Algebra Necessary for Innovative Thinking

Andrew Hacker, emeritus professor of political science at Queens College, City University of New York, gave his take on algebra education in a New York Times opinion piece in July. He argued for its elimination, claiming that algebra isn’t necessary for students’ future success. Even those who have advanced degrees in STEM subjects are unable to find jobs – the unemployment rates for those with engineering and computer science degrees are 7.5% and 8.2%, respectively – which must mean that too many people know too much math and science…right?

This post is in response to the radical idea that algebra should be omitted from the national curriculum. Okay, so there is an ~8% unemployment rate among those with advanced STEM degrees. This doesn’t necessarily mean there are too many engineers and our society can’t utilize people with these skill sets. Rather, innovation is growing at a slower rate than the number of people with STEM skill sets. Why? Not because we don’t have enough engineers or computer scientists, as the author pointed out with his unemployment figures, but because we don’t have enough people that can think mathematically. We have no shortage of people at the top end. But we need a lot more people with innovative thinking skills. Innovative, mathematical thinkers are the ones who can take society in new directions and in doing so create more jobs requiring more advanced skill sets (e.g. engineering, computer science). THIS is why we need to teach mathematics, and algebra in particular. But we need to teach them the right way.

This leads to two questions we must address. First of all, why do we need a focus on algebra? Students struggle the most with algebra because it is the beautiful albeit difficult art of transcending from numbers to variables. Algebra enables students to recognize and understand patterns of numbers, to put it simply. Second of all, what is the “right way”? There is not one simple answer to this question. Most agree that the “right way” is NOT rote memorization and formulaic, mechanical processing. Instead, students should be able to see mathematical concepts from multiple perspectives and use these perspectives to form their own meaning. Dr. Hacker says, “Making mathematics mandatory prevents us from discovering and developing young talent,” Well, yes and no. It depends on the way math is taught. When math is taught in a way that empowers students to think outside the box, we actually foster new talent.

Let me delve into a specific problem I see with the way math is taught. Currently, classes are classified and organized into categories – algebra, geometry, trigonometry, Calculus, etc. – and each takes place a different year. This leads students to believe that each “type” of math is unrelated, when in fact they are incredibly integrated. Separating them would be like separating all the many fantastic and beautiful colors of the world into the primary colors yellow, blue, and red. Just as we have varieties of proportions of primary colors that create the spectrum we see every day, varieties of mathematical methods are used together to analyze our many questions about the world. Algebra is not a solitary subject in relation to statistics, geometry, etc., and we can’t simply get rid of algebra without also eliminating aspects of these other methods of mathematical reasoning.

I agree with Dr. Hacker that we should reduce rather than expand the amount of math students learn. But that doesn’t mean eliminate algebra. In fact, I think algebra is one of the most important methods of mathematical reasoning. We need more algebra and less of certain other things, like long division. (Dr. Hacker says students should learn long division whether they like it or not, but I disagree since for the most part long division is a mechanical process. Instead, students should clearly understand the concept and use of division in general. Why memorize a formulaic process when technology can do it in the blink of an eye? But we can’t use technology as a tool without understanding the point of what we’re calculating. I also think quadratic equations are quite fundamental, which Dr. Hacker considers a “misuse” of teacher talent and student effort.)

I also agree with Dr. Hacker that mathematics should be more applicable to the real world. Statistics is one subject that has too weak an emphasis in classrooms, and I like his ideas for using it to understand societal constructs like the Consumer Price Index. But thinking algebraically is an integral part of thinking mathematically, and this is essential not only for student understanding of real-world phenomena, but the ability to advance these phenomena via innovative thinking.

Read other responses to Hacker’s article:

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