# The Pitfalls of Thinking Too Mathematically About Education

Joining us this week is guest blogger Alex Baron. Alex currently teaches high-school geometry and algebra, while also serving as program director at the Urban Leaders Fellowship. He has previously done research on cultural differences in pedagogy and taught pre-K and kindergarten for KIPP.

As a math teacher, I often feel like I run a basketball camp for 137 teens who despise dribbling, passing, and shooting. Throughout their education, students have had countless thorny math experiences that have accreted into a throbbingly painful mass. My hope is to dismantle that unsavory accretion and transform it into something that the students will, well, savor.

Let's just say it's a work in progress.

One reason students dislike math is that there's often a "right answer." Where there are right answers, there lurk wrong answers. Most people don't enjoy being wrong, hence the difficulty of selling math to students (and most everyone else).

Whereas math features correct answers, the complexities of life usually don't. In this post, I assert that we are too often looking for singular "right answers" in education. Although the education world lacks mathematical precision, we approach policy as if it did. Let's start the discussion with some algebra.

One foundational algebraic concept is that of functions (e.g., y = 2x + 700). A function describes a relationship between two things. For example, if Rick writes a book with a \$700 advance plus two dollars for each copy sold, then the function is y = 2x + 700, where y represents his total earnings and x represents the number of books sold.

The inviolable rule of functions is that each input can only correspond to one output. If Rick sells 10 books but could end up earning \$720 or \$738 or \$52, then the function breaks down—as in nascent romance, functions are all about defining the relationship, and defining it very clearly.

I bring up functions because their fundamental rule (i.e., each input corresponds to only one possible output) highlights the underlying flaw in our thinking about education. Most of us would likely maintain that every child has unique characteristics, skills, and needs. An input that works for one student may lead to a totally different outcome with another, and we celebrate that as a feature of students' individuality.

However, in schools, district offices, and statehouses, we often craft education policy in a strikingly function-based fashion. Specifically, we scour the planet for "evidence-based best practices" (e.g., child-centered learning, phonics instruction, project-based learning), as though the input were going to correspond to a singular output for all students.

Given that educational research, like nearly all social science research, is based on average effects, research can only tell us that some interventions might work in the "average" context for the "average child," who most of us would posit does not exist. Consequently, we are fairly lost when it comes to knowing how we should proceed with education policy.

Tolkien wrote that "not all those who wander are lost." That may be true, but in education policy, the converse also seems true: Not all those who are lost wander. Although most of us acknowledge the lack of a single path forward that will work for all—that is, we'll always be "lost" because there isn't a singular way to educate the infinitude of student needs—we don't seem to be open-mindedly wandering.

Instead, we often find some approach that seemed to work somewhere and try to scale it far and wide (e.g., replicating a teacher's practice throughout her school, expanding a curriculum from one school to other schools, trying to determine Finland's secret sauce in order to imitate it worldwide). In this context, the term "scale" comes from geometry; it means that we would reduce or enlarge a figure by proportional dimensions. The figure's shape stays exactly the same; only the size changes. For example, to scale the lower-case letter "o," we can capitalize it to "O."

However, when trying to scale something in education, the intervention's shape changes. For example, if we imagine "o" as an intervention to be scaled, then another teacher's implementation may resemble the number "0" instead of the capital letter "O." The two outcomes look similar in many respects, but they have different meanings and effects on those who encounter them.

In education, to implement an intervention is necessarily to modify it. A teacher's personality, attitude, and other qualities deeply affect how an intervention is rolled out to students, whose own limitless diversity also reciprocally changes the intervention. Obviously, the same is true for the diversity of school contexts.

By contrast, when different doctors in different hospitals prescribe the same drug to different patients, the chemical composition of the drug does not change—the dosage may vary across people, but the drug itself remains constant. The personality of a doctor has no effect on the drug's interaction with a patient's biology; conversely, a teacher's attitude and pedagogical philosophy profoundly affect the intervention itself. We can't simply scale "it" because the "it" is always changing in every educational context.

In sum, given the multifarious nature of students, teachers, and school contexts, it seems clear that no single prescription would work for all, or even most, students. However, policymakers proceed with "research-based" inputs as if they would work for everyone, even though this contravenes our foundational sense that no two students are the same.

Instead, it would seem best for us to do more open-minded exploring—to exercise the same humble curiosity we seek from students, even if the path itself occasionally feels tortuous and torturous. We may always feel a bit lost, but hopefully some thoughtful wandering will get us closer to where we, and our students, want to be.

Alex Baron

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