More Than Meets the Axis: Helping Social Studies Students Understand Graphs
by Marilyn DePietto
When James Baldwin wrote that “the purpose of education…is to create in a person the ability to look at the world for himself, to make his own decisions,” (Baldwin, 1963) he was not calling educators to produce agreement. He was calling us to find the courage to confront uncomfortable truths, to question what appears settled, and to resist the ease of acceptance. In today’s media-saturated world, that courage increasingly depends on a form of literacy that sits at the intersection of mathematics and social studies: the ability to critically interpret visual representations of data.
Mathematics is often framed as the domain of certainty and social studies as the domain of interpretation. Students are told that in mathematics, conclusions follow logically from established truths. In social studies, students weigh perspectives, contexts, and claims. But this division breaks down when we consider how quantitative information is used in public life. Graphs, charts, rankings, and statistics shape arguments about policy, economics, education, and justice. These representations carry the authority of mathematics while serving rhetorical purposes in ways that demand interpretation. If we teach students how to read and construct graphs but not how to interrogate them, we have only taught half the discipline.
The Myth of Neutral Numbers
There is a persistent belief among students and educators alike that numbers are inherently objective. “Numbers don’t lie” is often invoked as a shield against critique. Yet quantitative reasoning has historically been used to justify deeply flawed, oppressive, and harmful ideas. Pseudoscientific practices such as eugenics and phrenology relied heavily on measurement, classification, and statistical language to present social hierarchies as natural and inevitable. Their persuasive power depended not only on the claims themselves but on the perceived neutrality of the mathematical tools used to present them.
In contexts where numerical literacy is limited, the persuasive effect is amplified. When audiences are not equipped to question how data is gathered, represented, or framed, they are more likely to accept conclusions uncritically. The issue, therefore, is not whether the numbers themselves are “true,” but what viewers are urged to conclude from them. This distinction is crucial for both mathematics and social studies classrooms. It shifts the focus from accuracy alone to interpretation.
Why Graphs Matter
Graphs are particularly powerful tools for this kind of interdisciplinary work. They translate complex numerical information into visual form, allowing patterns and trends to emerge clearly. In a media environment dominated by images, headlines, and short-form content, graphs and charts often function as stand-alone arguments. A viewer may spend only a few seconds glancing at one before forming a conclusion.
This speed is precisely what makes graphs so potentially misleading. It is important to note that “misleading” does not mean “false.” A graph can accurately represent data while still encouraging interpretations that go beyond, or even contradict, the evidence. The “leading” in a misleading graph comes not from the data itself but from the choices made in its presentation including scale, labeling, comparison groups, visual emphasis, and omission.
Teaching students to recognize these choices is an essential component of both mathematical and civic thinking. New York State Next Generation Learning Standards in both mathematics and social studies call for students to analyze data, evaluate sources, and make evidence-based claims. Critically interpreting graphs sits squarely at the intersection of these expectations.
Seeing the Same Data Differently
One of the most effective ways to provide an entry point for this work is to present students with two graphs that display the same data in different ways (Figure 1). At first glance, students often assume that these wildly different visuals must reflect different datasets. When they discover that the underlying numbers are identical, it creates a productive moment of confusion and dissonance.
The two line graphs represent the same trend over time. In the left one, the vertical axis is truncated, which has the effect of exaggerating small changes. In the other, the axis begins at zero, making those same changes appear minimal. Technically, neither graph is “wrong.” Both accurately plot the data points. Note that in the exaggerated graph (left), the y-axis jumps from 0 to 6.9, but there is also a clearly visible break in the axis, properly indicating that part of the axis is not to scale. The break is indicated by the small zigzag line at the bottom. Yet they invite very different interpretations.
Figure 1 Source: Reconstructed from Identifying Misleading Graphs. Konst Math.
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Rather than immediately explaining the discrepancy, teachers may pose a series of questions:
- What claim might each graph support?
- What differences do you notice in how the data is displayed?
- Why might someone choose to present the data this way?
- What conclusions would go beyond what the data can actually support?
Students often begin by focusing on surface features (“This one goes up more”), but with guidance, they can move toward more sophisticated observations about scale, proportion, and visual emphasis. A common misconception is that if a graph is technically correct, it is also fair or neutral. This activity helps disrupt that assumption. The goal is not necessarily to accuse a creator of deception, but to analyze how representation shapes interpretation.
When Design Implies Argument
 | Figure 2 Source: The Society Pages In other examples, the persuasive elements of a graph become even more apparent. Figure 2 shows a famously misleading and widely circulated news graphic from several years ago depicting trends before and after Florida’s “Stand Your Ground” law was enacted. The graph includes dramatic shading and highlights a specific point in time, drawing the viewer’s attention and suggesting a causal relationship. At a glance, the message feels clear: gun deaths decreased because of this policy. Yet a closer and more critical look reveals that the y-axis is labeled in the opposite direction from established convention. Again, this graph is properly labeled, and there is nothing mathematically incorrect about it. But creating an axis that increases in the downward direction seems like an intentional effort to mislead viewers. |
Furthermore, the shading, while seemingly a design choice, functions rhetorically by guiding the viewer’s eye away from the deceptive y-axis, and towards the stark drop off after 2005. If this graph were conventionally constructed, it would show a sharp upward spike after that year.
Students often struggle here with this misconception; they assume that critique requires identifying an error. When no calculation is wrong, they may conclude there is nothing to question. This is an opportunity to expand their understanding of critique. The issue is not whether the graph is accurate, but whether the conclusions it suggests are warranted. Framing questions like the following can help students move beyond correctness toward reasoning:
- What is this graph encouraging us to believe?
- What evidence would we need to support that claim?
- Who designed this graph and why?
What’s Missing Matters
Another powerful example of misleading involves comparisons that appear straightforward but rest on incompatible measures. Figure 3 shows a graph that compares the cost of a college degree with annual earnings after graduation. Presented this way, the figure suggests that the cost drastically outweighs the benefit.
 | Figure 3 Source: The Atlantic Students should be prompted to ask: Are these quantities measured over the same time frame?What happens if we consider earnings over a lifetime rather than a single year?What alternative scenarios should be included for comparison?Which quantities here occur once and which are repeated? |
This last question gets to the central issue with this graph. The cost of a bachelor’s degree has indeed gone up in some cases by nearly 100%. However, this one-time cost is being compared to an annual salary, which not only repeats every year, but also increases for the earner over time. Equally important is attending to what is omitted. If a graph argues that college is not “worth it,” what is the implied alternative? What are the earnings for individuals without a degree? What would a graph directly comparing salaries of people with and without a degree look like? What about in varied geographical areas? What other factors, like job stability, benefits, career mobility, might matter but are not represented? In both mathematics and social studies, absence is as important as presence. What is not shown can shape conclusions just as powerfully as what is. Students must be taught to courageously interrogate absences in visual representations so that their conclusions are shaped by well-contextualized facts and not a creator’s agenda.
Questioning Rankings
Ranking charts provide another rich context for critical analysis. Lists of “top” education systems, happiest countries, or most livable cities circulate widely and are often treated as objective measurements. Yet these rankings are constructed through a series of decisions: which variables to include, how to weight them, and how to aggregate results. Presenting students with two different rankings of the same phenomenon produced by different organizations, can prompt important questions:
- Who created this ranking?
- What criteria were used?
- Why might those criteria have been chosen?
- How might different choices lead to different results?
Students may initially look for which ranking is “correct.” Redirecting them to consider how each ranking reflects particular values or priorities helps shift the conversation. These are not naturally occurring facts; they are constructed representations. This kind of inquiry aligns closely with social studies practices of sourcing and contextualization, while also reinforcing mathematical ideas about measurement, weighting, and aggregation.
Teaching Students to Be Critical Thinkers
Ultimately, the goal of this work is not to turn students into the type skeptics who reject all data, but into thoughtful interpreters who engage with evidence responsibly. This skill requires explicit instruction. We cannot assume that students will naturally develop these skills simply by working with graphs in procedural ways. One way to “wake students up” to how easy it is for graphs to be misleading is to assign them to create a graph that intentionally misleads. This type of task is inspired by the classic 1954 book, How to Lie with Statistics. Author Darrell Huff opined, “The crooks already know these tricks; honest men must learn them in self-defense” (Huff, 1954).
An example task might include giving students a set of numerical data and a point of view that their graph or chart must suggest. Their first attempt at visually representing the data might not align with that point of view, so they should brainstorm ways of contorting the representation while still keeping it mathematically sound so that it implies a different conclusion. Like Huff suggests, once students experience how easy it is to make a representation of data say something very different from what they initially thought, they will be more appropriately equipped to see it when other creators do it.
This practice cultivates several important habits of mind like wondering what a representation is designed to show and what it may obscure, asking who created it and for what purpose, distinguishing between what the data shows and what is being claimed, and recognizing that evidence has limits and that conclusions require justification. These habits support not only mathematical proficiency but also civic participation. In a democratic society, citizens are routinely asked to interpret data in order to make decisions about policy, voting, and public discourse. The ability to engage with that data critically is essential.
Courage in the Classroom
Baldwin’s call for courage in education is not limited to particular subjects. In the mathematics classroom, courage can take the form of resisting the comfort of neat answers and instead engaging with ambiguity, interpretation, and critique. It means acknowledging that even in a discipline grounded in logic, representations and conclusions can mislead. When we invite students to question graphs and consider alternative interpretations, we are not undermining mathematics, we are deepening it. We are showing students that mathematics is not just a set of procedures but a way of reasoning.
In a world of charts, headlines, TikTok reels, and YouTube shorts, this may be one of the most important lessons we can offer: every representation is created for an audience, for a purpose. The question students should carry with them is not simply “What does this show?” but “What is this trying to make me think, and why?” Helping students learn to ask that question, again and again, is both a mathematical responsibility and a civic one.
References
Baldwin, J. (1963). A talk to teachers. In The price of the ticket: Collected nonfiction 1948-1985. St. Martin’s Press.
Huff, D. (1954). How to lie with statistics. W. W. Norton & Company.
Konst, B. (n.d.). Identifying misleading graphs [Video]. YouTube. https://www.youtube.com/watch?v=ETbc8GIhfHo
The Society Pages. (2014). How to lie with statistics: Stand your ground and gun deaths. Sociological Images. https://thesocietypages.org/socimages/2014/12/28/how-to-lie-with-statistics-stand-your-ground-and-gun-deaths/
Thompson, D. (2012). Hey, everyone, don’t fall for this misleading graph about college costs. The Atlantic. https://www.theatlantic.com/business/archive/2012/06/hey-everyone-dont-fall-for-this-misleading-graph-about-college-costs/258299/
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