The introduction to this site suggests that many people are beginning to question the value of mathematics.  This page provides supporting evidence to that claim in the form of links to articles and blogs challenging math education.  Of course, I can’t help but respond to these suggestions.

Is Algebra Necessary by Andrew Hacker

The article begins with a discussion on the difficulty of algebra and how it is part of the reason many students do not complete high school or college programs.  This is used as a reason to drop algebra as a requirement.  I do not agree with this suggestion.  When students fail to meet a certain bar, the first instinct shouldn’t be to drop the bar.  I fear that this is the common trend in modern education.  No child will be left behind if we lower the standards enough.

Andrew Hacker argues that the typical algebra curriculum is not ideal for all students.  I agree.  To use Dr. Lewis’s analogy, algebra and arithmetic are the scaffolding of mathematics.  You wouldn’t hire a construction company to build just the scaffolding if you had no intentions of completing the building.  In the same way, it doesn’t make sense to have students end their math education on topics like solving quadratic equations.  Algebra is an awful last course in mathematics.  A course that tries share the true essence of mathematics and focuses on logic and problem solving would be far more valuable.

Why do we teach algebra?  The problem is that students do not necessarily know what they will do with their lives when they are 12.  Many careers do use algebra.  We wouldn’t want an 18-year-old who decides he’s going to be a financial engineer to have to go back and complete 4 years of high-school math before he can begin a college program.

High schools and colleges should strive to find an appropriate balance in their math curriculum between providing the tools most appropriate for students to continue upward into more advanced mathematics courses and polishing students’ ability to reason quantitatively.

Wrong Answer: The case against Algebra II by Nicholson Baker

On the second page, Baker discusses a problem that appears in an Algebra 2 text book, “Another [problem] is about a basketball player who has made 21 of her last 30 free throws, an average of 70 percent: ‘How many more consecutive free throws does she need to raise her free throw percentage to 75%?’  How very odd, you think: I don’t have to know any algebra at all in order to figure out that the answer to this free-throw question is 6.”

Baker’s reaction to the problem is at the heart of the issue with algebra education.  Baker sees the book’s algebraic approach to the problem, one with symbols (like x) and equations, as distinct from the thought process he used to arrive at the answer.

Actually, the two are the same.  Baker was doing algebra to arrive at the answer.  Those mysterious markings on the pages of the math book are a symbolic representation of what he’s thinking.

Consider the following math question.  Bobby and Billy are each holding the same number of lollipops.  Together they have 10 lollipops.  How many lollipops is each boy holding?  If you posed this question to kindergartners, you’d likely get a couple correct answers, and the students would respond with smiles on their faces.

In contrast, when some high school or college students see 2x=10, they begin to perspire, their hearts start racing, they get nauseous, and they’d willingly trade their current predicament for a seat in a dentist’s chair.

Baker contends that many students simply can’t do algebra.  I contend that many of those students can.  They can answer the basketball question.  They just don’t realize that’s algebra.

Something goes wrong in our educational system when we start to abstract with symbolic notation.  I suspect that not enough time is spent on that transition.  Without the proper understanding of what these symbols represent, students quickly resort to memorizing tricks and algorithms to “get by” in their math courses.  Over time, this catches up with students, and these students find themselves failing high school and college Algebra 2 courses.

When a student incorrectly solves 2x=10 by subtracting 2 from both sides, I will go back and ask them the lollipop question.  10 times out of 10, the student gets the lollipop question right.  Why then did they subtract 2 instead of dividing in this situation?  They thought they remembered seeing a similar thing done when faced with a similar question in the past.

The students are capable of doing the algebra.  Our educational system has confused them.

The rest of Baker’s article follows an argument that approximately goes like this.  Algebra is solving rational equations (or similar) through dry symbolic manipulations.  You memorize things like the quadratic formula and then plug and chug until you’ve worn your pencil down to a stub, and then repeat.

Baker and I agree that this is an awful course.  Forcing students through these activities is cruel and provides almost no value to most.

Baker concludes that since this is math, students shouldn’t take math.

I conclude that this is not mathematics.  I suggest students should take math instead.