Math Isn't the Problem, the Way It's Taught Is

Here's an interesting study by some Alabama college professors that claims the typical math sequence of American high schools isn't meeting students' needs. Their conclusion is that most kids need less algebra, trig, and calculus, but more statistics and data analysis.

I agree, and have said for years, that Statistics is probably the "math" class we teach in high school that is most useful to most students for their future. But I don't think the problem is the typical math sequence in high school.

Our problem is we (the math education professional community) have largely lost sight of WHY the math sequence is what it is. It was never implemented because everyone needs to know the sine of 30 degrees, or because everyone needs to know the quadratic formula, or that everyone needs to know the end behavior of a polynomial function.

The reason for the sequence is to grow and train PROBLEM SOLVERS. Taught correctly, the math conventional math sequence from 1st grade to Calculus builds on itself. What you learn today, you're supposed to apply tomorrow. The reason each course is a prerequisite for the next is because students NEED TO KNOW the content from the prerequisite to succeed in the course that follows. Taught correctly, the sequence teaches kids to use what they know to find solutions to problems they've not previously faced!

I tell my students all the time that PROBLEM SOLVING is the goal! It's what ALL math courses and teachers should be developing.

The study correctly recognizes that standards for most high school math courses are bloated with too many topics for teachers to dive deeply into the content. So many topics force teachers into a sort of race to cover everything, instead of develop everything from previously learned content. That leads to most students memorizing new content instead of constructing it from what they already know. This process has completely derailed the original intent of the heavy focus on math in K-12 curricula.

Mathematics is not knowing things. Mathematics is a process to develop knowledge. Mathematics isn't memorizing a bunch of different formulas, but the process of discovering those formulas from previous discoveries.

Along the way, students use some of these formulas and processes so often they can't help but remember them. But memorizing isn't the goal, because IF YOU UNDERSTAND HOW THEY WERE DEVELOPED, you can develop them again.

Our entire K-12 math curriculum can be constructed on an understanding of the real number system as an infinite ordered set and a handful of geometric assumptions. Somewhere along the way, we decided these basic foundational elements of all of mathematics aren't needed by our students. We passed students on to the next course or the next level without understanding them. We put technology in their hands and said this will do what you need to do. No need to understand there are an infinite number of real numbers between 0 and 1. No need to understand that all numbers aren't whole numbers. No need to understand that infinity is not a number but a concept that there is no largest real number. No need to understand that multiplication is just repeated addition or that a fraction is just one number divided by another.

The result?

Kids have for decades now resorted to memorizing STUFF long enough to take a test, but never understanding the foundational concepts upon which all that stuff was built.

In short, the mathematics sequence is not the problem. It's the way we teach the sequence. It's the way we assess the sequence. It's the way we move students from one level of the sequence to another even when they didn't get what they needed from the previous level to understand the next.

It would be better reteach addition to a second grader who didn't understand it as a first grader than to move on to subtraction with that kid before he understands addition. It would be better to reteach multiplication than to move on to division before a kid understands multiplication. How can a student understand how to reduce radicals if he doesn't even understand what the square root of 2 is? How can a student understand how to solve a quadratic equation if he can't solve a linear equation? I can carry this all the way through integration and derivatives in calculus, all the way through the entire sequence.

The math we teach isn't the problem. The way we teach the math, and the way we don't require students to really understand even the most basic foundational ideas that underlie the entire curriculum. That's the problem.

Our students would be better off graduating with Geometry as their highest level of math completed if that's the highest level they could understand. They'd be better off if Algebra I was as high as they reach if that's as high as they can understand. Even pre-Algebra, if that's the highest level they can understand, then so be it. But let's keep teaching until they learn, and stop just pushing them up to higher levels when they couldn't comprehend the lower level.

Let's not get rid of the math. Let's get back to teaching the math correctly.