Definitions, Scope, & Underpinnings

 Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 124-158. This seminal article serves as one of the first efforts to bring together ideas from varying research perspectives (e.g., psychology, statistics, literacy, education, and information processing) to explore a framework of critical factors that influence graph comprehension, which the authors define as the “graph readers’ ability to derive meaning from graphs created by others or by themselves”. Here, graph comprehension is proposed to involve four kinds of behaviors, including: (1) translation – a change in the form of communication between tables and graphs, (2) interpretation – identification of relationships, (3) extrapolation and interpolation – noting trends perceived in the data and potential implications, and (4) questioning – question asking and question posing that allows the reader to explore the presented data. Additionally, several critical factors that influence graph comprehension including the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics are identified and explored. The authors outline three levels of graph comprehension that “show a progression of attention” from local to global features of a graph focusing on directly extracting data from a graph, (b) finding relationships in the data (“seeing between the data”) to extrapolating or making inferences about relationships implicit in a graph (“seeing beyond the data”). In consideration of these factors, instructional recommendations are provided relating to behaviors that demonstrate one’s ability to use graphs, a suggested progression of graphs for K-12 instruction, and the creation and adaptation of graph data to promote sense making.

Freedman E.G., Shah P. (2002) Toward a Model of Knowledge-Based Graph Comprehension. In: Hegarty M., Meyer B., Narayanan N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2002. Lecture Notes in Computer Science, vol 2317. Springer, Berlin, Heidelberg. In characterization of the factors that influence graph comprehension, the authors propose the construction-integration (CI) model that incorporates the effects of prior knowledge and display characteristics. Within this model, successful graph comprehension occurs in two phases, occurring in alternating cycles, including one’s construction of a coherent representation of the presented information and then integration of disparate knowledge into the representation. The proposed model for graph comprehension accounts for the interactive influence of graphical display features, the viewer’s graph reading skills (interpretation propositions), and domain knowledge. As it relates to visual display, the authors explain how display features can influence graph processing (e.g., visual chunking, data transformation). The authors further outline how several types of prior knowledge (domain knowledge, graphical literacy skills, and explanatory skills), activated early during processing, can influence the viewer’s graph comprehension. The model highlights the potential interplay between one’s knowledge about graph formats and expected relationships between variables leads to a top-down influence on graph interpretation. This is particularly relevant in scientific reasoning as experts, in contrast to novices, may offer explanations beyond the presented data by drawing on prior knowledge automatically activated in the construction phase. One important consideration for instruction here, is that novices may be unable to activate their prior knowledge automatically, and may then rely on superficial aspects of the data rather than the relevant relationship. Thus, instructors (as well as practitioners presenting graphs to the general public) need to be attentive to presenting graph information in a means that is congruent to the viewer’s prior knowledge and task goal as non-optimal displays will lead to biased and inaccurate decision-making.

Hegarty, M. (2011). The Cognitive Science of Visual-Spatial Displays: Implications for Design Topics in Cognitive Science 3 (2011) 446–474 DOI: 10.1111/j.1756-8765.2011.01150.x. This review article provides a cognitive science perspective on the design and use of visual-spatial displays. The author begins by identifying and discussing three broad types of visual displays based on the relation between the representation and its referent (i.e. what the symbol/representation refers to) and the complexity of the information being represented, including: iconic, relational, and hybrid displays. The article then outlines how visual-spatial displays enhance cognition by freeing up working memory, utilizing spatial organization, offloading cognitive processes onto perceptual ones, and offloading internal mental computations onto the external manipulation of complex interactive displays. The author next outlines the cognitive and perceptual processes involved in understanding visual-spatial displays. As described, display comprehension involves the complex interactions between top-down (perception driven by prior knowledge and expectations) and bottom-up processes (perception driven by sensory information as it comes in) mediated by the visual features of the display and the viewer’s expectations of what is salient, display schema (a construction of a representation of a referent) that includes knowledge of display conventions, and domain knowledge or visual-spatial processes (e.g., mental rotation, comparison). Finally, the author discusses relevant findings (or principles) in cognitive science and related fields to inform the design of effective visual-spatial displays. Several of the summarized principles (e.g. those related to task specificity, perception of displays) are especially relevant to the use of graph displays in teaching as well as in training students best practices for presenting scientific data.

 Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21(1), 39-48. The ability to understand and use models and modeling is widely seen as being central to an understanding of science. In this review, the developmental trajectory of students’ model-based reasoning and key aspects of teaching and learning activities in science and mathematics that emphasizes systematic practice in the construction, evaluation, and revision of models is explored. Drawing on their work with elementary learners, the authors identify and discuss four forms of modeling as cognitive tools that they feel support student learning: physical, representational (e.g., graphs), syntactic, and hypothetico-deductive models. This is followed by a description of related modeling practices and how they relate to the development of learners’ model-based reasoning. While the authors’ insight stems from work with young children, the provided suggestions are also largely applicable to college science learners as model-based reasoning develops over years and is contextually situated. Of particular relevance to graph instruction, the authors make a case for the (a) iterative, cyclical nature of modeling in which students evaluate multiple models and receive explicit feedback to the appropriateness of their ideas; (b) situation of models in interesting and approachable problems; and (c) value of modeling in the domain of practice. The authors conclude by advocating for curricula that explicitly focus on models and modeling for the development of model-based reasoning over the “long journey” of one’s learning.

Wang, Z. H., Wei, S., Ding, W., Chen, X., Wang, X., & Hu, K. (2012). Students’ cognitive reasoning of graphs: Characteristics and progression. International Journal of Science Education, 34(13), 2015-2041. This article makes use of a graph information framework to characterize the types of reasoning high school science students employ when reading and interpreting graphs. Building from a review of the literature on the components of graph comprehension, the authors created a framework comprised of three types of graph information: 1) Explicit information presented in graphical elements (e.g. plotted variables, data points, straightforward variable relationships), 2) Tacit information that requires prior scientific knowledge and mathematical tools to draw inferences beyond the presented data, and 3) Conclusive information visible from deep reasoning in deduction and graphs analysis. To examine the characteristics and differences of graphing skills among students at different grade levels, ~3000 high school students in China a validated assessment consisting of open-ended items to reveal their ability to read and analyze scientific graphs. The authors used their framework to analyze student responses and categorize student reasoning with graphs. The authors found that across the grade bands, student use of explicit information did not vary, whereas, a difference in the use of tacit and conclusive information requiring an understanding of scientific concepts was observed. In comparison to their younger classmates, students in Grade 11 were more likely to “look” past the surface features of the graph and draw on their more advanced scientific knowledge to make sense of the presented data. However, the type of graph did have an impact on student responses with the more experienced students using tacit and conclusive information for graphs that depicted complex scientific concepts or for which the relevant concepts are not explicitly plotted.

Padilla, L. M., Creem-Regehr, S. H., Hegarty, M., & Stefanucci, J. K. (2018). Decision making with visualizations: a cognitive framework across disciplines. Cognitive research: principles and implications, 3(1), 1-25 This review outlines a generalizable cognitive model as to how people make decisions with visualizations to inform effective visualization design, including graphs. The integration of visualization cognition frameworks with a dual-process account of decision-making, including automatic, simple decisions (Type 1) and more complex, contemplative decisions (Type 2) are explored. The dual-process model outlines how individuals create a mental schema from a visualization and conceptual task using top-down (i.e. our thinking affects what we see) and bottom-up (i.e. Visualization affects our thinking) encoding mechanisms that includes working memory. Based on cross-domain findings, four common universal visualization principles relevant to graph design and instruction are suggested. First, early stages of decision-making are profoundly influenced by one’s bottom-up attention. This suggests that a graph designer’s effort should be placed on focusing the viewer’s attention on critical task-relevant information to positively capitalize on Type 1 processing while limiting potential distractors that result in poor decision outcomes. Second, in relation to Type 1 processing, is the potential for visual-spatial biases (e.g., tendency to use the first data point to make decisions, belief that higher-quality images reflect “better” data, etc.) that can be both beneficial and detrimental in early decision-making. Third, involving Type 2 processing, is that if a mismatch occurs between the visualization and one of the decision-making processes, then a mental transformation will be required that can be error-prone and increase time on task. Thus, efforts should be taken to identify and reduce potential mismatches to reduce the number of transformations required in the decision-making process by examining the alignment (cognitive fit) of the visualization and task. Fourth, is that an individual’s existing short- and long-term knowledge can interact with visualizations (bottom-down). The authors contend that there is an interplay between Type 1 and Type 2 processing in how viewers complete visualization tasks and they recommend practical recommendations for visualization designers and instructors.

Shah, P., & Freedman, E.G. (2011). Bar and line graph comprehension: An interaction of top-down and bottom-up processes. Topics in Cognitive Science, 3(3), 560–578. This study builds from a model of display comprehension in which the features of the display interact with the prior knowledge and viewers’ expectations which influences understanding of the display and inferences drawn. In particular, the authors aimed to examine how domain-specific knowledge of graph data and domain-general knowledge about data display affect one’s graph interpretation skills. Fifty-five undergraduates were randomly assigned to a set of 14 bar or line graphs that represented comparable data of medium complexity (i.e. multivariate data with three variables represented) and varying familiarity to examine their graph interpretation skills. Each graph had an accompanying paragraph contextualizing the data, but omitted the outcome of the study from which the data came from. Participants were prompted to write a short summary of what they perceived to be the important take-aways from the presented graphs as well as their familiarity with the included data relationships. In follow-up, participants completed a short graphicacy assessment as a measure of competence of both basic graphing skills and the tasks in the study. Results indicate that participants focused on x-y axis trends when viewing line and bar graphs with unfamiliar variables. In comparison, when the variables were familiar, participants were more attentive to y-z axis relationships, with this pattern being significant for those with measured high graph interpretation competence. These findings provide the first test of a top-down/bottom-up model for graph interpretation and highlights the interaction of domain-general graphing features (e.g., graph type) and the role of domain-specific knowledge for this process. Such insight can help instructors consider how to develop differentiated scaffolding (by graph type and familiarity with the variables) to support student development of graph interpretation skills.

 Quillin, K., & Thomas, S. (2015). Drawing-to-learn: a framework for using drawings to promote model-based reasoning in biology. CBE—Life Sciences Education, 14(1), es2. While not specific to graphing, this essay provides a drawing-to-learn framework that defines drawing, provides examples of various types of drawing in biology, and explains the cognitive benefits of students drawing models to reason in the biolo­gy classroom. Instructionally several tools and best practices are suggested to foster an environment that supports drawing-to-learn interventions. The authors also outline a Blooming tool for drawing model that provides a scaffolded framework that applies Bloom’s taxonomy to assessment exercises, including various examples and suggestions for instructors in how to work up cognitive levels. For graphing, a suggestion for the lowest-order cognitive level of knowledge, is to give students the independent and dependent variables and ask them to draw and label the axes on a graph. At the comprehension level, an example exercise is to have the student explain what a data point represents. At the application level, students draw a graph based on a given set of data. At the analysis level, the suggestion is to have students build on the application level and have them determine if the data support or reject a hypothesis. At the synthesis level, the suggestion is to design an experiment to answer a question and sketch a graph of the prediction. At the highest-order cognitive level, evaluation, it is suggested to have students evaluate a graph to determine whether it is constructed appropriately to the data provided. The drawing-to-learn framework and Blooming tool provide instructors a structure of best practices for the incorporation of drawing into the classroom in benefit to student learning.

Modeling in the Classroom Guide This guide describes the efficacy of the practice of scientific modeling for the development of students’ conceptual understanding and systems thinking skills. It also highlights a variety of common (non-graph) models, and practical approaches for instructors to incorporate models and modeling into the classroom, which could include graphing.

Tufte, E. R. (2001). The visual display of quantitative information (Vol. 2). Cheshire, CT: Graphics press. Widely held as the seminal text on how to understand and depict data, the book can help guide students and practitioners in the theory and practice of quantitative data visualizations. The book provides practical insight and examples (good and bad) to demonstrate how to effectively display data graphically. Highlighted topics include the design and selection of graphical displays, editing and improving graphics for aesthetics and analysis (e.g., data-ink ratios), and the detection of graphical deception.