collecting, understanding, and interpreting data are key skills that all students should master (8, 12, 22, 33). Research on graph interpretation and basic construction is extensive, and student difficulties, primarily in K-12 type settings, have been well documented [e.g., graph choice (30, 32, 45), labels for axes (30, 32), variables (45), and scaling axes (1, 7, 32, 34)].

Although many instructional books exist on graphing (5, 20, 28, 47), they do not focus on the complex reasoning behind graph choice and construction. It is insufficient to choose an appropriate graph for data (e.g., bar graph for categorical data) without evaluating the advantages and disadvantages of using a particular graph.

Metarepresentational competence (MRC) refers to the knowledge required for successful construction and reasoning with external representations, which includes graphs (14). MRC has several components that reveal students' ability and inability with graph choice, construction, and critique (15). Specifically, these areas are invention, critique, functioning, and learning or reflection (Table 1) (15). The first area, invention, reveals students' underlying skills and abilities that allow them to conceive novel graphical representations from data (15). The second area, critique, exposes students' critical knowledge that is essential for assessing various types of graphs and their strengths and weaknesses (15). The third area, functioning, unearths students' reasoning for understanding the purpose of different types of graphs and the usage being dependent on the type of data present (15). The final area, learning or reflection, reveals students' awareness of their own understanding of graphs (15).

### Overview of Graphing Literature

In addition to students, graphing difficulties have been documented in instructors (6), professionals (40, 49), and medical doctors (10, 11, 42, 43), with an interest to remediate graphing difficulties (16, 18, 41). Although Rougier et al. (40) suggested 10 simple rules to help with graph communication and Weissgerber et al. (49) stressed the importance of graph choice, focus on developing the invention, critique, functioning, and learning process, as suggested by MRC, is lacking. Furthermore, few reports on teaching interventions and assessments of student learning around graph choice and construction exist.

While graphing is not unique to biology, it is important to consider the learning and practice of that skill within the disciplinary context to best understand and remediate biology student difficulties. Two studies at the undergraduate level in biology have provided some useful insights into student difficulties and described learning experiences in both laboratory (32) and lecture (44) classroom settings. In both studies, graphing of data was an explicit learning outcome for undergraduate biology students, but the two studies varied in numerous, and potentially important, ways: classroom context, duration and focus of the intervention, the degree of scaffolding provided to students when graphing, whether students were encouraged to apply reflective and analytic skills consistent with promoting MRC, and the assessments used to evaluate student learning. McFarland (32) designed a laboratory class intervention devoted to graph choice and construction that included instructions on graphs, their usage, and student engagement in the reflection on appropriateness of graphs. Throughout the semester, students were required to respond to two self-assessment prompts about their graph choice and quality, engaging an important element of MRC. There was no explicit assessment of student graphs or reasoning reported in this study. However, it was noted that faculty members thought that the quality of student graphing improved and when students responded to a course evaluation question about their learning about graphs in the class, they reported, on average, that they learned “a lot.” In contrast to McFarland (32), Speth et al. (44) administered a pre/posttest to undergraduate students in a lecture class where quantitative skills, including data and graphing, were stressed throughout the semester. Although student gains were significant in graph mechanics, there was an inconsistency in graph choice. The diversity in these two studies makes it difficult to deduce best practices and instructional tools to promote the development of graphing proficiency. Furthermore, it is important to provide students with repeated opportunities to increase competency (32, 38) and practice critical reflection in graphing choices (14, 15).

To fill the gap in graphing literature, we designed materials that are easy to implement in K–16 classrooms, increase students' graph knowledge, and provide a systematic framework for data presentation. There are graphing resources available to assist with graph choice and construction (32a, 33a, 35, 37, 48); however, a limitation of these guides is the inefficient guidance to be reflective. In the present report, we highlight the purpose, development, and usage of two materials: *1*) a guide to data displays and *2*) a step-by-step guide to data communication. These materials are designed to facilitate the development of graphing competency and knowledge related to MRC.

### Description and Development of Graph Materials

#### Guide to data displays.

The purpose of this resource is to increase students' MRC by exposing them to different types of graphs, their usage, advantages, and disadvantages. Undergraduate biology students are often familiar with three common types of graphs: bar, line, and scatter, and can confidently articulate the advantages of these graphs (2). However, when asked to articulate the disadvantages, students either display uncertainty on elements that comprise disadvantages or they naively state no disadvantages (2). Critical graph evaluation is vital for refining critical thinking and argumentative skills and is an important part of MRC (14, 29, 32).

The guide to data displays (Fig. 1) shows six common types of graphs (bar, box and whisker, histogram, line, dot, and scatter) and tables used in the biological sciences along with relevant citations that describe the usage, advantages, and disadvantages of each graph. The decision to select these graphs was obtained from *1*) surveys from professors (3); *2*) think-aloud interviews with expert professors and novice students (3); *3*) data collected from an upper-level laboratory classroom at a large Midwestern university (2); and *4*) seminal literature, which included relevant books, undergraduate biology textbooks, articles from various fields of biology, and education literature. All six graphs are bound by the Cartesian coordinate system, which allows graphs to portray relationships between variables. Although students are exposed to pie charts on a daily basis (phone apps, magazines, television, etc.) (3), we found minimal presence of pie charts in biology textbooks and primary literature. This could be because pie charts are used to display frequency or percent data, which is useful for understanding emerging patterns in data (28, 42), but they cannot communicate relationships between experimental variables.

#### Step-by-step guide.

The purpose of this guide (Table 2) is to provide students with a framework for data presentation, which encompasses all four parts of the MRC (Table 1). Under an approved Institutional Review Board protocol (no. 1210012775), undergraduate students (*n* = 6) and professors (*n* = 7) were recruited from within the biological sciences for semistructured think-aloud interviews. Participants were given a simple data set and asked to plot the data graphically. Graphs were constructed by hand using a Livescribe pen and notebook paper instead of digitally on a computer. The Livescribe pen synchronizes written notes with recorded audio and has an embedded infrared camera that detects penstrokes when used with the Livescribe dot paper (31). The usage of this pen allowed us to understand the stepwise reasoning process necessary for graph construction and enabled the development of the step-by-step guide. A summary of the thought process for undergraduate students and professors is shown in Fig. 2. Individual data from the think-aloud interviews were coded and organized into 16 steps, which were further categorized into 3 phases: planning, execution, and reflection. The terminology for the phases was adapted from Koedinger and Anderson's (27) diagram configuration model used for solving geometry proofs. Our step-by-step guide to data communication and three phases are also comparable to Polya's problem-solving cycle in mathematics (36). Polya's first principle challenges the learner to understand the problem, which is similar to our planning phase, consisting of formulating a purpose for the graph and organizing the data. Polya's second principle instructs the learner to devise a plan. This principle is also embedded in our planning phase, consisting of classifying variables, deciding on data manipulations, and finalizing the graph choice. Polya's third principle instructs the learner to carry out the plan and parallels our execution phase as well as diSessa's invention step in the MRC, where the learner actively constructs the graph with appropriate mechanics. Polya's final principle instructs the learner to look back through the problem, check the result, and reflect on the problem-solving approach. This step closely resembles our reflection phase and diSessa's critique, functioning, and reflection steps in the MRC and consists of critical reflections on graph alignment, graph choice, and data presentation. The similarity in our work, Polya's work in mathematics, and diSessa's work on MRC is the interest to develop common steps that engages and challenges the learner to develop systematic independent and intellectual skills to solve problems. Differences lie in the nature of the task. Polya's work was developed in the context of mathematics, and the four principles apply broadly to all problems students may encounter in mathematics courses. diSessa's work is rooted in cognitive psychology to understand how students construct and interpret scientific representations. The materials we developed are focused even further on only graphical representations. Findings comparing thought processes between professors and undergraduate students revealed two things (Fig. 2). First, professors take four more steps during graph construction compared with undergraduate students. Specifically, after professors read the prompt, they pose the research question of the study. The second revelation is that when professors are nearing the end of their graph construction, they take time to reflect on their creation by thinking of other ways to graph data as well as the disadvantages of their creation, and they provide an interpretation of their graph by including a figure legend. The automatic reflection present during the construction task could be due to professors' extensive experiences with experiments, data analysis, and graph construction in their own research and teaching others (9, 38).

#### Implementation of graph materials.

As part of a bigger intervention study, these graph materials were tested in an advanced undergraduate physiology laboratory class in spring 2015. Students were given formal instruction on the usage of the materials followed by practice using the materials. Students had online access to these materials throughout the course and used them five times over the semester for appropriate graph choice and construction for their oral presentations. Preliminary analysis of student graphs suggests a significant improvement of graph quality over the course of the semester compared with graphs from previous semesters where students did not have access to these materials.

### Additional Suggestions for Implementation

As more students are involved in data collection and analysis as part of biology curricula (8, 12, 24, 33), they will be confronted with issues revolving around graph choice and construction. The two graphing materials can be used in three different ways. First, they can be integrated throughout multiweek or semester-long science laboratory courses where students are actively collecting data and communicating their findings. Actively engaging in the stepwise process will increase students' confidence with graph choice and construction and will enable them to critically think about their data and graphs within the classroom context and outside of the classroom. See Appendix Tables S2 and S3 and Appendix Figure S1 in the Supplemental Material for a sample scenario with a data set, a filled out example of the step-by-step guide, and the resulting graphs.^{1} Having students think about the type of data they are collecting and having them refer to the guide for data displays while they are planning their data will broaden their knowledge with graphs and force them to think about the utility, advantages, and disadvantages of different graphs. If students are not actively engaged in data collection, instructors can provide students data from publicly available sources (21) or from data repositories of peer-reviewed research articles to give students practice graphing data. A second suggestion is to use the guide for data displays to critique the authors' choice of graphical representations found in textbooks, primary literature, and popular media and link them to their claims. Having students think critically of existing graphs will encourage them to become data literate and informed citizens. A third suggestion is to use the graphing materials strictly as assessment tools. The instructor can give students access to the guide for data displays and quiz them periodically throughout the semester using the blank table version of this handout (Appendix Table 1S). Learning gains pertaining to graph knowledge and increasing MRC can be formally assessed by having students fill out the blank table at the beginning and end of the semester.

### Critique and Conclusions

The strengths of the step-by-step guide is its ability to successfully guide students in a sequential and methodological manner from raw data to a finished graphical representation. The guide prompts a reflective approach to the process of graph creation, which aids the development of MRC. Additionally, the instructor obtains instant formative feedback, which is essential for targeted instruction. The weakness of the step-by-step guide is the lack of explicit guidance to the types of graphs available for use. However, this limitation can be overlooked if the step-by-step guide is paired with our guide to data displays or other similar resources (18, 32a, 48). Since the step-by-step guide was developed from think-aloud interviews, in which the mode of graph construction was pen and paper, we bring to light another weakness that educators and practitioners can relate to. Since graphs are constructed using software, the step-by-step guide does not incorporate Tufte's tips for displaying data in an effective and aesthetically pleasing manner, devoid of chartjunk (47). To account for this weakness, we designed a general, analytic, multipart graph rubric (4), which encompasses Tufte's tips for data displays. The main strength of the guide to data displays is the organized manner in which information on graph usage, advantages, and disadvantages is presented. Consequently, one weakness is that only six graphs are represented. However, since extensive research was done looking at graphs from textbooks and primary literature to decide what graphs to display, we think that this is acceptable for beginning students. Instructors may use this table to expand to other graph types as they see fit for the students at more advanced levels of learning.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

Author contributions: A.A. and S.M.G. conception and design of research; A.A. and S.M.G. performed experiments; A.A. and S.M.G. analyzed data; A.A. and S.M.G. interpreted results of experiments; A.A. prepared figures; A.A. drafted manuscript; A.A. and S.M.G. edited and revised manuscript; A.A. and S.M.G. approved final version of manuscript.

## ACKNOWLEDGMENTS

The authors thank all of the biology undergraduate students, graduate students, and professors who have participated in all of our studies so far. The authors also thank our research group, PIBERG, for the early feedback on this project. This project emerged from ideas initiated within the Biology Scholars Research Residency program.

## Footnotes

↵1 Supplemental Material for this article is available at the

*Advances in Physiology Education*website.

- Copyright © 2016 The American Physiological Society