The Pitfalls of Teaching Math: Rules Without Intuition
When people hear that I enjoy math, they cringe, usually responding with an anecdote about how it was their least favorite subject in school. One time in high school, my friend sat next to me while I did a calculus project. Upon seeing the assignment, she remarked that it “looked like the most miserable thing in the world.”
The sentiment surrounding math is clear: people hate it, and it’s easy to understand why. While not all, most people dislike math because they find it difficult and lacking application. The way math is taught today portrays it as a discipline of memorization without any reasoning behind these processes. This issue of student disengagement has posed a significant problem to educators today as they grapple with how to increase student interest–and competence–in math. To do this, educators should place greater emphasis on the intuition that underpins mathematical concepts.
In schools today, humanities are taught with an inherent logic and relevance. In history, past events have a cause-and-effect relationship with later developments. In literature, textual themes are closely related to human experiences. In math, concepts are too often taught as “this is how things are”–you use this equation at this time, and that equation at that time.
When students can make intuitive sense of what they are being taught, they understand it better. When students are taught about the American Civil War, the focus is on why it happened: slavery, regional factionalism, and so forth. When students are taught trigonometry, the focus is on what to do and when to do it–never why. The lack of emphasis on reasoning treats students as computers, programmed to run a series of meaningless commands. This is opposed to equipping them with (more productive) mathematical problem-solving tools that make practical sense and apply more clearly to the world around them. This lack of intuition makes math more difficult to understand, fostering antipathy for the subject.
Difficulty in understanding also undermines the confidence of students in the subject, in turn undermining performance. When student confidence is low, they often resign into simply accepting they do not understand the subject. When I ask why people do not like math, the answer is often some variation of “I am not a math person,” indicating that they, somewhere during their studies, concluded they were not designed for it. In math, where every unit builds on the next, foundations decide your success, so when students decide they simply “don’t get” math, any learning in the future will be adversely impacted.
The lack of logic also makes math appear abstract and aloof. It is a common joke among students who are not mathematically inclined that math is “made up” and that its rules were arbitrarily decided by “random people.” Viral memes lampoon math education, joking about how “people do not use y = mx + b in life.” While made in jest, these comments reveal how many people see math as irrelevant balderdash–something you need to bear for a degree. Sentiments like these arise when math is taught a series of rules to memorize without any true reasoning behind them. A common area I help students in is logarithms which I like to first explain as a tool used to manipulate exponential equations to make them easier to understand. I do this so students understand logarithms as having a clear purpose rather than as mysterious figures in their equations. This is in contrast to most classrooms where logarithmic properties are listed out in the fashion of “these are the rules,” and it is left to the students to make sense of them.
To remedy this, the pedagogical approach to math must change to emphasize practicality. In my experience, confusion in math arises when students do not know how to approach problems because they do not understand the logic behind the different problem-solving techniques they are taught. After explaining concepts practically, students often demonstrate a greater understanding, as this turns math into a problem-solving discipline it should be rather than the field of rote memorization it is taught as. The human mind best understands concepts when presented logically, and to repair math’s reputation, educators should ensure students understand the intuition behind the math they study.
The added benefit of ensuring students understand the rationale behind mathematical concepts is that it trains their brains to understand the world and approach problems in different ways. Math is embedded in everything we do, and understanding math means understanding the world better. Take, for example, the Law School Admissions. While one would assume that pre-law students are this test’s top performers, math-related majors (math, physics, economics, and engineering) score highest–even though the LSAT is a reasoning test with no traditional math section. Math is incredibly useful, even to those who will never need more than basic arithmetic in their daily lives. The brain is a muscle, and math is a powerful exercise that expands one’s ability to understand the world at large in a different (and improved) way.
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Louis Gleason is a student at Boston College working toward a bachelor’s in economics and math in 2023. Louis specializes in math, physics, and history. Outside of academics, Louis enjoys skiing and journalism and is heavily involved in nationally competitive debate.