JUDY WOODRUFF: Now a look at how required math classes may factor into the academic success or failure of high school and college students.

Hari Sreenivasan has the story as part of our weekly education series, Making the Grade.

ANDREW HACKER, Author, "The Math Myth": Words and numbers, we use them both. We use them for different reasons.

HARI SREENIVASAN: Even if you aren't going to be an engineer, getting through high school or college means getting through math.

MICHAEL GENAO, Student, Queens College: Why do we need to take all these math classes? It's not necessary. It's not needed for what we are actually learning.

HARI SREENIVASAN: Andrew Hacker, the college professor teaching at the front of this classroom at New York's Queens College, agrees.

ANDREW HACKER: The goal is to have everybody do a full menu of mathematics, up to and including calculus.

And I don't see any rational reason for this at all. What I'm suggesting is that at least there should be other options, alternatives, instead of this rigid math curriculum for everyone.

HARI SREENIVASAN: Minimum requirements for math are different across the country, but many states today demand getting through the quadratic equations and two years of algebra to graduate high school, and most college degrees also require some math credits.

Hacker writes about this perceived disconnect between academic requirements and the everyday needs of graduates in his recent book, "The Math Myth."

ANDREW HACKER: It's actually several myths. One of the myths is that every one of us is going to have to know algebra, geometry, trigonometry in the 21st century, because that's the way a high-tech age is going.

It's a total myth. At most, 5 percent of people really use math, advanced math, in their work.

HARI SREENIVASAN: You're also drawing a distinction in your book between mathematics and arithmetic. Explain that.

ANDREW HACKER: Yes.

We use math, the term, indiscriminately. I think we teach arithmetic really very well up through grades, let's say, five or six. We do it. But then, instead of continuing with arithmetic to what I would call adult arithmetic, or sophisticated arithmetic, we immediately plunge people into geometry and algebra.

And, as a result, Americans are really quite illiterate in terms of numbers.

HARI SREENIVASAN: Hacker's alternative? Teaching what he calls numeracy.

ANDREW HACKER: It's income per hour, essentially, per person. Is Norway well ahead of the United States? OK. Let's continue with that.

HARI SREENIVASAN: Where he focuses on developing his students' mathematical literacy by giving them some real-world perspective on the subject.

ANDREW HACKER: How to read a corporate report, how to look at the federal budget, how to parse the numbers on the campaign trail, how votes are cast, and how many seats are won, all sorts of assignments like this, which only require arithmetic, but adult arithmetic.

HARI SREENIVASAN: A political scientist by training, Hacker and his assertions have predictably put college and high school math departments across the country on the defensive.

DIANE BRIARS, President, National Council of Teachers of Mathematics: We need algebra as a basic way of making sense of our world. Many mathematical relationships are described using algebra.

HARI SREENIVASAN: Diane Briars is president of the National Council of Teachers of Mathematics. We chatted with her on nearly her home turf, the National Museum of Mathematics in Manhattan.

DIANE BRIARS: Algebra gives us a way of representing relationships in general, so that we can reason about them in the general case, instead of specific cases. Algebraic equations and expressions are also ways of describing patterns that we may see and differences between those patterns.

ANDREW HACKER: This is put about by the mathematicians. I think they have to say this: Mathematics trains the mind.

There's no evidence for this whatever. Mathematics trains the mind for mathematics.

HARI SREENIVASAN: Hacker thinks math is a powerful divider of high school success. A number of students succeed and move onward, while a sizable fraction do not.

ANDREW HACKER: One out of every five of our citizens has not finished high school. We have a 20 percent dropout rate. It's one of the highest in the developed world. And the chief academic reason for this dropout rate is algebra in the ninth grade.

HARI SREENIVASAN: The fail rate is something Diane Briars doesn't dispute.

DIANE BRIARS: The fact that failing algebra I as a ninth grader is — makes a student more likely to drop out is a huge problem that the mathematics education community is actively engaged in. One of the ways we're addressing that is by building a stronger foundation in K-8 mathematics.

With a more solid conceptual understanding in K-8 mathematics, students are going to be much better prepared to be successful in algebra I.

HARI SREENIVASAN: But Hacker says the math failure is greater than just high school.

ANDREW HACKER: Forty-seven percent of people who start a four-year college do not get a degree. That's a very high dropout rate, close to half. Chief academic reason, freshman math course, which people fail and don't make up. And why don't we ask ourselves, look at the talent we're losing.

HARI SREENIVASAN: Why are the institutions in high school and in college structured the way they are to emphasize math, as we do today?

ANDREW HACKER: Here's the big word I always hear: Let's be rigorous, the big R. Let's be rigorous, so let's make everybody coming into community college pass a stiff algebra test. That shows how rigorous we are.

Same thing at a higher level. If you take Princeton, Stanford, Yale, they want virtually all of their incoming students, except for athletes and a few alumni children, to have an SAT score on math of at least 700. That's very high. That's the top 7 percent. Why? We're Princeton, we're rigorous.

And in the name of rigor, we have this irrational math barrier.

HARI SREENIVASAN: Diane Briars agrees with that too, but only up to a point.

DIANE BRIARS: You can argue that, for some of them, that requirement may have been put there to ensure that they filter people out. On the other hand, being able to be facile with symbols and equations is necessary for a number of trades. For example, the electricians union has passing a course in algebra I as a requirement for an apprenticeship program.

HARI SREENIVASAN: So both sides agree that the formula for the right amount of math isn't optimal. Figuring out the right equation may be one of the first major problems for new graduates everywhere.

For the "PBS NewsHour," I'm Hari Sreenivasan in New York.