How to Teach Graphing

Graphs were a big part of my STEM career and I taught graphing regularly. Students had the mechanics of constructing graphs with appropriate axes, labels, and scales. But there was often a lack of understanding of why you may want to make a particular graph and how to tell a story with the data you have. Even reading graphs to glean necessary information could be a challenge. The global pandemic revealed a lack of graphical literacy among the general public. Further research revealed that even undergraduate students lack graphical literacy. But how do we best teach graphical literacy? While there are a couple of recent articles, much of the research on how to teach graphing occurred over 20 years ago. In the absence of more recent research, we need to look towards the past. We also need to analyze articles that may not be of the highest quality in terms of research to see what lessons can be learned on teaching graphing.

Here I highlight three relatively recent articles that break down graphing instruction and assessment and give us some general lessons on how we can help teach our students necessary graphing skills. To access this research, we need to veer from strict mathematics instruction to incorporate science instruction as data is at the intersection of these fields.

Expert vs. Novice

In teaching graphing skills, we first need to examine the difference between experts and novices and identify different thought processes and skills. A 2016 article by Angra and Gardner, published in Advances of Physiology Education show that experts have a couple of extra steps when creating graphs. Notably, experts pose research questions early in the process that could be answered with a graph. They also evaluate graphs the graphs they create, considering the disadvantages of a constructed graph and other ways to graph the data.

Through this research of experts and novices, the authors created and tested materials to support the teaching of graphs to K-16 students. Two of the materials developed: a guide to data displays and a guide to data communication are highlighted in the published study. The authors suggest using these tools by integrating them throughout a course where students are actively collecting data and communicating findings, like a traditional lab. A table of data display types, when they are typically used, advantages, and disadvantages of each type can be used as an assessment tool, giving students the background knowledge needed to create different graphs.

Non-STEM students do not need to become experts with creating graphs, but they need to be able to utilize data to make decisions. You can use the materials highlighted in the article as a guide for students to critique textbook authors’ choice of graphical representations. You may also use news articles as graphs can be used to lead a reader to a particular conclusion that may or may not accurately represent the data. Discussions like these could lead to a deeper understanding how graphs are used to tell a story,  and help students to recognize biased graphs, and then utilize graphical data to make decisions.

Graphs During Direct Instruction

An article by Michael Allan A. Bahtaji explored the use of different levels of instructional support and how those levels affected physics students’ graphing skills and conceptual understanding. The study itself is rudimentary and somewhat lacking in details, but we can still glean one unsurprising lesson. The study compared three groups of physics undergraduate students. One group was exposed to ready-made graphs during lecture, another was given direct, explicit instruction on graphs, and the third was engaged in an activity with graphs. There was an extensive 50-item multiple choice questionnaire on force and motion and a five-item test where students created graphs. These tests were given to students before and after the intervention to allow for direct comparison of students’ learning.

It is no surprise that simply exposing students to graphing during a lecture was the least effective instructional method.  Explicit instruction on graphing during lecture did improve student learning over active instruction, however, there were little to no details on either of these interventions. We know that small details in how active instruction is conducted can affect students’ learning, so we cannot draw conclusions comparing these two methods. What can be said is that assuming our undergraduate students know how to read graphs and so providing little to no support is not effective with learning graphing skills. The take-away here is that if you are going to use lectures, be sure to include explicit instruction on graphing skills.

Platform Matters

Graphs can be challenging to assess This led to the development of a digital tool, GraphSmarts, that automatically assesses practices of graph creation. As the tool was being developed, it was revealed that there were differences in how students created graphs digitally versus using pen-and-paper. An article by Gardner, et al. examines these differences in detail.

Digital graphing tools like GraphSmarts described in the paper, Create-a-Graph from the National Center for Education Statistics, or even the Desmos graphing calculator, have built in constraints. There is only one x and one y axis so it is difficult to combine data into one graph and there is often a suggested scale to help with visualization. When students are given graph paper, these constraints are removed and students are free to construct whatever they think will best fit the data. For example, some students in the study chose to include multiple variables on the same y-axis or added a second y-axis to explain the data.

When students are given pen and paper, they are likely to make only one graph as opposed to several graphs in a digital environment. In interviews, students mentioned that it is easy to make several graphs in a digital environment, but creating several graphs by hand takes time and effort. As for quality of graphs, ease of drawing a graph by hand was the most common answer when students’ were asked why they created particular graphs. What happened after the first graphs were created using these different platforms, pen and paper versus digital, was of particular significance. While the amount of time needed for students to create their first graphs, students using a digital tool ‘played’ with the data and created more graphs, often resulting in a high-level graph as the final graph submitted. This act of ‘playing’ with the data allows for students to self-teach what a high-quality graph may look like.

Table 1: Differences between constructing graphs using pen-and-paper and the digital tool GraphSmarts (Gardner et al., 2021).

The difference in graphing between digital and pen-and-paper can influence our use of these platforms in the classroom. If you want to expose students’ thinking before instruction, give students pen-and-paper with data and have them create a graph. Allowing free-reign to create can reveal how your students deal with data. At the end of instruction, give students their original graph and ask them to revise using what they have learned. During instruction, while students are learning about quality graphs, allow them to work in a digital environment so they can ‘play’ with the data, easily creating multiple graphs.  

There is ample evidence demonstrating that our students, and the general public, lack skills with reading and utilizing data in graph form. But there is very little research on how to teach these skills effectively. The few articles reviewed here give you a taste of what may be possible. I encourage you to be your own researcher. Try some of the suggestions in this article and see how it goes with your students.

Take Aways

• Students lack graphing skills, but there are things we can do to improve these skills, as guided by the scant research on this topic.

• Allow non-STEM students to critique published graphs, considering the pros and cons and considering other ways to represent the data.

• Do not assume students know how to read graphs. Be explicit about the graphs used during instruction, explaining how they are created and how they accurately represent the data.

• To assess student’ graphing skills before and after instruction, use pen-and-paper. During instruction, use digital tools so students are easily able to ‘play’ with the data and how it can be represented.