, richly connected understanding of science topics through multiple visual representations is desirable ( Ainsworth and Newton, 2014 ), implementing this type of instruction requires careful consideration of the cognitive processes involved, and the implications for sequencing presentation of such representations are not yet clear. Classroom instruction that effectively supports children in making deep conceptual connections is challenging for teachers (e.g., Stein et al. , 2008 ; Smith et al. , 2009 ), so more information about these details of instruction have important applied implications.

The Current Studies

The studies reported in this article explore teachers’ and learners’ intuitive beliefs about learning from visual representations of related science concepts (Study 1) and tests those beliefs experimentally in a computer-based classroom lesson with middle school students (Study 2). Learning from multiple representations is a key pedagogical consideration in teaching science for reasoning ( NGSS Lead States, 2013 ) and raises questions about whether optimal learning emerges from two representations displayed simultaneously, where EF resources could be focused on drawing connections and generating inferences, or displayed serially, where EF resource demands on processing each representation would be reduced.

This study focused on the two processes of cellular reproduction: mitosis and meiosis. This is a critical component of most introductory biology curricula and one that every high school student must master ( NGSS Lead States, 2013 ). While mastery of these topics requires more depth than introduced here, this is an ideal pedagogical context for examining intuitions and learning from multiple representations, as these two processes are highly related but have core structural differences that are regularly made visible through diagrammatic representations. Thus, the findings here will have direct implications for teaching this core biological topic and also will provide insights for any of the many pedagogical contexts in the sciences where representations are necessary to support students in building from the understanding of one case to a second with related but different structure. This might include comparing representations of plant and animal cells or, at a more complex level, anatomical systems such as respiratory and circulatory systems.

The first study explored implicit beliefs of pre-service teachers, adult non-educators who were currently undergraduates, and middle school children, regarding whether people learn better from multiple visual representations that are presented simultaneously or serially and the reasons they gave for holding these beliefs. The three groups were asked how they themselves learned best, as well as how they believed a younger set of learners would learn best to distinguish between their understanding of their own cognition and their beliefs based on their own naïve theories of pedagogy. The primary research questions were whether these two sets of learning beliefs would diverge, assessing whether there were differences between peoples’ beliefs about their own learning and their beliefs about pedagogy—how others would learn best.

The second study tested how these implicit beliefs related to the mental representations children gained from instruction that involved comparisons between multiple representations with lower or higher levels of support for drawing connections between them, including serial versus simultaneous presentation, as well as more explicit prompts to actively align and compare the representations. To answer these questions, we developed an experiment wherein children were randomly assigned to learn from a computerized instructional module in which only the method of presenting diagrams varied across conditions.

The preponderance of research regarding how people process multiple representations has been conducted with adults rather than children ( Cook, 2006 ). This is an important oversight, given that visual representations are the most commonly used instructional supports in American K–12 science classes ( Roth et al. , 2006 ). This study aimed to test predictions made by the cognitive science literature regarding best practices for supporting students in learning from multiple representations. We tested both the mode of ordering the representations (sequentially vs. simultaneously), as well as the level of pedagogical support provided. Thus, Study 1 and 2 together allowed us to gain insight into adults’ and youths’ teaching beliefs about ordering multiple representations and the alignment between these beliefs and students’ actual learning.

Study 1: SURVEY OF IMPLICIT BELIEFS ABOUT LEARNING FROM MULTIPLE REPRESENTATIONS

While both cognitive scientists and science teachers agree that visual representations are important tools in teaching science, the alignment of research to teaching practice is not always direct, and in the demands of real classroom practice, teachers rely heavily on personal judgment in deciding what visual representations to use and how they will be presented ( Ainsworth and Newton, 2014 ). Yet little is known about what informs these judgments, particularly when it comes to multiple representations of related science concepts.

One concern that teachers have is about student competency in interpreting visual representations ( Eilam and Gilbert, 2014 ). But students are not blank slates when they approach a diagram or picture. They have their own metacognitive beliefs about how they learn best. Students, however, are not always the best judges of what helps them learn, particularly when it comes to passive versus effortful learning ( Deslauriers et al. , 2019 ).

The metacognitive beliefs people hold can influence what and how they can learn ( Greeno et al. , 1996 ; Pamuk et al. , 2016 ). Teacher beliefs about learning can influence their classroom practices of teaching, and in turn, indirectly affect student achievement ( Muijs and Reynolds, 2015 ). Further, beginning science teachers and experienced science teachers can have different views of their role in helping students learn. Beginning teachers may hold more teacher-centered traditional views of delivering information ( Luft and Roehrig, 2007 ). Part of building learning theory in educational contexts involves understanding the teaching and learning beliefs that teachers bring to the classroom. Here we collect data to understand beliefs about teaching and learning expressed by pre-service teachers, adult non-educators, and children. We specifically focus on the pedagogical context of how to best sequence visual presentations of multiple representations—simultaneous versus serial presentation.

Participants.

The survey sample included 89 pre-service teachers, 211 adult non-educators, and 385 middle school children. The 89 pre-service teachers were enrolled in a combined credential/master of arts in teaching program at a large suburban university. They were enrolled in a basic cognition class but had not yet received any explicit instruction about either EFs or the use of visual representations. The 211 adult non-educators were undergraduate students at the same university and represented a wide variety of different majors. All adult participants consented to participation in the study. The 385 middle school students were seventh-grade students of three science teachers at two different suburban schools from the same upper-middle-class district. The middle school participants were recruited through their science teachers. The day before the study, students were given a letter to take home that described the study. The letter informed parents/guardians that students were not required to participate, and that no student-identifiable data would be collected. On the day of data collection, students were read a description of the study and indicated assent through the raising of hands. Students were informed that they could remove themselves from the study at any time and receive the same instruction through text-based instruction provided by their teacher. One student opted out of the study and was not included in further analyses.

Materials and Procedure.

The surveys administered to each population were slightly different in framing due to the different educational background of the children, adults, and teacher candidates, but the key questions analyzed in this study were the same. Also, we intentionally asked each population about their beliefs of how a younger population would learn best, so this differed across participant groups.

Adult participants were given a pencil-and-paper survey as part of a larger, unrelated study. Participants were told that their responses would be used to inform development of new science teaching materials. They were asked about their own science backgrounds and whether they felt they could describe the related processes of mitosis and meiosis to a friend. They were then given a forced-choice item that asked whether they thought they would learn better from a combined (simultaneous presentation) diagram of mitosis and meiosis, or if they thought it would be better to learn from separate diagrams (presented serially). A free-response question asked them to justify their choices. A follow-up question asked them to predict how a middle school student would learn better, and again, participants were asked why they made that choice. The entire survey took approximately 5 minutes to complete, and the key questions are available in the Supplemental Material.

Middle school students answered the same basic questions as the adults, but as they had not yet been exposed to instruction about mitosis and meiosis, the forced-choice item asked whether they would prefer to learn about the related topics of animal and plant cells through representations of each cell presented simultaneously or serially, and why. This was followed up by items asking how they thought a fourth-grade student would learn best and why.

Measures and Data Coding.

Forced-choice responses asking how people would best learn from related diagrams were simply coded “simultaneous” or “serial.” For free-response items asking participants why they made the choice they did, categorical codes were developed to quantify data for comparison. These codes were developed through an iterative process informed by EF literature on learning and its relationship to comparing and contrasting representations (e.g., Krawczyk et al. , 2008 ; Holyoak, 2012 ; Begolli et al. , 2018 ) and refined by the responses themselves. Interrater reliability across codes was set at kappa ≥0.80. Two raters coded a training data set of student responses to allow for discussion and resolution of any discrepancies in codes assigned. The two raters then independently coded 20% of each data set to attain reliability. A single rater (J.H.) coded the remaining data independently. The coding manual is available in the Supplemental Material.

Four codes scored responses to items that asked why people would learn best from either simultaneous or serial presentation of visual representations. These codes were 1) ability to compare and contrast; 2) promotes deeper understanding; 3) described as easier or not as difficult; and 4) cites reducing confusion as a goal. The codes were not mutually exclusive, and a response could receive more than one code. The differences between each of these codes rested on the participants’ explicit use of words that highlighted each of these ideas (e.g., to compare or to reduce confusion) or a clear framing that allowed a coder to differentiate their intention. “Easier versus difficult” provided only a graded description of difficulty and was coded separately from any statements regarding confusion as a mechanism that would form the source of any difficulty. These codes (reported with their associated kappa statistics) are detailed in Table 1 .

Beliefs results are provided for the three sets of participants separately, with overall means and results shown in Figure 1 . Each is discussed in turn, analyzing frequency of endorsing simultaneous versus serial representations both for their own learning and for teaching others who were younger than themselves.

FIGURE 1. Adult, pre-service teacher, and middle school student beliefs about optimal presentation of multiple representations for one’s own learning versus instruction of others.

Pre-service Teachers.

Pre-service teachers ( n = 89) did not overwhelmingly endorse one way of presenting conceptually related visual representations for their own learning, with beliefs split between simultaneous and serial presentation orders as optimal. This difference was not significant; χ 2 (1, N = 89) = 0.91, p = 0.34. Interestingly, their reasons for selecting each of these two different orders were different. Among teachers who endorsed serial presentation of related diagrams for their own learning, avoiding confusion was the most often cited reason ( n = 17, 34.7%). Those who said they preferred related diagrams presented simultaneously cited the ability to compare and contrast as the reason this was desirable ( n = 34, 85.0%).

When asked how middle school students would learn best, however, pre-service teachers significantly often changed their beliefs, and indicated that the learning needs of middle school students differed from their own; χ 2 (1, N = 89) = 22.48, p < 0.01. As shown in Figure 1 , most indicated that serial presentation would be optimal for middle school students. This suggests that the pre-service teachers held a tacit belief that there is a developmental difference in the learning needs of middle school students versus adults when analyzing multiple representations.

The reasons preservice teachers gave for these decisions are similar to those described for how they would themselves learn. Of the 59 respondents who said middle school students would learn best from serially presented diagrams, the most-cited reasons for endorsing this style were avoiding confusion ( n = 22, 37.2%), ease of interpretation ( n = 15, 25.4%), and promoting deeper understanding ( n = 11, 18.6%). Of the 30 pre-service educators who said middle school students would learn best from simultaneously presented diagrams, 80.0% ( n = 24) cited the ability to compare and contrast as the reason why this method was preferable.

Adult Non-educators.

In contrast to pre-service teachers, the adult non-educators, who were currently undergraduate students, indicated a clear preference for simultaneous presentation for their own learning; χ 2 (1, N = 211) = 50.28, p < 0.01. Again, the reasons for endorsing simultaneous ordering were the same. Among the 54 participants who endorsed serial presentation for their own learning, the most common reasons cited were ease of interpretation ( n = 23, 42.6%), and avoiding confusion ( n = 22, 40.7%). Of the 157 people who preferred simultaneous presentation, 89.2% cited the ability to compare and contrast as the reason ( n = 140).

When asked whether serial or simultaneous visual representations were preferable for middle school students, like pre-service teachers, a significant number of adult non-educators felt middle school students would benefit from a different manner of presentation than themselves as adults; χ 2 (1, N = 211) = 21.96, p < 0.01. This shifted to more recommendations for serial presentation for children than for themselves, though there were not significant differences between these two; χ 2 (1, N = 211) = 3.99, p = 0.05.

The main reason one style of presentation was preferred over the other was similar for the adult non-educators as for the pre-service teachers. For those endorsing serial presentation, avoiding confusion was cited by 48 of the 91 respondents (52.7%). Among 120 people who felt simultaneous presentation would be better, 89 (74.2%) cited the ability to compare and contrast as important.

Middle School Students.

Like their adult counterparts, middle school students had strong opinions about the way related visual representations should be presented. Students of color in the proportion of participation as a result of the transition online. As shown in Figure 1 , simultaneous presentation was preferred for their own learning. This difference was significant; χ 2 (1, N = 385) = 124.57, p < 0.01. Again of interest is that these youth cited the same reasons for preferring simultaneous versus serial presentation order as the adults did. Those who preferred serial presentation endorsed its role in avoiding confusion (46.9%, n = 39), and the belief that it would lead to greater understanding (24.1%, n = 20). The significant reason for endorsing simultaneous presentation was the ability to compare and contrast (86.4%, n = 261).

As in adults, the children’s beliefs about how they would learn best differed significantly from how they thought younger students would learn; χ 2 (1, N = 384) = 19.02, p < 0.01. When asked what presentation would be better for fourth-grade students, the middle school students were split, with 197 (51.3%) endorsing simultaneous presentation. Respondents who selected serial presentation were more likely than those selecting simultaneous presentation to say it would help younger children avoid confusion or distraction (12.8%, n = 24) and lead to greater depth of understanding (7.0%, n = 13). Those who selected simultaneous presentation were most likely to suggest that the ability to compare and contrast would be enhanced (23.3%, n = 46).

Importantly, the beliefs of middle school students about how they would learn best differed significantly from the beliefs pre-service teachers held about the students’ learning needs. Middle school students strongly preferred simultaneous presentation for their own learning, but the pre-service teachers felt that the students would learn better from serial presentation; χ 2 (1, N = 474) = 68.94, p < 0.01.

Previous research has indicated that beliefs about learning are important for their influence on teacher instructional practice ( Friedrichsen et al. , 2011 ). Collected survey data from the 211 adult non-educator and 385 middle school student samples were fairly consistent, in that both groups preferred to learn from simultaneous presentation of visual representations when learning about conceptually connected science concepts. The 89 pre-service teachers differed in that they did not significantly choose one manner of presentation over the other for their own learning. All of the adults were more likely to prefer serial presentation for middle school students, though the students themselves strongly preferred simultaneous presentation. This difference was significant when comparing pre-service teacher preference for middle school student learning and the middle school student preferences.

For participants who were drawn to serially presented visual representations, concern about the amount of information to be processed was commonly expressed. A typical response reads, “With just one [simultaneously presented diagram] it might get jumbled together and confusing.” Those who preferred simultaneous presentation were more likely to cite the ability to compare and contrast as being desirable. This suggests that, across all three groups, participants had a sense that the EF resources required to process simultaneously presented diagrams would be much higher, at least initially, than the cognitive demand of processing serially presented diagrams.

Pre-service teachers felt strongly that middle school students needed serial presentation of diagrams of conceptually related content in order to learn best, while the responses of non-educators were evenly split between endorsing serial and simultaneous presentation. As one teacher pointed out, “Two diagrams would keep each process separate. This would help students get a clear idea of both processes before they are shown together.” Non-educator adults and middle school children were mixed on what method of presentation children younger than themselves would need, and the difference did not rise to the level of significance. This indicates that the pre-service teachers held stronger beliefs that developmental processes underlie the ability to process complex science diagrams.

One interesting area where pre-service teachers and middle school students disagreed was on how middle school students would learn best from multiple visual representations. While the pre-educators felt students would need serial presentation, 78.4% of students preferred simultaneous presentation and the ability to compare and contrast across related representations shown together. This mismatch between the beliefs that pre-service teachers held about student learning, and the students’ own metacognitive beliefs may signal misunderstandings about learner capabilities. Pre-service teachers appear to take a cautious view of the limits of the EFs of students as they grapple with complex diagrams, while students may overestimate their abilities to make meaningful connections between related science representations.

A second study was designed to examine how different presentation styles affected student learning. The results of that study are summarized in the next section.

Study 2: EXPERIMENT VARYING PRESENTATION OF VISUAL REPRESENTATIONS IN A MIDDLE SCHOOL LESSON ON MITOSIS AND MEIOSIS

While the survey results of Study 1 suggest that both adults and children have deeply held beliefs about the ways students learn from conceptually connected visual representations, the literature is not clear on how these beliefs align with actual learning outcomes. The second study provides data on student learning from two representations aligned in different ways. This study compared not only serial versus simple simultaneous diagram presentation, but also added two simultaneous presentation conditions suggested by cognitive scientists interested in EFs: simultaneous presentation with support for noticing and simultaneous presentation with structure mapping support.

The students in Study 1 also participated in Study 2 and were recruited through three seventh grade science teachers at two suburban schools. Both schools were from the same upper-middle-class district. Two of the teachers were from school A, and across their eight classes, they taught 224 of the study participants. The teacher at school B had five classes and a total of 161 study participants. Due to course work planning constraints of the teachers, researchers had only 1 day to collect data. Though no individual demographic data were collected, the students in the study group were described by participating teachers as representative of the school population, as summarized in Table 2 .

The day before the study, students in all classes were given a letter to take home that described the study. The letter informed parents/guardians that students were not required to participate, and that no student-identifiable data would be collected. On the day of data collection, students were read a description of the study and indicated assent through the raising of hands. Students were informed that they could remove themselves from the study at any time and receive the same instruction through text-based instruction provided by their teacher. One student opted out of the study and was not included in further analyses.

This study was completed under the IRB approval of the University of California, Irvine, HS no. 2012-9111.

Materials and Procedure

Instructional lesson..

A computer-based instructional module was designed using the Web-based Inquiry Science Environment. The students first responded to a survey (described in Study 1) that asked them how they thought they would learn best from related diagrams. This was followed by a lesson that introduced the related concepts of cell replication and reproduction through mitosis and meiosis. The module forced students to complete learning tasks on each screen before moving forward. After advancing the module, they were not able to move backward. This ensured that students completed all steps of instruction in order.

Regardless of the method of presenting diagrams, the text of the lesson itself remained constant and was based on the printed life sciences textbook used by seventh-grade classrooms throughout the school district ( Padilla, 2007 ). Five screens were included in mitosis instruction, one each for interphase, metaphase, anaphase/telophase, and cytokinesis. This aligned with the textbook presentation of the same material. Each screen included a diagram alongside the text. A sample of the instructional diagram for mitosis is provided in Figure 2 .

FIGURE 2. Mitosis diagram from instructional model.

After completing the mitosis instruction, students were given a constructed-response item that asked them to recall information from the lesson. This page did not include any diagrams, only a box that simply asked, “How would you describe the process of mitosis to a friend? Describe as many steps as you can.” At the completion of this screen, students saw a graphic that praised them for their hard work.

The second segment of instruction introduced the concept of meiosis through a series of seven different screens: Introduction; Interphase; Prophase I; Metaphase I; Anaphase I and Telophase I; Cytokinesis I; and Meiosis II. These segments were designed to closely align with the mitosis screens in the module. The instructional text was adapted from the ninth-grade science textbook from the same publisher as the seventh-grade textbook ( Miller and Levine, 2011 ). Some of the text was simplified to eliminate vocabulary to which the students had not yet been exposed and to match the instruction in the mitosis portion of the module. The meiosis diagram that appeared in the instructional module is shown in Figure 3 .

FIGURE 3. Meiosis diagram from instructional model.

Once students completed the meiosis instructional module, they again received a recall item on a screen containing only text. Similar to the prior recall item, students were asked how they would describe meiosis to a friend, describing as many steps as they could. Upon submission, students were provided a screen praising their hard work and their completion of this section.

The experiment sought to test whether students’ beliefs about learning from multiple representations were aligned with their patterns of learning from multiple representations. Specifically, the learning context was knowledge gain from conceptually related science diagrams rather than different diagrams of the same concept. The experimental manipulations therefore involved providing diagrams organized in four different ways within the lesson: 1) serial presentation of separate mitosis and meiosis diagrams; 2) simultaneous presentation of the diagrams side by side; 3) simultaneously presented diagrams that signaled the learner to key similarities and differences; and 4) simultaneously presented diagrams with support for structure mapping. Computer-generated random assignment to experimental condition was achieved within each classroom using dummy codes for each student, such that the researchers did not know which student was assigned which code or experimental condition. The classrooms were all existing, mixed-ability classes. Random assignment at the student level allowed us to minimize any effects of classroom teacher or classroom-level characteristics and maximize ecological validity, as the instruction took place in a whole-classroom setting with peers and everyday social context. Written materials are provided in the Supplemental Material.

Serial Presentation .

In the serial presentation condition, a mitosis diagram (see example in Figure 2 ) was provided to learners during all instruction related to learning about mitosis. A diagram of meiosis (see example in Figure 3 ) was provided to learners during all instruction related to meiosis. Diagrams were never shown on screen at the same time. No additional supports were provided. Serial presentation was included in all classrooms studied ( n = 128).

Simultaneous Presentation .

In the simultaneous presentation condition, a combined diagram showing mitosis and meiosis side-by-side ( Figures 2 and 3 with initial cells aligned side-by-side) was shown during all instruction. Therefore, when students were reading text about mitosis, they could also see the diagram for meiosis, and vice versa. There were no additional supports for noticing or interpreting the diagrams. Simultaneous diagrams were presented in all classrooms studied ( n = 124).

Simultaneous with Signaling .

In the simultaneous with signaling condition, students received the same combined diagram as in the simultaneous condition. The only difference was the addition of signaling prompts highlighted in red within the diagrams. These signals were designed to alert students to key features of the diagrams. For instance, when a diagram with instruction on cytokinesis was shown, red text asked, “Do the daughter cells look like the parent cells?” (see Supplemental Figure S1). This signaled learners to attend to an important phase in cell division that leads to miotic daughter cells that are identical to parents, while in meiotic cells, the daughter cells are each unique. Simultaneous diagrams with signaling were only offered at school A, with two teachers ( n = 80).

Simultaneous with Structure Mapping Support.

A fourth condition, simultaneous presentation with structure mapping support, draws on prior research that suggests that learners are better able to reason about representations with support (e.g., Gick and Holyoak, 1980 , 1983 ) and better able to generalize their learning when actively participating in mapping the comparative relationships ( Richland and McDonough, 2010 ). In this condition, learners received the screen that presented mitosis and meiosis simultaneously. However, before students left each instructional page, a mouse click would call up a question with a response box. For instance, the meiosis cytokinesis page read, “Take a close look at the picture, comparing the end of mitosis with the end of meiosis. In your own words, describe what is created by meiosis.”

Active generation, or testing, is known to facilitate memory and retention (e.g., see Roediger and Karpicke, 2006 ), which suggests that by having students specifically generate alignments and comparisons, one can facilitate this learning. Similar to the signaling condition, students were alerted through highlighted text to key similarities or differences between the diagrams. But in addition to having their attention guided to the important element (signaling), students were asked to actively reason about what they were noticing, identifying the relationship between the diagrams themselves. Simultaneous diagrams with structure mapping support were only offered at school B ( n = 53).

Outcome Measures and Data Coding

Outcome measures were derived from the free-response data written by students in response to prompts requesting students to describe mitosis and meiosis after instruction. This was designed to allow for a more nuanced understanding of the mental models of these systems that were developed by students, rather than simple accuracy rates in response to smaller, more explicit questions. Participant responses were downloaded directly from the teaching module into spreadsheet format for coding. Categorical codes were developed to quantify qualitative data coded by highly trained coders. At least two coders (including JH) independently scored 20% of the data, yielding above 80% agreement (high to acceptable rates of agreement) using Cohen’s kappa to control for chance reliability.

Descriptor codes for describing mitosis and meiosis were based on instructional text and iteratively refined through comparison to student responses at the development phase. Codes were derived from key principles within the biology of mitosis and meiosis, as well as characteristics of cognitive work that were predicted by the literature to indicate deep thinking, such as drawing connections and making inferences.

At the conclusion of mitosis instruction, all participants were asked to respond to the following prompt: “How would you describe mitosis to a friend? Fully describe as many steps as you can.” Eight separate features when describing mitosis were identified. These features, along with their interrater reliability (kappa) score, are listed in Table 3 .

Additional codes were added for “9: misconception” (e.g., “the male sperm and female egg meet”; K = 0.95), and “10: identification of surface features” (K = 0.81) such as size (e.g., “The process keeps … dividing into smaller parts”), color (e.g., “attached to a yellow string”), or nonspecific use of diagram labels (e.g., “It goes through interphase, prophase, metaphase, anaphase, telophase, and cytokinesis”) or references stages (e.g., “I learned that mitosis is a process that has lots of steps to the cycle”) as the whole response.

At the end of meiosis instruction, all participants were presented with a constructed-response item that asked: “How would you describe meiosis to a friend? Fully describe as many steps as you can.” Student responses mentioned 10 different structural features of meiosis, shown in Table 4 , along with their interrater reliability (kappa) statistic.

As with mitosis, coders scored when students mentioned surface features (K = 1.0), like size or color, or simply listed names of phases rather than describing them. Some students mistakenly described the cell replication process of mitosis when responding to the “describe meiosis” prompt, and these responses were coded separately as well (K = 0.90).

Principal Component Analyses.

Principal component analysis for categorical data of the characteristics of mitosis and for meiosis was used to identify underlying patterns of responses. These analyses were completed using the Statistical Package for Social Sciences (SPSS) software. Principal component analysis was appropriate, as all data were categorical. Direct oblimin rotation was applied. An oblique rotation was preferred, as the individual components all refer to parts of the same process of cell division, and therefore correlation among variables was expected. Each component met the Kaiser criterion (Kaiser, 1960) for selection with an eigenvalue greater than 1.0. Component loadings greater than 0.40 were retained.

Students’ free responses to the “describe mitosis” and “describe meiosis” prompts provide data not only about student understanding of each process, but also on their inference errors across conditions.

Mitosis Free-Response Analyses.

All cell features and cell processes noted by students were included in the principal component analysis. The descriptors clustered into three factors: rich description , which explained 29.05% of variance in the data; simple description , which explained 14.62% of the variance; and surface-level description , which explained 12.64% of total variance. Taken together, these factors explained 56.32% of variance in participant responses. The individual component loadings are described in Table 5 .

a Component loadings < 0.40 are suppressed.

b Variable principal normalization.

Rich responses, factor 1, meant that participants discussed several of the key features of mitosis and highlighted the role of spindle fibers and chromosomes. These can be contrasted with simple responses, factor 2, which were responses that focused primarily on the cell growing and dividing, with little additional meaningful detail. Further, identification of identical cell creation as a feature of mitosis was negatively correlated within a simple response (see Table 5 ). Surface-level descriptions, factor 3, showed reliance on colors, shapes, sizes, or the use of labels without describing the process of replication or the creation of identical cells. These are important, because they reflect responses that are purely descriptive of the appearance of the diagrams and fail to engage in the abstract structure that is key to cell reproduction. These are responses that suggest the learner has not engaged in the higher-order, relational thinking that was intended in the instruction. Examples of each type of response are shown in Table 6 .

Regression scores for each component were obtained using SPSS and were then compared across conditions using a one-way between-subjects analysis of variance (ANOVA). There was no significant differences in the distributions of either rich description, F (3, 353) = 0.34, p = 0.80, or simple description, F (3, 353) = 1.33, p = 0.27, across condition, but there was an overall significant effect for surface-level description by condition, F (3, 353) = 5.26, p = <0.01.

To further understand group differences for relying on surface features in descriptions of mitosis, we conducted a series of t tests for independent means of the regression scores. Participants in the signaling condition (M = 0.24) were more likely to rely on surface features than those in the serial, M = −0.08, t (193) = −2.86, p = <0.01, or support for structure mapping, M = 0.00, t (119) = −0.24, p = <0.01, conditions. Further, participants who received support for structure mapping outperformed those who saw the diagrams combined with no support, M = 0.03, t (160) = 2.4, p = 0.02. These results are summarized in Table 7 .

*Denotes significant difference, p < 0.05.

Meiosis Free-Response Analyses.

The same analysis was repeated for free-response data to a meiosis prompt. At the end of meiosis instruction, all participants were presented with a constructed-response item that asked: “How would you describe meiosis to a friend? Fully describe as many steps as you can.” A total of 320 participants responded to this prompt, and this was coded as described in the study 2 Methods section.

Student responses were coded for mention of 10 different structural features of meiosis and for whether they made errors confusing meiosis for mitosis. These features are described more fully in Table 4 .

These data were analyzed using principal component analysis to see whether and how each coded descriptor would contribute to overall patterns of responses. A total of three were identified: rich description, simplistic description, and confused with mitosis.

The three factors together explained 53.02% of variance in responses. Rich description explained 27.87%; simplistic description explained 13.25%; and confusing mitosis with meiosis explained 11.90% of variance in participant responses. The individual factor loadings are described in Table 8 .

As with the “describe mitosis” prompt, we provide examples of the three patterns here. A rich description in answer to the “describe meiosis” prompt was associated with noting several different structural features of the replication process. A simplistic description might correctly identify meiosis as a process of cell division, but little else was fully described. While first and second cell division might be included, little more detail was described. The third type of response identified by components analysis was one that confused mitosis with meiosis. Although the student may correctly identify cell growth, the defining factors of meiosis are not described. Examples of each type of response are shown in Table 9 .

Regression scores for each of the three factors were calculated and compared across experimental condition using ANOVA. There were no significant differences in the distributions of either rich description, F (3, 316) = 1.35, p = 0.26, or simplistic description, F (3, 316) = 0.07, p = 0.98, responses across condition. There was, however, a significant condition effect for confusing meiosis with mitosis, F (3, 316) = 3.43, p = 0.02.

The error component of confusing mitosis with meiosis was isolated for further analysis across the data using t tests for independent means. As shown in Figure 4 , those in the simultaneous condition with structure mapping support (M = −0.32) were significantly less likely to be in the group that confused mitosis and meiosis than those in the serial, (M = 0.00, t (133) = 2.5, p = 0.01), simultaneous, (M = −0.01), t (140) = 2.24, p = 0.03), or signaling, (M = 0.15), t (107) = 3.77, p < 0.01), conditions.

FIGURE 4. Mean component factor scores showing rates of errors confusing mitosis and meiosis across conditions.

Like their adult non-educator counterparts, middle school children felt they would learn better from simultaneously presented visual representations of related science information. And, like the adults, they described the ability to compare and contrast across diagrams as desirable.

The experimental learning data provided insight into the validity of these beliefs and a more nuanced implication for instruction. While simultaneously presented representations did enhance student ability to make sense of science information concerning related concepts, they were only optimized when they included explicit supports for actively engaging learners in making the key connections across the representations. Simply having the two related diagrams presented together was not enough to engage and sustain the higher cognitive processes of the EF system, nor was directly drawing the learner’s attention to key features of the diagrams. Middle school children did need support for the perceived benefit of comparison and contrast to be achieved

Though this experiment revealed that students in all conditions learned from instruction supported by visual representations, there were two important ways in which students in the supported structure mapping group outperformed the others. First, in describing mitosis, these students were far less likely to rely on surface features than those who received diagrams presented simultaneously either with no support or with only signaling support. They were not distracted by the number of steps, colors, shapes, or labels of the diagrams. Instead, active mapping of the correspondences appeared to draw attention to the processes rather than the drawings or the textual labels themselves.

Second, when presented with conceptually related science content, they were less likely to confuse the two processes, even though the diagrams were visible simultaneously during all instruction. This finding was robust, with the support for structure mapping group outperforming serial, simultaneous, and signaling conditions. It suggests that the students who received structure mapping support had a clearer picture of the key conceptual similarities and differences between the two cellular processes at the conclusion of instruction.

The greatest differences were seen when comparing the simultaneous presentation with signaling presentation and the structure mapping group. This is surprising, in that prior research has suggested that signaling can aid learners in identifying important aspects of complex diagrams. In the case of diagrams of related processes, however, adding only the written signals may have added too much to the overall cognitive load for learners whose EFs, without additional support, were not sufficient to handle both the simultaneous diagrams and the signals intended to direct their attention to key correspondences (for a description of other research on outcomes related to signaling, see Mayer and Fiorella, 2019 ). This is contrasted with the support for structure mapping condition, which also included additional visual input, but actively engaged learners in describing what they saw instead of simply directing them to consider a specific aspect of the diagrams. Structure mapping prompts did appear to support learner ability to make sense of the same aspect of the diagram to which cueing only drew their attention. This is particularly notable, as the presence of both diagrams simultaneously did not overwhelm the learners in the supported condition, and it also appeared to enhance IC for information irrelevant to the task at hand.

OVERALL DISCUSSION

These studies elicited privately held beliefs from pre-service teachers, adult undergraduates, and middle school children about learning from visual representations of related science concepts and compared these beliefs to learning outcomes.

As predicted by prior research on EF development, and as shown in Figure 4 , children did need support for mapping key elements across diagrams of the related science concepts of mitosis and meiosis in order to avoid surface-level understanding and errors confusing the represented ideas. But learners who received that support were able to develop more complex understandings of the key relationships between the two processes. This brings to light a possible misalignment between the beliefs of pre-service teachers, who as seen in Figure 1 , endorsed serial presentation as easier for students to understand, and the metacognitive beliefs of children, who preferred the challenge of comparing and contrasting. While the pre-service teachers may be underestimating the EF of children’s minds, children may overestimate what they can do without support.

Consistent with theory based in the relational reasoning literature (see Richland and McDonough, 2010 ; Begolli et al. , 2018 ), this study found that children were able to process and create a deeper understanding of complex, related science topics when they had support for making connections across representations. This active involvement in making connections led to a lessened reliance on surface features of diagrams. More importantly, supporting students in structure mapping across related representations led to a deeper understanding of the key similarities and differences of the science concepts described and fewer misconceptions confusing mitosis with meiosis. The conditions that included active generation during learning may also have received a boost through the generation process supporting memory itself (e.g., see Roediger and Karpicke, 2006 ).

These studies show that focusing on addressing only the limitations of WM by limiting the presentation of simultaneous visual representations may lead to missed opportunities to help learners develop more complex mental models. Providing students with simultaneous representations of related science concepts can lead to learning that relies on structural correspondences rather than featural similarities and differences, but only if adequate support for EFs is provided. That these results held true in a real instructional setting with child learners is exciting, as they suggest that, when presented with support for mapping key relations, simultaneously presented visual representations of related science concepts can help students in science classrooms develop a greater understanding of complex interconnections in science.

Limitations

The main limitation of this study was the brevity of the overall delay to test. The constrained design allowed us high control in order to examine the effects of varying the instructional order and support for presenting materials. At the same time, it will be important to follow this work with an examination of how these effects persist over time.

Additionally, researchers were only able to test three conditions in each school. Though assignment was randomized across classrooms within those schools, comparison directly across schools was not possible for every condition. This may have underestimated school-level effects. Future studies would be further enhanced by the collection of student demographic and pretest and posttest data that could not be collected in the current study.

Implications for Practice

Together, these results provide new insights into how to optimize student learning from visual representations, and they also provide science educators with an important lens through which to consider their beliefs and practices of using visualizations. Integrating the theories of relational thinking and EFs helps to clarify why teachers must go beyond simply providing multiple visual models, diagrams, or other types of representations in sequence. We can infer that students may learn the details being shown in the representations when presented serially, and perhaps retention could even be facilitated in that way by reducing the amount of information to attend to, thereby reducing the overall EF load. But to promote broader understanding of how concepts fit together or to recognize commonalities and differences, this presentation style may not be optimal. Students may struggle to align and connect the ideas from two representations and ideas presented serially, which will limit the inferences they can make and may lead to misconceptions or misunderstandings. Thus, this report demonstrates the utility of supporting students in deepening their understanding of biology concepts by simultaneously showing two representations that are intended to be compared.

To best support teachers in incorporating this into their practice, we must also take note of the beliefs data we found. As shown in Figure 1 , these data in particular suggest that teachers would benefit from being shown the distinctions between their beliefs about their own learning and their beliefs about teaching their students. We found that pre-service educators tended to believe that they learn differently than their students, which is an extremely important point for teacher education and science education researchers to consider. People’s intuitions about their own learning did mirror the results we found in favor of better learning through supported simultaneous presentation. But pre-service teachers’ intuition was to teach child learners through serial presentation of diagrams. We know that educators’ beliefs are powerfully related to practice, which means that interventions and educational reforms that do not align with beliefs can be very difficult to change (see Munby, 1984 ; Wallace 2014 ).

Rather than aiming to convince teachers that their beliefs about teaching are incorrect, it likely will be more productive to highlight how their beliefs about their own learning are more in line with student learning in this case. That being said, their teaching beliefs seem to highlight that more support can be needed for younger learners to notice and draw connections across visual representations, which is also demonstrated in our data. So the overall implication is that learning can be optimized by presenting related visual representations simultaneously, but with additional support to help learners identify the relevant correspondences and differences without overloading their cognitive systems. Adding prompts for students to discuss and connect what they notice between these visual representations was a particularly powerful strategy. This has implications for both classroom teaching and visual texts, such as textbook design.

ACKNOWLEDGMENTS

This work was conducted with support from the National Science Foundation (grant no. 32027447) and the Institute of Education Sciences, through R305A190467 to the University of Chicago and the University of California, Irvine. The opinions expressed are those of the authors and do not necessarily represent views of the institute, the National Science Foundation, or the U.S. Department of Education.

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Submitted: 19 November 2019 Revised: 14 September 2020 Accepted: 29 September 2020

© 2020 J. Hansen and L. Richland. CBE—Life Sciences Education © 2020 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

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Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise cognitively inaccessible. Despite their important functional roles in scientific practices, philosophers of science have more or less neglected visual representations in their analyses of epistemic methods and tools of reasoning in science. This book is meant to fill this gap. It presents a detailed investigation into central conceptual issues and into the epistemology of visual representations in science.

Chapter 4 of this book is freely available as a downloadable Open Access PDF at https://www.taylorfrancis.com under a Creative Commons Attribution (CC-BY) 4.0 license.

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Chapter 1 | 9  pages, introduction, chapter 2 | 124  pages, what are scientific visualisations, chapter 3 | 75  pages, functional roles, appearances and the problem of diversity, chapter 4 | 124  pages, the epistemic status of scientific visualisations, chapter 5 | 9  pages.

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Visual Representations in Science Concept and Epistemology

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Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise cognitively inaccessible. Despite their important functional roles in scientific practices, philosophers of science have more or less neglected visual representations in their analyses of epistemic methods and tools of reasoning in science. This book is meant to fill this gap. It presents a detailed investigation into central conceptual issues and into the epistemology of visual representations in science. Chapter 4 of this book are freely available as downloadable Open Access PDFs  under a CC-BY 3.0 license. https://s3-us-west-2.amazonaws.com/tandfbis/rt-files/docs/Open+Access+Chapters/9781138089938_CCBYoachapter4.pdf

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Nicola Mößner currently holds a position as a lecturer at the Department of Philosophy at the RWTH Aachen University, Germany. Between 2015 and 2016, she was a Junior Fellow at the Alfried Krupp Wissenschaftskolleg Greifswald, Germany. In the philosophy of science her main interests of research comprise, on the one hand, Ludwik Fleck’s theory of social dynamics and infl uences on epistemic processes in science and, on the other, the epistemic status of visual representations in processes of scientifi c reasoning and communication. She edited (together with Alfred Nordmann) Reasoning in Measurement (2017) and (together with Dimitri Liebsch) Visualisierung und Erkenntnis – Bildverstehen und Bildverwenden in Natur- und Geisteswissenschaften (2012). Another area of her specialisation is social epistemology. In this context she worked on the epistemology of testimony and published Wissen aus dem Zeugnis anderer – der Sonderfall medialer Berichterstattung (2010).

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Creating visual explanations improves learning

Eliza bobek.

1 University of Massachusetts Lowell, Lowell, MA USA

Barbara Tversky

2 Stanford University, Columbia University Teachers College, New York, NY USA

Associated Data

Many topics in science are notoriously difficult for students to learn. Mechanisms and processes outside student experience present particular challenges. While instruction typically involves visualizations, students usually explain in words. Because visual explanations can show parts and processes of complex systems directly, creating them should have benefits beyond creating verbal explanations. We compared learning from creating visual or verbal explanations for two STEM domains, a mechanical system (bicycle pump) and a chemical system (bonding). Both kinds of explanations were analyzed for content and learning assess by a post-test. For the mechanical system, creating a visual explanation increased understanding particularly for participants of low spatial ability. For the chemical system, creating both visual and verbal explanations improved learning without new teaching. Creating a visual explanation was superior and benefitted participants of both high and low spatial ability. Visual explanations often included crucial yet invisible features. The greater effectiveness of visual explanations appears attributable to the checks they provide for completeness and coherence as well as to their roles as platforms for inference. The benefits should generalize to other domains like the social sciences, history, and archeology where important information can be visualized. Together, the findings provide support for the use of learner-generated visual explanations as a powerful learning tool.

Electronic supplementary material

The online version of this article (doi:10.1186/s41235-016-0031-6) contains supplementary material, which is available to authorized users.

Significance

Uncovering cognitive principles for effective teaching and learning is a central application of cognitive psychology. Here we show: (1) creating explanations of STEM phenomena improves learning without additional teaching; and (2) creating visual explanations is superior to creating verbal ones. There are several notable differences between visual and verbal explanations; visual explanations map thought more directly than words and provide checks for completeness and coherence as well as a platform for inference, notably from structure to process. Extensions of the technique to other domains should be possible. Creating visual explanations is likely to enhance students’ spatial thinking skills, skills that are increasingly needed in the contemporary and future world.

Dynamic systems such as those in science and engineering, but also in history, politics, and other domains, are notoriously difficult to learn (e.g. Chi, DeLeeuw, Chiu, & Lavancher, 1994 ; Hmelo-Silver & Pfeffer, 2004 ; Johnstone, 1991 ; Perkins & Grotzer, 2005 ). Mechanisms, processes, and behavior of complex systems present particular challenges. Learners must master not only the individual components of the system or process (structure) but also the interactions and mechanisms (function), which may be complex and frequently invisible. If the phenomena are macroscopic, sub-microscopic, or abstract, there is an additional level of difficulty. Although the teaching of STEM phenomena typically relies on visualizations, such as pictures, graphs, and diagrams, learning is typically revealed in words, both spoken and written. Visualizations have many advantages over verbal explanations for teaching; can creating visual explanations promote learning?

Learning from visual representations in STEM

Given the inherent challenges in teaching and learning complex or invisible processes in science, educators have developed ways of representing these processes to enable and enhance student understanding. External visual representations, including diagrams, photographs, illustrations, flow charts, and graphs, are often used in science to both illustrate and explain concepts (e.g., Hegarty, Carpenter, & Just, 1990 ; Mayer, 1989 ). Visualizations can directly represent many structural and behavioral properties. They also help to draw inferences (Larkin & Simon, 1987 ), find routes in maps (Levine, 1982 ), spot trends in graphs (Kessell & Tversky, 2011 ; Zacks & Tversky, 1999 ), imagine traffic flow or seasonal changes in light from architectural sketches (e.g. Tversky & Suwa, 2009 ), and determine the consequences of movements of gears and pulleys in mechanical systems (e.g. Hegarty & Just, 1993 ; Hegarty, Kriz, & Cate, 2003 ). The use of visual elements such as arrows is another benefit to learning with visualizations. Arrows are widely produced and comprehended as representing a range of kinds of forces as well as changes over time (e.g. Heiser & Tversky, 2002 ; Tversky, Heiser, MacKenzie, Lozano, & Morrison, 2007 ). Visualizations are thus readily able to depict the parts and configurations of systems; presenting the same content via language may be more difficult. Although words can describe spatial properties, because the correspondences of meaning to language are purely symbolic, comprehension and construction of mental representations from descriptions is far more effortful and error prone (e.g. Glenberg & Langston, 1992 ; Hegarty & Just, 1993 ; Larkin & Simon, 1987 ; Mayer, 1989 ). Given the differences in how visual and verbal information is processed, how learners draw inferences and construct understanding in these two modes warrants further investigation.

Benefits of generating explanations

Learner-generated explanations of scientific phenomena may be an important learning strategy to consider beyond the utility of learning from a provided external visualization. Explanations convey information about concepts or processes with the goal of making clear and comprehensible an idea or set of ideas. Explanations may involve a variety of elements, such as the use of examples and analogies (Roscoe & Chi, 2007 ). When explaining something new, learners may have to think carefully about the relationships between elements in the process and prioritize the multitude of information available to them. Generating explanations may require learners to reorganize their mental models by allowing them to make and refine connections between and among elements and concepts. Explaining may also help learners metacognitively address their own knowledge gaps and misconceptions.

Many studies have shown that learning is enhanced when students are actively engaged in creative, generative activities (e.g. Chi, 2009 ; Hall, Bailey, & Tillman, 1997 ). Generative activities have been shown to benefit comprehension of domains involving invisible components, including electric circuits (Johnson & Mayer, 2010 ) and the chemistry of detergents (Schwamborn, Mayer, Thillmann, Leopold, & Leutner, 2010 ). Wittrock’s ( 1990 ) generative theory stresses the importance of learners actively constructing and developing relationships. Generative activities require learners to select information and choose how to integrate and represent the information in a unified way. When learners make connections between pieces of information, knowledge, and experience, by generating headings, summaries, pictures, and analogies, deeper understanding develops.

The information learners draw upon to construct their explanations is likely important. For example, Ainsworth and Loizou ( 2003 ) found that asking participants to self-explain with a diagram resulted in greater learning than self-explaining from text. How might learners explain with physical mechanisms or materials with multi-modal information?

Generating visual explanations

Learner-generated visualizations have been explored in several domains. Gobert and Clement ( 1999 ) investigated the effectiveness of student-generated diagrams versus student-generated summaries on understanding plate tectonics after reading an expository text. Students who generated diagrams scored significantly higher on a post-test measuring spatial and causal/dynamic content, even though the diagrams contained less domain-related information. Hall et al. ( 1997 ) showed that learners who generated their own illustrations from text performed equally as well as learners provided with text and illustrations. Both groups outperformed learners only provided with text. In a study concerning the law of conservation of energy, participants who generated drawings scored higher on a post-test than participants who wrote their own narrative of the process (Edens & Potter, 2003 ). In addition, the quality and number of concept units present in the drawing/science log correlated with performance on the post-test. Van Meter ( 2001 ) found that drawing while reading a text about Newton’s Laws was more effective than answering prompts in writing.

One aspect to explore is whether visual and verbal productions contain different types of information. Learning advantages for the generation of visualizations could be attributed to learners’ translating across modalities, from a verbal format into a visual format. Translating verbal information from the text into a visual explanation may promote deeper processing of the material and more complete and comprehensive mental models (Craik & Lockhart, 1972 ). Ainsworth and Iacovides ( 2005 ) addressed this issue by asking two groups of learners to self-explain while learning about the circulatory system of the human body. Learners given diagrams were asked to self-explain in writing and learners given text were asked to explain using a diagram. The results showed no overall differences in learning outcomes, however the learners provided text included significantly more information in their diagrams than the other group. Aleven and Koedinger ( 2002 ) argue that explanations are most helpful if they can integrate visual and verbal information. Translating across modalities may serve this purpose, although translating is not necessarily an easy task (Ainsworth, Bibby, & Wood, 2002 ).

It is important to remember that not all studies have found advantages to generating explanations. Wilkin ( 1997 ) found that directions to self-explain using a diagram hindered understanding in examples in physical motion when students were presented with text and instructed to draw a diagram. She argues that the diagrams encouraged learners to connect familiar but unrelated knowledge. In particular, “low benefit learners” in her study inappropriately used spatial adjacency and location to connect parts of diagrams, instead of the particular properties of those parts. Wilkin argues that these learners are novices and that experts may not make the same mistake since they have the skills to analyze features of a diagram according to their relevant properties. She also argues that the benefits of self-explaining are highest when the learning activity is constrained so that learners are limited in their possible interpretations. Other studies that have not found a learning advantage from generating drawings have in common an absence of support for the learner (Alesandrini, 1981 ; Leutner, Leopold, & Sumfleth, 2009 ). Another mediating factor may be the learner’s spatial ability.

The role of spatial ability

Spatial thinking involves objects, their size, location, shape, their relation to one another, and how and where they move through space. How then, might learners with different levels of spatial ability gain structural and functional understanding in science and how might this ability affect the utility of learner-generated visual explanations? Several lines of research have sought to explore the role of spatial ability in learning science. Kozhevnikov, Hegarty, and Mayer ( 2002 ) found that low spatial ability participants interpreted graphs as pictures, whereas high spatial ability participants were able to construct more schematic images and manipulate them spatially. Hegarty and Just ( 1993 ) found that the ability to mentally animate mechanical systems correlated with spatial ability, but not verbal ability. In their study, low spatial ability participants made more errors in movement verification tasks. Leutner et al. ( 2009 ) found no effect of spatial ability on the effectiveness of drawing compared to mentally imagining text content. Mayer and Sims ( 1994 ) found that spatial ability played a role in participants’ ability to integrate visual and verbal information presented in an animation. The authors argue that their results can be interpreted within the context of dual-coding theory. They suggest that low spatial ability participants must devote large amounts of cognitive effort into building a visual representation of the system. High spatial ability participants, on the other hand, are more able to allocate sufficient cognitive resources to building referential connections between visual and verbal information.

Benefits of testing

Although not presented that way, creating an explanation could be regarded as a form of testing. Considerable research has documented positive effects of testing on learning. Presumably taking a test requires retrieving and sometimes integrating the learned material and those processes can augment learning without additional teaching or study (e.g. Roediger & Karpicke, 2006 ; Roediger, Putnam, & Smith, 2011 ; Wheeler & Roediger, 1992 ). Hausmann and Vanlehn ( 2007 ) addressed the possibility that generating explanations is beneficial because learners merely spend more time with the content material than learners who are not required to generate an explanation. In their study, they compared the effects of using instructions to self-explain with instructions to merely paraphrase physics (electrodynamics) material. Attending to provided explanations by paraphrasing was not as effective as generating explanations as evidenced by retention scores on an exam 29 days after the experiment and transfer scores within and across domains. Their study concludes, “the important variable for learning was the process of producing an explanation” (p. 423). Thus, we expect benefits from creating either kind of explanation but for the reasons outlined previously, we expect larger benefits from creating visual explanations.

Present experiments

This study set out to answer a number of related questions about the role of learner-generated explanations in learning and understanding of invisible processes. (1) Do students learn more when they generate visual or verbal explanations? We anticipate that learning will be greater with the creation of visual explanations, as they encourage completeness and the integration of structure and function. (2) Does the inclusion of structural and functional information correlate with learning as measured by a post-test? We predict that including greater counts of information, particularly invisible and functional information, will positively correlate with higher post-test scores. (3) Does spatial ability predict the inclusion of structural and functional information in explanations, and does spatial ability predict post-test scores? We predict that high spatial ability participants will include more information in their explanations, and will score higher on post-tests.

Experiment 1

The first experiment examines the effects of creating visual or verbal explanations on the comprehension of a bicycle tire pump’s operation in participants with low and high spatial ability. Although the pump itself is not invisible, the components crucial to its function, notably the inlet and outlet valves, and the movement of air, are located inside the pump. It was predicted that visual explanations would include more information than verbal explanations, particularly structural information, since their construction encourages completeness and the production of a whole mechanical system. It was also predicted that functional information would be biased towards a verbal format, since much of the function of the pump is hidden and difficult to express in pictures. Finally, it was predicted that high spatial ability participants would be able to produce more complete explanations and would thus also demonstrate better performance on the post-test. Explanations were coded for structural and functional content, essential features, invisible features, arrows, and multiple steps.

Participants

Participants were 127 (59 female) seventh and eighth grade students, aged 12–14 years, enrolled in an independent school in New York City. The school’s student body is 70% white, 30% other ethnicities. Approximately 25% of the student body receives financial aid. The sample consisted of three class sections of seventh grade students and three class sections of eighth grade students. Both seventh and eighth grade classes were integrated science (earth, life, and physical sciences) and students were not grouped according to ability in any section. Written parental consent was obtained by means of signed informed consent forms. Each participant was randomly assigned to one of two conditions within each class. There were 64 participants in the visual condition explained the bicycle pump’s function by drawing and 63 participants explained the pump’s function by writing.

The materials consisted of a 12-inch Spalding bicycle pump, a blank 8.5 × 11 in. sheet of paper, and a post-test (Additional file 1 ). The pump’s chamber and hose were made of clear plastic; the handle and piston were black plastic. The parts of the pump (e.g. inlet valve, piston) were labeled.

Spatial ability was assessed using the Vandenberg and Kuse ( 1978 ) mental rotation test (MRT). The MRT is a 20-item test in which two-dimensional drawings of three-dimensional objects are compared. Each item consists of one “target” drawing and four drawings that are to be compared to the target. Two of the four drawings are rotated versions of the target drawing and the other two are not. The task is to identify the two rotated versions of the target. A score was determined by assigning one point to each question if both of the correct rotated versions were chosen. The maximum score was 20 points.

The post-test consisted of 16 true/false questions printed on a single sheet of paper measuring 8.5 × 11 in. Half of the questions related to the structure of the pump and the other half related to its function. The questions were adapted from Heiser and Tversky ( 2002 ) in order to be clear and comprehensible for this age group.

The experiment was conducted over the course of two non-consecutive days during the normal school day and during regularly scheduled class time. On the first day, participants completed the MRT as a whole-class activity. After completing an untimed practice test, they were given 3 min for each of the two parts of the MRT. On the second day, occurring between two and four days after completing the MRT, participants were individually asked to study an actual bicycle tire pump and were then asked to generate explanations of its function. The participants were tested individually in a quiet room away from the rest of the class. In addition to the pump, each participant was one instruction sheet and one blank sheet of paper for their explanations. The post-test was given upon completion of the explanation. The instruction sheet was read aloud to participants and they were instructed to read along. The first set of instructions was as follows: “A bicycle pump is a mechanical device that pumps air into bicycle tires. First, take this bicycle pump and try to understand how it works. Spend as much time as you need to understand the pump.” The next set of instructions differed for participants in each condition. The instructions for the visual condition were as follows: “Then, we would like you to draw your own diagram or set of diagrams that explain how the bike pump works. Draw your explanation so that someone else who has not seen the pump could understand the bike pump from your explanation. Don’t worry about the artistic quality of the diagrams; in fact, if something is hard for you to draw, you can explain what you would draw. What’s important is that the explanation should be primarily visual, in a diagram or diagrams.” The instructions for the verbal condition were as follows: “Then, we would like you to write an explanation of how the bike pump works. Write your explanation so that someone else who has not seen the pump could understand the bike pump from your explanation.” All participants then received these instructions: “You may not use the pump while you create your explanations. Please return it to me when you are ready to begin your explanation. When you are finished with the explanation, you will hand in your explanation to me and I will then give you 16 true/false questions about the bike pump. You will not be able to look at your explanation while you complete the questions.” Study and test were untimed. All students finished within the 45-min class period.

Spatial ability

The mean score on the MRT was 10.56, with a median of 11. Boys scored significantly higher (M = 13.5, SD = 4.4) than girls (M = 8.8, SD = 4.5), F(1, 126) = 19.07, p  < 0.01, a typical finding (Voyer, Voyer, & Bryden, 1995 ). Participants were split into high or low spatial ability by the median. Low and high spatial ability participants were equally distributed in the visual and verbal groups.

Learning outcomes

It was predicted that high spatial ability participants would be better able to mentally animate the bicycle pump system and therefore score higher on the post-test and that post-test scores would be higher for those who created visual explanations. Table  1 shows the scores on the post-test by condition and spatial ability. A two-way factorial ANOVA revealed marginally significant main effect of spatial ability F(1, 124) = 3.680, p  = 0.06, with high spatial ability participants scoring higher on the post-test. There was also a significant interaction between spatial ability and explanation type F(1, 124) = 4.094, p  < 0.01, see Fig.  1 . Creating a visual explanation of the bicycle pump selectively helped low spatial participants.

Post-test scores, by explanation type and spatial ability

Scores on the post-test by condition and spatial ability

Coding explanations

Explanations (see Fig.  2 ) were coded for structural and functional content, essential features, invisible features, arrows, and multiple steps. A subset of the explanations (20%) was coded by the first author and another researcher using the same coding system as a guide. The agreement between scores was above 90% for all measures. Disagreements were resolved through discussion. The first author then scored the remaining explanations.

Examples of visual and verbal explanations of the bicycle pump

Coding for structure and function

A maximum score of 12 points was awarded for the inclusion and labeling of six structural components: chamber, piston, inlet valve, outlet valve, handle, and hose. For the visual explanations, 1 point was given for a component drawn correctly and 1 additional point if the component was labeled correctly. For verbal explanations, sentences were divided into propositions, the smallest unit of meaning in a sentence. Descriptions of structural location e.g. “at the end of the piston is the inlet valve,” or of features of the components, e.g. the shape of a part, counted as structural components. Information was coded as functional if it depicted (typically with an arrow) or described the function/movement of an individual part, or the way multiple parts interact. No explanation contained more than ten functional units.

Visual explanations contained significantly more structural components (M = 6.05, SD = 2.76) than verbal explanations (M = 4.27, SD = 1.54), F(1, 126) = 20.53, p  < 0.05. The number of functional components did not differ between visual and verbal explanations as displayed in Figs.  3 and ​ and4. 4 . Many visual explanations (67%) contained verbal components; the structural and functional information in explanations was coded as depictive or descriptive. Structural and functional information were equally likely to be expressed in words or pictures in visual explanations. It was predicted that explanations created by high spatial participants would include more functional information. However, there were no significant differences found between low spatial (M = 5.15, SD = 2.21) and high spatial (M = 4.62, SD = 2.16) participants in the number of structural units or between low spatial (M = 3.83, SD = 2.51) and high spatial (M = 4.10, SD = 2.13) participants in the number of functional units.

Average number of structural and functional components in visual and verbal explanations

Visual and verbal explanations of chemical bonding

Coding of essential features

To further establish a relationship between the explanations generated and outcomes on the post-test, explanations were also coded for the inclusion of information essential to its function according to a 4-point scale (adapted from Hall et al., 1997 ). One point was given if both the inlet and the outlet valve were clearly present in the drawing or described in writing, 1 point was given if the piston inserted into the chamber was shown or described to be airtight, and 1 point was given for each of the two valves if they were shown or described to be opening/closing in the correct direction.

Visual explanations contained significantly more essential information (M = 1.78, SD = 1.0) than verbal explanations (M = 1.20, SD = 1.21), F(1, 126) = 7.63, p  < 0.05. Inclusion of essential features correlated positively with post-test scores, r = 0.197, p  < 0.05).

Coding arrows and multiple steps

For the visual explanations, three uses of arrows were coded and tallied: labeling a part or action, showing motion, or indicating sequence. Analysis of visual explanations revealed that 87% contained arrows. No significant differences were found between low and high spatial participants’ use of arrows to label and no signification correlations were found between the use of arrows and learning outcomes measured on the post-test.

The explanations were coded for the number of discrete steps used to explain the process of using the bike pump. The number of steps used by participants ranged from one to six. Participants whose explanations, whether verbal or visual, contained multiple steps scored significantly higher (M = 0.76, SD = 0.18) on the post-test than participants whose explanations consisted of a single step (M = 0.67, SD = 0.19), F(1, 126) = 5.02, p  < 0.05.

Coding invisible features

The bicycle tire pump, like many mechanical devices, contains several structural features that are hidden or invisible and must be inferred from the function of the pump. For the bicycle pump the invisible features are the inlet and outlet valves and the three phases of movement of air, entering the pump, moving through the pump, exiting the pump. Each feature received 1 point for a total of 5 possible points.

The mean score for the inclusion of invisible features was 3.26, SD = 1.25. The data were analyzed using linear regression and revealed that the total score for invisible parts significantly predicted scores on the post-test, F(1, 118) = 3.80, p  = 0.05.

In the first experiment, students learned the workings of a bicycle pump from interacting with an actual pump and creating a visual or verbal explanation of its function. Understanding the functionality of a bike pump depends on the actions and consequences of parts that are not visible. Overall, the results provide support for the use of learner-generated visual explanations in developing understanding of a new scientific system. The results show that low spatial ability participants were able to learn as successfully as high spatial ability participants when they first generated an explanation in a visual format.

Visual explanations may have led to greater understanding for a number of reasons. As discussed previously, visual explanations encourage completeness. They force learners to decide on the size, shape, and location of parts/objects. Understanding the “hidden” function of the invisible parts is key to understanding the function of the entire system and requires an understanding of how both the visible and invisible parts interact. The visual format may have been able to elicit components and concepts that are invisible and difficult to integrate into the formation of a mental model. The results show that including more of the essential features and showing multiple steps correlated with superior test performance. Understanding the bicycle pump requires understanding how all of these components are connected through movement, force, and function. Many (67%) of the visual explanations also contained written components to accompany their explanation. Arguably, some types of information may be difficult to depict visually and verbal language has many possibilities that allow for specificity. The inclusion of text as a complement to visual explanations may be key to the success of learner-generated explanations and the development of understanding.

A limitation of this experiment is that participants were not provided with detailed instructions for completing their explanations. In addition, this experiment does not fully clarify the role of spatial ability, since high spatial participants in the visual and verbal groups demonstrated equivalent knowledge of the pump on the post-test. One possibility is that the interaction with the bicycle pump prior to generating explanations was a sufficient learning experience for the high spatial participants. Other researchers (e.g. Flick, 1993 ) have shown that hands-on interactive experiences can be effective learning situations. High spatial ability participants may be better able to imagine the movement and function of a system (e.g. Hegarty, 1992 ).

Experiment 1 examined learning a mechanical system with invisible (hidden) parts. Participants were introduced to the system by being able to interact with an actual bicycle pump. While we did not assess participants’ prior knowledge of the pump with a pre-test, participants were randomly assigned to each condition. The findings have promising implications for teaching. Creating visual explanations should be an effective way to improve performance, especially in low spatial students. Instructors can guide the creation of visual explanations toward the features that augment learning. For example, students can be encouraged to show every step and action and to focus on the essential parts, even if invisible. The coding system shows that visual explanations can be objectively evaluated to provide feedback on students’ understanding. The utility of visual explanations may differ for scientific phenomena that are more abstract, or contain elements that are invisible due to their scale. Experiment 2 addresses this possibility by examining a sub-microscopic area of science: chemical bonding.

Experiment 2

In this experiment, we examine visual and verbal explanations in an area of chemistry: ionic and covalent bonding. Chemistry is often regarded as a difficult subject; one of the essential or inherent features of chemistry which presents difficulty is the interplay between the macroscopic, sub-microscopic, and representational levels (e.g. Bradley & Brand, 1985 ; Johnstone, 1991 ; Taber, 1997 ). In chemical bonding, invisible components engage in complex processes whose scale makes them impossible to observe. Chemists routinely use visual representations to investigate relationships and move between the observable, physical level and the invisible particulate level (Kozma, Chin, Russell, & Marx, 2002 ). Generating explanations in a visual format may be a particularly useful learning tool for this domain.

For this topic, we expect that creating a visual rather than verbal explanation will aid students of both high and low spatial abilities. Visual explanations demand completeness; they were predicted to include more information than verbal explanations, particularly structural information. The inclusion of functional information should lead to better performance on the post-test since understanding how and why atoms bond is crucial to understanding the process. Participants with high spatial ability may be better able to explain function since the sub-microscopic nature of bonding requires mentally imagining invisible particles and how they interact. This experiment also asks whether creating an explanation per se can increase learning in the absence of additional teaching by administering two post-tests of knowledge, one immediately following instruction but before creating an explanation and one after creating an explanation. The scores on this immediate post-test were used to confirm that the visual and verbal groups were equivalent prior to the generation of explanations. Explanations were coded for structural and functional information, arrows, specific examples, and multiple representations. Do the acts of selecting, integrating, and explaining knowledge serve learning even in the absence of further study or teaching?

Participants were 126 (58 female) eighth grade students, aged 13–14 years, with written parental consent and enrolled in the same independent school described in Experiment 1. None of the students previously participated in Experiment 1. As in Experiment 1, randomization occurred within-class, with participants assigned to either the visual or verbal explanation condition.

The materials consisted of the MRT (same as Experiment 1), a video lesson on chemical bonding, two versions of the instructions, the immediate post-test, the delayed post-test, and a blank page for the explanations. All paper materials were typed on 8.5 × 11 in. sheets of paper. Both immediate and delayed post-tests consisted of seven multiple-choice items and three free-response items. The video lesson on chemical bonding consisted of a video that was 13 min 22 s. The video began with a brief review of atoms and their structure and introduced the idea that atoms combine to form molecules. Next, the lesson showed that location in the periodic table reveals the behavior and reactivity of atoms, in particular the gain, loss, or sharing of electrons. Examples of atoms, their valence shell structure, stability, charges, transfer and sharing of electrons, and the formation of ionic, covalent, and polar covalent bonds were discussed. The example of NaCl (table salt) was used to illustrate ionic bonding and the examples of O 2 and H 2 O (water) were used to illustrate covalent bonding. Information was presented verbally, accompanied by drawings, written notes of keywords and terms, and a color-coded periodic table.

On the first of three non-consecutive school days, participants completed the MRT as a whole-class activity. On the second day (occurring between two and three days after completing the MRT), participants viewed the recorded lesson on chemical bonding. They were instructed to pay close attention to the material but were not allowed to take notes. Immediately following the video, participants had 20 min to complete the immediate post-test; all finished within this time frame. On the third day (occurring on the next school day after viewing the video and completing the immediate post-test), the participants were randomly assigned to either the visual or verbal explanation condition. The typed instructions were given to participants along with a blank 8.5 × 11 in. sheet of paper for their explanations. The instructions differed for each condition. For the visual condition, the instructions were as follows: “You have just finished learning about chemical bonding. On the next piece of paper, draw an explanation of how atoms bond and how ionic and covalent bonds differ. Draw your explanation so that another student your age who has never studied this topic will be able to understand it. Be as clear and complete as possible, and remember to use pictures/diagrams only. After you complete your explanation, you will be asked to answer a series of questions about bonding.”

For the verbal condition the instructions were: “You have just finished learning about chemical bonding. On the next piece of paper, write an explanation of how atoms bond and how ionic and covalent bonds differ. Write your explanation so that another student your age who has never studied this topic will be able to understand it. Be as clear and complete as possible. After you complete your explanation, you will be asked to answer a series of questions about bonding.”

Participants were instructed to read the instructions carefully before beginning the task. The participants completed their explanations as a whole-class activity. Participants were given unlimited time to complete their explanations. Upon completion of their explanations, participants were asked to complete the ten-question delayed post-test (comparable to but different from the first) and were given a maximum of 20 min to do so. All participants completed their explanations as well as the post-test during the 45-min class period.

The mean score on the MRT was 10.39, with a median of 11. Boys (M = 12.5, SD = 4.8) scored significantly higher than girls (M = 8.0, SD = 4.0), F(1, 125) = 24.49, p  < 0.01. Participants were split into low and high spatial ability based on the median.

The maximum score for both the immediate and delayed post-test was 10 points. A repeated measures ANOVA showed that the difference between the immediate post-test scores (M = 4.63, SD = 0.469) and delayed post-test scores (M = 7.04, SD = 0.299) was statistically significant F(1, 125) = 18.501, p  < 0.05). Without any further instruction, scores increased following the generation of a visual or verbal explanation. Both groups improved significantly; those who created visual explanations (M = 8.22, SD = 0.208), F(1, 125) = 51.24, p  < 0.01, Cohen’s d  = 1.27 as well as those who created verbal explanations (M = 6.31, SD = 0.273), F(1,125) = 15.796, p  < 0.05, Cohen’s d  = 0.71. As seen in Fig.  5 , participants who generated visual explanations (M = 0.822, SD = 0.208) scored considerably higher on the delayed post-test than participants who generated verbal explanations (M = 0.631, SD = 0.273), F(1, 125) = 19.707, p  < 0.01, Cohen’s d  = 0.88. In addition, high spatial participants (M = 0.824, SD = 0.273) scored significantly higher than low spatial participants (M = 0.636, SD = 0.207), F(1, 125) = 19.94, p  < 0.01, Cohen’s d  = 0.87. The results of the test of the interaction between group and spatial ability was not significant.

Scores on the post-tests by explanation type and spatial ability

Explanations were coded for structural and functional content, arrows, specific examples, and multiple representations. A subset of the explanations (20%) was coded by both the first author and a middle school science teacher with expertise in Chemistry. Both scorers used the same coding system as a guide. The percentage of agreement between scores was above 90 for all measures. The first author then scored the remainder of the explanations. As evident from Fig.  4 , the visual explanations were individual inventions; they neither resembled each other nor those used in teaching. Most contained language, especially labels and symbolic language such as NaCl.

Structure, function, and modality

Visual and verbal explanations were coded for depicting or describing structural and functional components. The structural components included the following: the correct number of valence electrons, the correct charges of atoms, the bonds between non-metals for covalent molecules and between a metal and non-metal for ionic molecules, the crystalline structure of ionic molecules, and that covalent bonds were individual molecules. The functional components included the following: transfer of electrons in ionic bonds, sharing of electrons in covalent bonds, attraction between ions of opposite charge, bonding resulting in atoms with neutral charge and stable electron shell configurations, and outcome of bonding shows molecules with overall neutral charge. The presence of each component was awarded 1 point; the maximum possible points was 5 for structural and 5 for functional information. The modality, visual or verbal, of each component was also coded; if the information was given in both formats, both were coded.

As displayed in Fig.  6 , visual explanations contained a significantly greater number of structural components (M = 2.81, SD = 1.56) than verbal explanations (M = 1.30, SD = 1.54), F(1, 125) = 13.69, p  < 0.05. There were no differences between verbal and visual explanations in the number of functional components. Structural information was more likely to be depicted (M = 3.38, SD = 1.49) than described (M = 0.429, SD = 1.03), F(1, 62) = 21.49, p  < 0.05, but functional information was equally likely to be depicted (M = 1.86, SD = 1.10) or described (M = 1.71, SD = 1.87).

Functional information expressed verbally in the visual explanations significantly predicted scores on the post-test, F(1, 62) = 21.603, p  < 0.01, while functional information in verbal explanations did not. The inclusion of structural information did not significantly predict test scores. As seen Fig.  7 , explanations created by high spatial participants contained significantly more functional components, F(1, 125) = 7.13, p  < 0.05, but there were no ability differences in the amount of structural information created by high spatial participants in either visual or verbal explanations.

Average number of structural and functional components created by low and high spatial ability learners

Ninety-two percent of visual explanations contained arrows. Arrows were used to indicate motion as well as to label. The use of arrows was positively correlated with scores on the post-test, r = 0.293, p  < 0.05. There were no significant differences in the use of arrows between low and high spatial participants.

Specific examples

Explanations were coded for the use of specific examples, such as NaCl, to illustrate ionic bonding and CO 2 and O 2 to illustrate covalent bonding. High spatial participants (M = 1.6, SD = 0.69) used specific examples in their verbal and visual explanations more often than low spatial participants (M = 1.07, SD = 0.79), a marginally significant effect F(1, 125) = 3.65, p  = 0.06. Visual and verbal explanations did not differ in the presence of specific examples. The inclusion of a specific example was positively correlated with delayed test scores, r = 0.555, p  < 0.05.

Use of multiple representations

Many of the explanations (65%) contained multiple representations of bonding. For example, ionic bonding and its properties can be represented at the level of individual atoms or at the level of many atoms bonded together in a crystalline compound. The representations that were coded were as follows: symbolic (e.g. NaCl), atomic (showing structure of atom(s), and macroscopic (visible). Participants who created visual explanations generated significantly more (M =1.79, SD = 1.20) than those who created verbal explanations (M = 1.33, SD = 0.48), F (125) = 6.03, p  < 0.05. However, the use of multiple representations did not significantly correlate with delayed post-test scores on the delayed post-test.

Metaphoric explanations

Although there were too few examples to be included in the statistical analyses, some participants in the visual group created explanations that used metaphors and/or analogies to illustrate the differences between the types of bonding. Figure  4 shows examples of metaphoric explanations. In one example, two stick figures are used to show “transfer” and “sharing” of an object between people. In another, two sharks are used to represent sodium and chlorine, and the transfer of fish instead of electrons.

In the second experiment, students were introduced to chemical bonding, a more abstract and complex set of phenomena than the bicycle pump used in the first experiment. Students were tested immediately after instruction. The following day, half the students created visual explanations and half created verbal explanations. Following creation of the explanations, students were tested again, with different questions. Performance was considerably higher as a consequence of creating either explanation despite the absence of new teaching. Generating an explanation in this way could be regarded as a test of learning. Seen this way, the results echo and amplify previous research showing the advantages of testing over study (e.g. Roediger et al., 2011 ; Roediger & Karpicke, 2006 ; Wheeler & Roediger, 1992 ). Specifically, creating an explanation requires selecting the crucial information, integrating it temporally and causally, and expressing it clearly, processes that seem to augment learning and understanding without additional teaching. Importantly, creating a visual explanation gave an extra boost to learning outcomes over and above the gains provided by creating a verbal explanation. This is most likely due to the directness of mapping complex systems to a visual-spatial format, a format that can also provide a natural check for completeness and coherence as well as a platform for inference. In the case of this more abstract and complex material, generating a visual explanation benefited both low spatial and high spatial participants even if it did not bring low spatial participants up to the level of high spatial participants as for the bicycle pump.

Participants high in spatial ability not only scored better, they also generated better explanations, including more of the information that predicted learning. Their explanations contained more functional information and more specific examples. Their visual explanations also contained more functional information.

As in Experiment 1, qualities of the explanations predicted learning outcomes. Including more arrows, typically used to indicate function, predicted delayed test scores as did articulating more functional information in words in visual explanations. Including more specific examples in both types of explanation also improved learning outcomes. These are all indications of deeper understanding of the processes, primarily expressed in the visual explanations. As before, these findings provide ways that educators can guide students to craft better visual explanations and augment learning.

General discussion

Two experiments examined how learner-generated explanations, particularly visual explanations, can be used to increase understanding in scientific domains, notably those that contain “invisible” components. It was proposed that visual explanations would be more effective than verbal explanations because they encourage completeness and coherence, are more explicit, and are typically multimodal. These two experiments differ meaningfully from previous studies in that the information selected for drawing was not taken from a written text, but from a physical object (bicycle pump) and a class lesson with multiple representations (chemical bonding).

The results show that creating an explanation of a STEM phenomenon benefits learning, even when the explanations are created after learning and in the absence of new instruction. These gains in performance in the absence of teaching bear similarities to recent research showing gains in learning from testing in the absence of new instruction (e.g. Roediger et al., 2011 ; Roediger & Karpicke, 2006 ; Wheeler & Roediger, 1992 ). Many researchers have argued that the retrieval of information required during testing strengthens or enhances the retrieval process itself. Formulating explanations may be an especially effective form of testing for post-instruction learning. Creating an explanation of a complex system requires the retrieval of critical information and then the integration of that information into a coherent and plausible account. Other factors, such as the timing of the creation of the explanations, and whether feedback is provided to students, should help clarify the benefits of generating explanations and how they may be seen as a form of testing. There may even be additional benefits to learners, including increasing their engagement and motivation in school, and increasing their communication and reasoning skills (Ainsworth, Prain, & Tytler, 2011 ). Formulating a visual explanation draws upon students’ creativity and imagination as they actively create their own product.

As in previous research, students with high spatial ability both produced better explanations and performed better on tests of learning (e.g. Uttal et al., 2013 ). The visual explanations of high spatial students contained more information and more of the information that predicts learning outcomes. For the workings of a bicycle pump, creating a visual as opposed to verbal explanation had little impact on students of high spatial ability but brought students of lower spatial ability up to the level of students with high spatial abilities. For the more difficult set of concepts, chemical bonding, creating a visual explanation led to much larger gains than creating a verbal one for students both high and low in spatial ability. It is likely a mistake to assume that how and high spatial learners will remain that way; there is evidence that spatial ability develops with experience (Baenninger & Newcombe, 1989 ). It is possible that low spatial learners need more support in constructing explanations that require imagining the movement and manipulation of objects in space. Students learned the function of the bike pump by examining an actual pump and learned bonding through a video presentation. Future work to investigate methods of presenting material to students may also help to clarify the utility of generating explanations.

Creating visual explanations had greater benefits than those accruing from creating verbal ones. Surely some of the effectiveness of visual explanations is because they represent and communicate more directly than language. Elements of a complex system can be depicted and arrayed spatially to reflect actual or metaphoric spatial configurations of the system parts. They also allow, indeed, encourage, the use of well-honed spatial inferences to substitute for and support abstract inferences (e.g. Larkin & Simon, 1987 ; Tversky, 2011 ). As noted, visual explanations provide checks for completeness and coherence, that is, verification that all the necessary elements of the system are represented and that they work together properly to produce the outcomes of the processes. Visual explanations also provide a concrete reference for making and checking inferences about the behavior, causality, and function of the system. Thus, creating a visual explanation facilitates the selection and integration of information underlying learning even more than creating a verbal explanation.

Creating visual explanations appears to be an underused method of supporting and evaluating students’ understanding of dynamic processes. Two obstacles to using visual explanations in classrooms seem to be developing guidelines for creating visual explanations and developing objective scoring systems for evaluating them. The present findings give insights into both. Creating a complete and coherent visual explanation entails selecting the essential components and linking them by behavior, process, or causality. This structure and organization is familiar from recipes or construction sets: first the ingredients or parts, then the sequence of actions. It is also the ingredients of theater or stories: the players and their actions. In fact, the creation of visual explanations can be practiced on these more familiar cases and then applied to new ones in other domains. Deconstructing and reconstructing knowledge and information in these ways has more generality than visual explanations: these techniques of analysis serve thought and provide skills and tools that underlie creative thought. Next, we have shown that objective scoring systems can be devised, beginning with separating the information into structure and function, then further decomposing the structure into the central parts or actors and the function into the qualities of the sequence of actions and their consequences. Assessing students’ prior knowledge and misconceptions can also easily be accomplished by having students create explanations at different times in a unit of study. Teachers can see how their students’ ideas change and if students can apply their understanding by analyzing visual explanations as a culminating activity.

Creating visual explanations of a range of phenomena should be an effective way to augment students’ spatial thinking skills, thereby increasing the effectiveness of these explanations as spatial ability increases. The proverbial reading, writing, and arithmetic are routinely regarded as the basic curriculum of school learning and teaching. Spatial skills are not typically taught in schools, but should be: these skills can be learned and are essential to functioning in the contemporary and future world (see Uttal et al., 2013 ). In our lives, both daily and professional, we need to understand the maps, charts, diagrams, and graphs that appear in the media and public places, with our apps and appliances, in forms we complete, in equipment we operate. In particular, spatial thinking underlies the skills needed for professional and amateur understanding in STEM fields and knowledge and understanding STEM concepts is increasingly required in what have not been regarded as STEM fields, notably the largest employers, business, and service.

This research has shown that creating visual explanations has clear benefits to students, both specific and potentially general. There are also benefits to teachers, specifically, revealing misunderstandings and gaps in knowledge. Visualizations could be used by teachers as a formative assessment tool to guide further instructional activities and scoring rubrics could allow for the identification of specific misconceptions. The bottom line is clear. Creating a visual explanation is an excellent way to learn and master complex systems.

Additional file

Post-tests. (DOC 44 kb)

Acknowledgments

The authors are indebted to the Varieties of Understanding Project at Fordham University and The John Templeton Foundation and to the following National Science Foundation grants for facilitating the research and/or preparing the manuscript: National Science Foundation NSF CHS-1513841, HHC 0905417, IIS-0725223, IIS-0855995, and REC 0440103. We are grateful to James E. Corter for his helpful suggestions and to Felice Frankel for her inspiration. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the funders. Please address correspondence to Barbara Tversky at the Columbia Teachers College, 525 W. 120th St., New York, NY 10025, USA. Email: [email protected].

Authors’ contributions

This research was part of EB’s doctoral dissertation under the advisement of BT. Both authors contributed to the design, analysis, and drafting of the manuscript. Both authors read and approved the final manuscript.

Competing interests

The author declares that they have no competing interests.

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Using Graphs and Visual Data in Science: Reading and interpreting graphs

by Anne E. Egger, Ph.D., Anthony Carpi, Ph.D.

Listen to this reading

Did you know that the phrase "a picture is worth a thousand words" certainly applies to science? Complex data can be very hard to understand without being displayed in a visual form, so scientists commonly use visual displays to help during data analysis.

• Visual representations of data are essential for both data analysis and interpretation.
• Visualization highlights trends and patterns in numeric datasets that might not otherwise be apparent.
• Understanding and interpreting graphs and other visual forms of data is a critical skill for scientists and students of science.

Flip through any scientific journal or textbook and you'll notice quickly that the text is interspersed with graphs and figures. In some journals, as much as 30% of the space is taken up by graphs (Cleveland, 1984), perhaps surpassing the adage that "a picture is worth a thousand words." Although many magazines and newspapers also include graphs, the visual depiction of data is fundamental to science and represents something very different from the photographs and illustrations published in magazines and newspapers. Although numerical data are initially compiled in tables or databases, they are often displayed in a graphic form to help scientists visualize and interpret the variation, patterns, and trends within the data.

Data lie at the heart of any scientific endeavor. Scientists in different fields collect data in many different forms, from the magnitude and location of earthquakes , to the length of finch beaks, to the concentration of carbon dioxide in the atmosphere and so on. Visual representations of scientific data have been used for centuries – in the 1500s, for example, Copernicus drew schematic sketches of planetary orbits around the sun – but the visual presentation of numerical data in the form of graphs is a more recent development.

• Using graphs to present numerical data

In 1786, William Playfair, a Scottish economist, published The Commercial and Political Atlas , which contained a variety of economic statistics presented in graphs. Among these was the image shown in Figure 1, a graph comparing exports from England with imports into England from Denmark and Norway from 1708 to 1780 (Playfair, 1786). (Incidentally, William Playfair was the brother of John Playfair, the geologist who elucidated James Hutton 's fundamental work on geological processes to the broader public. To learn more, see our module The Rock Cycle: Uniformitarianism and Recycling .)

Figure 1: William Playfair's graph was one of the first examples of the visual representation of numerical data.

Playfair's graph displayed a powerful message very succinctly. The graph shows time on the horizontal (x) axis and money in English pounds on the vertical (y) axis. The yellow line shows the monetary value of imports to England from Denmark and Norway; the red line shows the monetary value of exports to Denmark and Norway from England. Although a table of numerical data would show the same information, it would not be immediately apparent that something important happened in about 1753: England began exporting more than it imported, placing the "balance in favour of England." This simple visualization of a large numerical dataset made it easy to comprehend quickly.

Graphs and figures quickly became standard components of science and scientific communication, and the use of graphs has increased dramatically in scientific journals in recent years, almost doubling from an average of 35 graphs per journal issue to more than 60 between 1985 and 1994 (Zacks et al., 2002). This increase has been attributed to a number of causes, including the use of computer software programs that make producing graphs easy, as well as the production of increasingly large and complex datasets that require visualization to be interpreted.

Graphs are not the only form of visualized data , however – maps, satellite imagery, animations, and more specialized images like atomic orbital depictions are also composed of data, and have also become more common. Creating, using, and reading visual forms of data is just one type of data analysis and interpretation (see our Data Analysis and Interpretation module), but it is ubiquitous throughout all fields and methods of scientific investigation.

Comprehension Checkpoint

• Interpreting graphs

The majority of graphs published in scientific journals relate two variables . As many as 85% of graphs published in the journal Science , in fact, show the relationship between two variables, one on the x-axis and another on the y-axis (Cleveland, 1984). Although many other kinds of graphs exist, knowing how to fully interpret a two-variable graph can not only help anyone decipher the vast majority of graphs in the scientific literature but also offers a starting point for examining more complex graphs. As an example, imagine trying to identify any long-term trends in the data table that follows of atmospheric carbon dioxide concentrations taken over several years at Mauna Loa (Table 1; click on the excerpt below to see the complete data table).

Table 1: This is a small portion of a data table containing atmospheric carbon dioxide concentrations measured at Mauna Loa - click on it to see the full table. Download the data from the CDIAC (Carbon Dioxide Information Analysis Center).

The variables are straightforward – time in months in the top row of the table, years in the far left column of the table, and carbon dioxide (CO 2 ) concentrations within the individual table cells . Yet, it is challenging for most people to make sense of that much numerical information. You would have to look carefully at the entire table to see any trends. But if we take the exact same data and plot it on a graph, this is what it looks like (Figure 2):

Figure 2: Data plotted from Table 1, atmospheric CO 2 measured at Mauna Loa (Keeling & Whorf, 2005).

Reading a graph involves the following steps:

Describing the graph: The x-axis shows the variable of time in units of years, and the y-axis shows the range of the variable of CO 2 concentration in units of parts per million (ppm). The dots are individual measurements of concentrations – the numbers shown in Table 1. Thus, the graph is showing us the change in atmospheric CO 2 concentrations over time.

Describing the data and trends: The line connects consecutive measurements, making it easier to see both the short- and long-term trends within the data . On the graph, it is easy to see that the concentration of atmospheric CO 2 steadily rose over time, from a low of about 315 ppm in 1958 to a current level of about 375 ppm. Within that long-term trend, it's also easy to see that there are short-term, annual cycles of about 5 ppm.

Making interpretations: On the graph, scientists can derive additional information from the numerical data , such as how fast CO 2 concentration is rising. This rate can be determined by calculating the slope of the long-term trend in the numerical data, and seeing this rate on a graph makes it easily apparent. While a keen observer may have been able to pick out of the table the increase in CO 2 concentrations over the five decades provided, it would be difficult for even a highly trained scientist to note the yearly cycling in atmospheric CO 2 in the numerical data – a feature elegantly demonstrated in the sawtooth pattern of the line.

Putting data into a visual format is one step in data analysis and interpretation , and well-designed graphs can help scientists interpret their data. Interpretation involves explaining why there is a long-term rise in atmospheric CO 2 concentrations on top of an annual fluctuation, thus moving beyond the graph itself to put the data into context. Seeing the regular and repeating cycle of about 5 ppm, scientists realized that this fluctuation must be related to natural changes on the planet due to seasonal plant activity. Visual representation of these data also helped scientists to realize that the increase in CO 2 concentrations over the five decades shown occurs in parallel with the industrial revolution and thus are almost certainly related to the growing number of human activities that release CO 2 (IPCC, 2007).

It is important to note that neither one of these trends (the long-term rise or the annual cycling) nor the interpretation can be seen in a single measurement or data point. That's one reason why you almost never hear scientists use the singular of the word data – datum. Imagine just one point on a graph. You could draw a trend line going through it in any direction. Rigorous scientific practice requires multiple data points to make a clear interpretation, and a graph can be critical not only in showing the data themselves, but in demonstrating on how much data a scientist is basing his or her interpretation.

We just followed a short, logical process to extract a lot of information from this graph. Although an infinite variety of data can appear in graphical form, this same procedure can apply when reading any kind of graph. To reiterate:

• Describe the graph: What does the title say? What variable is represented on the x-axis? What is on the y-axis? What are the units of measurement? What do the symbols and colors mean?
• Describe the data: What is the numerical range of the data? What kinds of patterns can you see in the distribution of the data as they are plotted?
• Interpret the data: How do the patterns you see in the graph relate to other things you know?

The same questions apply whether you are looking at a graph of two variables or something more complex. Because creating graphs is a form of data analysis and interpretation , it is important to scrutinize a scientist's graphs as much as his or her written interpretation.

• Error and uncertainty estimation in visual data

Graphs and other visual representations of scientific information also commonly contain another key element of scientific data analysis – a measure of the uncertainty or error within measurements (see our Uncertainty, Error, and Confidence module). For example, the graph in Figure 3 presents mean measurements of mercury emissions from soil at various times over the course of a single day. The error bars on each vertical bar provide the standard deviation of each measurement. These error bars are included to demonstrate that the change in emissions with time are greater than the inherent variability within each measurement (see our Statistics in Science module for more information).

Figure 3: Error bars within this graphical display of data are used to demonstrate that the change in measurement value (red bars) with time is greater than the inherent variability within the data (shown as black error bars). Adapted from Carpi et al. (2007).

Graphical displays of data can also be used not just to display error, but to quantify error and uncertainty in a system . For example, Figure 4 shows a gas chromatograph of a fuel oil spill. Peaks in the chromatograph (the blue line) provide information about the chemicals identified in the spill, and the peak size can provide an estimate of the relative concentration of that specific chemical in the spill. However, before this information can be extracted from the graph, instrument error and uncertainty must be calculated (the red line) and subtracted from the peak area. As you can see in Figure 4, instrument variability decreases as you move from left to right in the graph, and in this case, the graphical display of the error is therefore critical to accurate analysis of the data.

Figure 4: Graphical displays of data can be used to estimate system error and uncertainty (red line) as well as present this uncertainty.

• Misuse of scientific images

Poor use of graphics can highlight trends that don't really exist, or can make real trends disappear. Some have tried to point out errors with the now widely accepted notion of climate change by using misleading graphics. Figure 5, below, is one such graphic that has appeared in print. The point drawn by the creator of this is that the bottom graph, which shows relatively little change in temperature over the past 1,000 years, disputes the top graph used by the Intergovernmental Panel on Climate Change that shows a recent, rapid temperature increase.

Figure 5: Poor use of graphical displays can confuse and obscure data.

At first glance the bottom graph does seem to contradict the top graph. However, looking more closely you realize:

• The two graphs actually represent completely different datasets . The top graph is a representation of change in annual mean global temperature normalized to a 30-year period, 1960-1990, whereas the bottom graph represents average temperatures in Europe compared to an average over the 20th-century.
• In addition, the y-axes of the two graphs are displayed on differing scales – the bottom graph has more space between the 0.5° lines.

Both of these techniques tend to exaggerate the variability in the lower graph. However, the primary reason for the difference in the graphs is not actually shown in the graphs. The author of the graphic created the image on the bottom using different calculations that did not take into account all of the variables that climate scientists used to create the top graph. In other words, the graphs simply do not show the same data .

These are common techniques used to distort visual forms of data – manipulating axes, changing one of the variables in a comparison, changing calculations without full explanation – that can obscure a true comparison.

• Visualizing spatial and three-dimensional data

There are other kinds of visual data aside from graphs. You might think of a topographic map or a satellite image as a picture or a sketch of the surface of the earth, but both of these images are ways of visualizing spatial data. A topographic map shows data collected on elevation and the location of geographic features like lakes or mountain peaks (see Figure 6). These data may have been collected in the field by surveyors or by looking at aerial photographs, but nonetheless the map is not a picture of a region – it is a visual representation of data. The topographic map in Figure 6 is actually accomplishing a second goal beyond simply visualizing data: It is taking three-dimensional data (variations in land elevation) and displaying them in two dimensions on a flat piece of paper.

Figure 6: Portion of the Warren Peak USGS 7.5' topographic map. Solid brown lines are elevation contours. This image takes 3-dimensional data on elevation and depicts it in two dimensions.

Likewise, satellite images are commonly misunderstood to be photographs of the Earth from space, but in reality they are much more complex than that. A satellite records numerical data for each pixel, and it does so at certain predefined wavelengths in the electromagnetic spectrum (see our Light II: Electromagnetism module for more information). In other words, the image itself is a visualization of data that has been processed from the raw data received from the satellite. For example, the Landsat satellites record data in seven different wavelengths: three in the visible spectrum and four in the infrared wavelengths. The composite image of four of those wavelengths is displayed in the image of a portion of the Colorado Rocky Mountains shown in Figure 7. The large red region in the lower portion of the image is not red vegetation in the mountains; instead, it is a region with high values for emission of infrared (or thermal) wavelengths. In fact, this region was the site of a large forest fire, known as the Hayman Fire, a month prior to the acquisition of the satellite image in July 2002.

Figure 7: July 2002 Landsat satellite image of the Hayman Fire, central Colorado.

• Working with image-based data

The advent of satellite imagery vastly expanded one data collection method: extracting data from an image. For example, from a series of satellite images of the Hayman Fire acquired while it was burning, scientists and forest managers were able to extract data about the extent of the fire (which burned deep into National Forest land where it could not be monitored by people on the ground), the rate of spread, and the temperature at which it was burning. By comparing two satellite images, they could find the area that had burned over the course of a day, a week, or a month. Thus, although the images themselves consist of numerical data, additional information can be extracted from these images as a form of data collection.

Another example can be taken from the realm of atomic physics. In 1666, Sir Isaac Newton discovered that when light from the sun is passed through a prism, it separates into a characteristic rainbow of light. Almost 200 years after Newton, John Herschel and W. H. Fox Talbot demonstrated that when substances are heated and the light they give off is passed through a prism, each element gives off a characteristic pattern of bright lines of color, but they did not understand why (see Figure 8). In 1913, the Danish physicist Niels Bohr used these images to make a startling proposal: He suggested that the line spectra of elements were due to the movement of electrons between different orbitals, and thus these spectra could provide information regarding the electron configuration of the elements (see our Atomic Theory II: Ions, Isotopes, and Electron Shells module for more information). You can actually calculate the potential energy difference between electron orbitals in atoms by analyzing the color (and thus wavelength) of light emitted.

Figure 8: Line spectra for helium (top) and neon (bottom). The location and color of the lines represents a unique wavelength that defines the electron configuration of the atoms.

Photographs and videos are also visual data . In 2005, a group of scientists based in part at the Cornell Ornithology lab published their findings that a bird believed to be extinct in North America, the Ivory-billed Woodpecker, had been spotted in Arkansas (Fitzpatrick et al., 2005). Their primary evidence consisted of video footage and photographs of a bird in flight, which they included in their paper along with a detailed analysis of the features of the images and video that suggested that the bird was an Ivory-billed Woodpecker. (You can read the article and see the photographs here .)

• Graphs for scientific communication

Many areas of study within science have more specialized graphs used for specific kinds of data . Evolutionary biologists, for example, use evolutionary trees or cladograms to show how species are related to each other, what characteristics they share, and how they evolve over time. Geologists use a type of graph called a stereonet that represents the inside of a hemisphere in order to depict the orientation of rock layers in three-dimensional space. Many fields now use three-dimensional graphs to represent three variables , though they may not actually represent three-dimensional space.

Regardless of the exact type of graph, the creation of clear, understandable visualizations of data is of fundamental importance in all branches of science. In recognition of the critical contribution of visuals to science, the National Science Foundation and the American Association for the Advancement of Science sponsor an annual Science and Engineering Visualization Challenge, in which submissions are judged based on their visual impact, effective communication, and originality (NSF, 2007). Likewise, reading and interpreting graphs is a key skill at all levels, from the introductory student to the research scientist. Graphs are a key component of scientific research papers, where new data are routinely presented. Presenting the data from which conclusions are drawn allows other scientists the opportunity to analyze the data for themselves, a process whose purpose is to keep scientific experiments and analysis as objective as possible. Although tables are necessary to record the data, graphs allow readers to visualize complex datasets in a simple, concise manner.

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17 Data Visualization Techniques All Professionals Should Know

• 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

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What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

• Gantt Chart
• Box and Whisker Plot
• Waterfall Chart
• Scatter Plot
• Pictogram Chart
• Highlight Table
• Bullet Graph
• Choropleth Map
• Network Diagram
• Correlation Matrices

1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

• Bubble clouds
• Circle views
• Dendrograms
• Dot distribution maps
• Open-high-low-close charts
• Polar areas
• Radial trees
• Ring Charts
• Sankey diagram
• Span charts
• Streamgraphs
• Wedge stack graphs
• Violin plots

Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

About the Author

Understanding Without Words: Visual Representations in Math, Science and Art

• First Online: 02 November 2021

Cite this chapter

• Kathleen Coessens 5 ,
• Karen François 6 &
• Jean Paul Van Bendegem 7  

Part of the book series: Educational Research ((EDRE,volume 11))

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As knowledge can be condensed in different non-verbal ways of representation, the integration of graphic and visual representations and design in research output helps to expand insight and understanding. Layers of visual charts, maps, diagrams not only aim at synergizing the complexity of a topic with visual simplicity, but also to guide a personal search for and insights into knowledge. However, from research over graphic representation to interpretation and understanding implies a move that is scientific, epistemic, artistic and, last but not least, ethical. This article will consider these four aspects from both the side of the researcher and the receiver/interpreter from three different perspectives. The first perspective will consider the importance of visual representations in science and its recent developments. As a second perspective, we will analyse the discussion concerning the use of diagrams in the philosophy of mathematics. A third perspective will be from an artistic perspective on diagrams, where the visual tells us (sometimes) more than the verbal.

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Visual Reasoning in Science and Mathematics

Diagrams in Mathematics: On Visual Experience in Peirce

Why Do Mathematicians Need Diagrams? Peirce’s Existential Graphs and the Idea of Immanent Visuality

This is the school typically associated with the mathematician David Hilbert. Although he himself saw formalism as a particular strategy to solve certain specific mathematical questions such as the consistency of arithmetic, nevertheless in the hands mainly of the French Bourbaki group it became an overall philosophy and the famous expression that mathematics is a game of meaningless signs was born. See (Detlefsen, 2005 ).

This seemingly simple graph consisting of 10 vertices and 15 edges is nevertheless of supreme importance in graph theory because of the impressive list of properties it possesses. Starikova ( 2017 ) presents a nice and thorough analysis of the graph (in order to discuss its aesthetic qualities). We just mention that the graph has 120 symmetries.

To be found at http://mathworld.wolfram.com/PetersenGraph.html , consulted Sunday, 17 September 2017.

A famous example is a proof of Augustin Cauchy wherein he made the mistake of inverting the quantifiers. A statement of the form ‘For all x, there is a y such that …’ was interpreted as ‘There is a y, such that for all x …’, which is a stronger statement. It is interesting to mention that this case was already (partially) studied by Imre Lakatos, see (Lakatos, 1976 , Appendix 1), who is often seen as the founding father of the study of mathematical practices.

That being said, the interest in the topic is growing. We just mention (Giaquinto, ), (Manders, ), (Giardino, ) and (Carter, 2010 ) as initiators. Of special interest is the connection that is being made between the philosophical approach and the opportunities offered by cognitive science to study the multiple ways that diagrams can be used an interpreted, see (Mumma & Hamami, 2013 ).

It is interesting that, under the same topic, David Bridges (this volume) develops a similar point of view on arts-based research for education. While Bridges questions the ambiguity of the potential and use of artistic means and expressions as research, we rather consider artistic expressions as enriching methods for knowledge construction, opening new insights by their complexity and layeredness.

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Acknowledgements

Thanks to Joachim Frans (2017) who directed my attention to the work of Nelsen (1993, 2000) in his inspiring Ph.D. thesis on ‘Mathematical explanation’.

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Coessens, K., François, K., Van Bendegem, J.P. (2021). Understanding Without Words: Visual Representations in Math, Science and Art. In: Smeyers, P., Depaepe, M. (eds) Production, Presentation, and Acceleration of Educational Research: Could Less be More?. Educational Research, vol 11. Springer, Singapore. https://doi.org/10.1007/978-981-16-3017-0_9

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Inference and Representation: A Study in Modeling Science

Mauricio Suárez, Inference and Representation: A Study in Modeling Science , University of Chicago Press, 2024, 328pp., $35.00 (pbk), ISBN 9780226830049.

Reviewed by Robert Hudson, University of Saskatchewan

What is involved when someone, such as a scientist, uses a model to represent the world? According to Mauricio Suárez, we can examine this question in one of two ways: in terms of an analytic inquiry that answers a ‘constitutional’ question, or in terms of a practical inquiry that answers a ‘means’ question (84–89).

Traditionally, representation is understood constitutionally, “identifying [representation] entirely with the set of facts about the properties of the relata” (7). Here, the relata are the source of representation, “the object doing the representational work”, and the target of representation, “the object getting represented” (6). The traditional approach, which Suárez labels ‘reductive naturalism’, provides a metaphysical analysis of the representational relation, one that “[avoids] any reference to human values [and] . . . the interests, desires, and purposes of the inquirers” (7).

Suárez’s recommended approach is to examine representation in terms of its means, “focusing instead on the very diverse range of models and modeling techniques employed in the sciences”, while paying close attention to “the purposes of those who use and develop the representations” (86). This change of focus reflects, on Suárez’s view, a disciplinary shift in the philosophy of science where analytic inquiries are replaced with “an attempt to understand modeling practices”, a shift indicated by “the intense intention that philosophers have paid to scientific models and modeling practice in the last decades” (85).

Where does this refocusing on matters of scientific practice, and away from questions of metaphysical analysis, lead us? Suárez starts in Chapter 2 by examining the reflections on scientific practice of a unique set of 19th century physicists, Herman von Helmholtz, Heinrich Hertz, James Clerk Maxwell, and Ludwig Boltzmann, and identifies in these reflections an expression of what Suárez calls the ‘modeling attitude’, “a rather loose set of normative commitments . . . that bounds and informs [this] practice within recognized parameters” (44). He continues in Chapter 3 by reviewing a further unique set of contemporary modeling practices rooted in 19th century science, “the engineering model of the 1890 Forth Rail Bridge, the billiard ball model of gases, and stellar structure models in astrophysics” (79). For those familiar with Suárez’s previous work, chapters 2 and 3 constitute new material (xi).

In comparison, chapters 4 to 7 are reworkings of previously published material, developing and arguing for the details of Suárez’s inferential, deflationist theory of model representation, now ‘inspired’ by the 19th century modeling attitude and employing the three case studies as ‘benchmarks’ (84). Chapter 8 presents novel material in support of a deflationist conception. The classic source of philosophical discussion of representation occurs in the philosophy of art and Suárez finds that his representational deflationism “exhibits a notable fit” (223) with Richard Wollheim’s view of the experience of ‘seeing-in’. Chapter 9 concludes the book with original assessments of familiar debates in the philosophy of science. Concerning the realism/anti-realism debate, deflationism resuscitates the tenability of Ian Hacking’s entity realism, Bas van Fraassen’s constructive empiricism, and Arthur Fine’s natural ontological attitude. Further, the turn to emphasizing the role of social practice, characteristic of Suárez’s deflationism, enhances both Philip Kitcher’s ‘real realism’ and Helen Longino’s social epistemology. Finally, the absence of a facticity requirement on successful modeling, as Suárez sees it, provides support for Henk de Regt’s account of scientific understanding.

Suárez’s book rewards the attentive reader with its thorough detail, meticulous argumentation, and scholarly richness. Whether it provides a defensible view of scientific representation turns on whether we describe the representational relation analytically, in terms of the ‘substance’ of this relation (as with reductive naturalism, a substance devoid of “pragmatic elements”; see 91), or practically, deflating this relation and focusing instead on the use of representational sources in generating corroborated inferences about their targets. Classic substantivism views representation in terms of the similarity of a target and a source, or their isomorphism (or weaker, their homomorphism, or other morphism). A recognized problem with substantivism is the phenomenon of misrepresentation (113): where there is no target, or where a target lacks relevant properties, there can be no representation on the substance view as there are no grounds for similarity or isomorphism, and so no misrepresentation.

In contrast, Suárez’s theory of model representation has two components. First, a source represents a target only if the ‘representational force’ of the source “points toward” (9) the target (166). The notion of representational force is understood weakly: a source is directed to the target, and nothing else. The significance of representational force is that this direction is determined practically, in accordance with intended social use (119). This is the deflationary aspect of Suárez’s conception. There’s nothing about the source or the target, in themselves, that necessitates representational force. It follows that anything can represent anything else, the relevant social practice willing (47, 85, 189).

Secondly, on Suárez’s view, a source represents a target only if a source has a “specific inferential capacity” toward a target (166). Inferential capacity comes in two forms. First, there are vertical rules of inference, rules that “apply to the internal workings of the sources considered as self-standing objects” (184). Drawing from Heinrich Hertz, models ( Bilder , for Hertz; 38–39) exhibit ‘conformity’. They possess an internal, “inferential structure” (39) that grants them “a life of their own” (184), one that is “thoroughly social” (227). On the other hand, to serve the purpose of representing a target, a source’s inferential capacity involves horizontal rules of inference “essentially linked to [this source’s social] purposes in surrogative reasoning”, here reasoning about a target to the point of making licensed predictions about the target’s behaviour.

The implications of Suárez’s theory of representation are many. Chapter 7 illustrates the valuable use of surrogative reasoning in Suárez’s chosen case studies, cited above. Also, the application of Suárez’s theory to the philosophy of art opens “a Pandora's box of new questions” as soon as one draws licensed inferences from artworks in a “cultural and political context” (222). Further, Suárez’s deflationism breathes new life into van Fraassen’s constructive empiricism (242–243), now freed of cumbersome metaphysics.

Overall, one would have expected Suárez, given his retrospective position, to have spent more time reviewing published objections to his view. He orients his deflationism in the context of R.I.G. Hughes’ (1997) DDI account (141), arguing that his notion of representational force (“denotative function”) is an improvement on what Hughes calls ‘denotation’ (147–151). On the other hand, Roman Frigg and James Nguyen’s recent DEKI account is ignored, along with its critique of Suárez’s inferentialism. For example, Nguyen and Frigg (2022) object that Suárez fails to satisfactorily answer the “Semantic question: in virtue of what does a model represent its target” (7). Typically, we have an idea about the ‘meaning’ of a model prior to saying what inferences a model prescribes. Inferentialism works the other way. Since representational force, as noted above, is utterly deflated—anything can represent anything else—inferential capacity is the primary driver of meaning. With only inferences at hand, “there is no substantial analysis to be given about scientific representation” (Nguyen and Frigg 2022, 45), about what models represent or mean.

In specifying what it is in virtue of which a model represents a target, we need to say something about what a model is (about what Nguyen and Frigg call a “model object”, 66). This is not to ask for the necessary or sufficient conditions for being a model (its ‘constitution’). It is to ask, in a case where a model represents target, what specifically the model is—what thing it is—that is doing the targeting, just as when someone drives a car we ask, specifically, who is doing the driving, and not for the necessary or sufficient conditions for being a driver. Take, then, Suárez’s case of the Forth Rail Bridge. The (scale) model in this case is a set of engineering blueprints, some of which Suárez reproduces (62–63). These blueprints are the source, the model, and the target is the physical bridge. This is almost right. I have another copy of Suárez’s book, with the same blueprints. I don’t, therefore, have two distinct models of the bridge. It’s one model reproduced twice, reproduced many times in all the copies of the book, reproduced anthropomorphically as on the cover of Suárez’s book, which is itself reproduced multiple times with multiple copies of the book, and so on. So, in specifying what model it is that targets the physical Forth Rail Bridge, we need to look beyond the blueprints. This has nothing to do with the abstractness of the blueprints as a representation of the bridge. The anthropomorphic model is concrete, and with it, too, we need to look beyond the people in the depiction, to the same model that is at issue with the blueprints.

These comments are not original. They speak to the need for caution in talking in a facile way about models, or model objects. Nguyen and Frigg are aware of this need and highlight the relevant ontological issues. One can look at models as (set-theoretic) structures or as fictional entities (2022, 66). Suárez focuses on disputing the structure approach (138). For example, the Forth Rail Bridge blueprints are not set-theoretic. Their creator was not a modern logician. On the other hand, Suárez does not discuss a fictional approach. Arguably, the blueprints are not fictional since both they and the bridge are physically real. The question, for us, is whether Suárez’s deflationism handles this ontological quandary about models.

Consider again the question of the car and who the driver of the car is. A deflationist on this matter sidelines questions about the identity of this individual. Substantivist approaches, such as those based on similarity or isomorphism, encounter counterexamples since, analogously to Suárez’s arguments about models, potential car drivers need not be similar nor isomorphic to one another. The turn to a practical, or ‘means’ inquiry recommends that we look at the socially sanctioned practices of car drivers, without settling on the constitution of these drivers. For example, we might note that car drivers perform certain actions under certain circumstances, and different actions under different circumstances. A full description of these contextualized practices answers the question for a deflationist about who the driver is.

Is this a satisfactory answer to the analogous ontological question about drivers? Not if we think it matters who the driver is, leaving aside the question of their constitutional identity. At the traffic stop, a police officer will ask for the driver’s license and registration in order to pick out the relevant legal individual, not to define this person in terms of the necessary or sufficient conditions for being a driver. It’s a matter of ascribing responsibility for the driver's actions. A deflationist answer, substituting the legal individual with a set of actions practically distinguished by the interests of a community, is misleading since the same individual could perform a different set of actions, and a different individual could perform the same set of actions.

Consider now the Forth Rail Bridge. If one wants a reason for why the bridge has not toppled, one points to the relevant model. We access this model by viewing the blueprints. The blueprints aren’t the model since the blueprints are not responsible for why the bridge has not toppled. One can destroy all the blueprints and the bridge will still not topple. That the bridge has not toppled, or in more scientific cases, the success of one’s inferential practices, does not explain the lack of toppling or the bridge’s continued standing. These points are not distant from Suárez’s thinking. In discussing the Lotke-Volterra equations, Suárez notes that merely satisfying these equations is not enough to explain an observable phenomenon, such as the correlation between predator and prey numbers in the Adriatic Sea, since this correlation could be “entirely spurious or arbitrary” (114). Thus, the Lotke-Volterra theoretical model is more than just the equations and the inferential practices they prescribe. There is something in the world that corresponds to this model, something we have captured in our thinking, something ensuring that the model is not, as Suárez says, “predictively inane” (114). If the Lotke-Volterra model simply prescribes “a nonlinear pair of intermingled equations” and imposes “no requirements whatever on the nature of the objects involved as source or target or their relation” (172), there will be “no explanatory fact underlying the correlation” (114). To me, this sounds like an abandonment of inferentialism.

These critical points aside, Suárez’s book is a richly argued model of scholarship that sets the standard for future investigations into scientific representation.

Hughes, R.I.G. (1997), “Models and Representation,” Philosophy of Science 64: S325–S336.

Nguyen, J. and R. Frigg (2022), Scientific Representation . Cambridge University Press.

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Computer Science > Robotics

Title: where to fetch: extracting visual scene representation from large pre-trained models for robotic goal navigation.

Abstract: To complete a complex task where a robot navigates to a goal object and fetches it, the robot needs to have a good understanding of the instructions and the surrounding environment. Large pre-trained models have shown capabilities to interpret tasks defined via language descriptions. However, previous methods attempting to integrate large pre-trained models with daily tasks are not competent in many robotic goal navigation tasks due to poor understanding of the environment. In this work, we present a visual scene representation built with large-scale visual language models to form a feature representation of the environment capable of handling natural language queries. Combined with large language models, this method can parse language instructions into action sequences for a robot to follow, and accomplish goal navigation with querying the scene representation. Experiments demonstrate that our method enables the robot to follow a wide range of instructions and complete complex goal navigation tasks.

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Visual representations of weddings in the middle ages: reflections of legal, religious, and cultural aspects.

1. Introduction

2. materials and methods, 3. the legal background of the wedding ritual, 4. religious and cultural background of the medieval wedding ritual, 5. the mediatization of medieval weddings through visual representations.

Click here to enlarge figure

6. Conclusions

Data availability statement, acknowledgments, conflicts of interest.

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Wettlaufer, J. Visual Representations of Weddings in the Middle Ages: Reflections of Legal, Religious, and Cultural Aspects. Religions 2024 , 15 , 1011. https://doi.org/10.3390/rel15081011

Wettlaufer J. Visual Representations of Weddings in the Middle Ages: Reflections of Legal, Religious, and Cultural Aspects. Religions . 2024; 15(8):1011. https://doi.org/10.3390/rel15081011

Wettlaufer, Jörg. 2024. "Visual Representations of Weddings in the Middle Ages: Reflections of Legal, Religious, and Cultural Aspects" Religions 15, no. 8: 1011. https://doi.org/10.3390/rel15081011

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