School Mathematics

To me, it seems as though our school system is of two minds.

On the one hand, we seek to prepare our youth to have a facility of mathematics. It has been shown that mathematical literacy is a necessity in industry, in finance, and in business. In an economy that finds itself more and more technological, mathematical literacy has become more and more essential. Therefore, it behooves our society to produce workers with increasing facilities of mathematics. To do this, we must discover how people learn best, develop methodologies which will enable us to implement these discoveries, and use them in the classroom to increase facility of mathematics.

On the other hand, the teaching of mathematics is seen by most as synonymous with traditional teaching styles: teacher-centric classrooms that employ the banking method of teaching and learning, memorization, and drill-and-kill homework assignments. There are other teaching methods, true, but those styles are “ineffective”: They produce students who are over-reliant on technologies; these students are button-pushers, not thinkers. They lack the facility of basic skills required of students of mathematics.

The great irony, here, is self-evident: That in a system that wishes to see its students succeed, both sides work against each other, allowing for the inevitable failure of our students. To me, this is why when so many math students enter college—no matter their ethnicity—they find themselves unprepared.

In order to cease the continual failure of our students, changes need to be made. Traditionalists, of course, would deny that the system needs amelioration: After all, not all students are math students. I refute this belief. We no longer live in a world where the least the students must do is read contracts and sign their names. Students must do more. They must be able to compute, negotiate math texts (graphs, equations, spreadsheets), and problem-solve. They must be able to analyze a situation, model it abstractly, use critical thinking to determine a solution, and then determine if that solution has applications in reality. To me, the notion that all students are not math students is antiquated: just as all students are readers and writers, so are all students math students.

Given this notion that all students are math students, I feel that the teaching of math needs to change, not only in high school, but especially in college. But let me be clear just as to what I mean. I am not arguing for an integrated approach to mathematics: I like the Algebra/Geometry/Algebra II course progression, even though I feel that each is at best a misnomer of a three-part high school mathematics sequence. I am, instead, arguing for a revision in approach. I am asking that teaching be more dynamic, less the static instance of teaching found in the college lecture hall.

Allow me to embellish this point: During our NSF group projects, some of my team members felt that the ARISE curriculum would not adequately prepare students for college mathematics in that the curriculum was student-centric. They argued that college mathematics is a singular, non-collective activity. It is all lecture, study, problem sets, and test. There is no group-function. And as such, ARISE would not prepare students for the passivity of college mathematics.

Let me reiterate: “ARISE would not prepare students for the passivity of college mathematics.” The passivity of college mathematics—Is this truly the goal of college mathematics? No. College mathematics aims to develop thinkers—thinkers—who will become captains of industry and pioneers working at the frontiers of mathematics. And yet, how can this aim truly be met if its students are docile, quiet, and passive?

Another problem is inherent: Our society needs not only thinkers, but creativity. It requires vibrant creators of thought who can analyze a problem, interact with others in a group capacity, and together synthesize new and different solutions. But if all thinking is taught using one, uniform and singular methodology—a methodology understood by only by those who think in said way—can originality truly develop? And further, if learning is developed alone—and not collectively—how can we expect our thinkers to work together to further the development of ideas once graduated from college mathematics? Truly, if all these aims are to be met, college mathematics must broaden its approach beyond that of the lecture hall.

At the same time, school mathematics must not be ignored. Unlike college mathematics, there have been efforts to reform it. There needs to be more. If college mathematics’s aim is to produce thinkers, school mathematics’s goals should be similar. Clearly, it needs to develop skills and procedures so that when students reach college, they are second nature. But it needs to do so much more. Skills and procedures are nice, but they mean nothing without context. It is like much like Plato’s metaphorical cave. Teaching skills and procedures are like looking at shadows on a cave wall—they mean nothing without a context. School mathematics should provide that context. It should make the math real.

And maybe if it were real, more students would understand it. Or try to.