Truly learning math makes wise thinkers
The question that educators and legislators in Texas should be discussing right now is not whether high school students should be required to take two years of algebra. This is an excellent example of investing time, money and effort to thoughtfully and carefully answer the wrong question.
The right questions for all of us are: What positive and profound lifelong habits of effective thinking are we offering within all of our math classes? And if the content of the algebra curriculum will be quickly forgotten after the last required exam (or even before), then why bother to offer any algebra?
Currently, too many of our math classes — as well as other classes — focus on mindless memorization and repetition that is designed to game a system focused on scores on standardized tests that measure the ability to perform a certain act — an act that requires neither deep understanding of the content nor the necessity to make meaning of the material. Like magic, the moment the final exam is over, poof, the material is forgotten and magically disappears. Think it’s a joke? Math educators know otherwise. The overlap in middle school algebra, Algebra I and Algebra II is conservatively around 60 percent, and more realistically around 75 percent. Our curriculum acknowledges its ineffectiveness at inviting students to make meaning of algebra: Those who study algebra in school are doomed to repeat it.
We need to replace our current math classes with meaningful mathematical experiences that teach students how to think through math rather than simply memorize formulas about math.
By thinking through math, I mean understanding the material in a very deep way so that the student can appreciate and (ideally) discover connections between seemingly disparate ideas. Discovering relationships and patterns is not only at the heart of mathematical discovery but also the requisite trait to innovate and create in any space — from big business to the fine arts, from sports to technology, from politics to education.
In mathematics, we need to delve deep into the simplest of ideas until we see how complex they truly are. Only then can we pull back and see the bigger picture more clearly. One of the greatest triumphs of the human mind is that, by intent, we can take our current understanding and challenge ourselves to understand that much deeper—and, of course, that’s at the very core of education. These habits of the mind are what we need to be instilling in our students to enable them to become wise and creative leaders in an ever-changing, multifaceted world.
Algebra provides a perfect example of this. Calculus is one of the most beautiful constructs of humankind (of course, as a mathematician, I’m slightly biased). However, the whole subject revolves around just two basic ideas. So why do masses of students every year struggle with and eventually give up on calculus? The answer is because they never made meaning of the basic ideas of algebra. Even after manipulating the same equations for years in algebra, those students never were exposed to a curriculum that invited them to think through those equations and make them sing in their minds. In my nearly 4,000 online math videos, I have attempted to make those ideas meaningful and, ideally, intuitive.
This point can be applied to other subjects as well. In music classes, for example, students can simply memorize the finger movements in a piece. Or they could learn to hear each note and understand the structure of the piece. In history classes, students can memorize basic facts about the Civil War such as the names of the generals. Or they could try to understand the background, competing forces and evolving social values that ignited the conflict.
When teachers give assignments, they should always be asking themselves “What permanent benefit — what habit of thinking — will students get out of this exercise?” Teachers should craft assignments that promote long-term goals such as understanding deeply, learning from mistakes, asking probing questions, and seeing the flow of ideas. In other words, instilling lifelong habits of effective thinking.
Sure, I would be happy to see more students become math majors in college. But it is even more important to me that they learn to become wise, original and creative thinkers. Math classes should not offer a mindless checklist of mechanics, most of which will never be applied directly to students’ lives. Rather, all classes should be an opportunity for students to develop habits of living and thinking that empower them to probe deep, uncover structure and connections, make meaning and discovery, and realize that with enough effort and perseverance, whatever they put their minds to can be understood with a little more clarity and focus.
Edward Burger is president of Southwestern University and an award-winning professor of mathematics. His latest book is “The Five Elements of Effective Thinking,” which he co-authored with Michael Starbird from the University of Texas at Austin.