# Does Algebra Get in the Way of Student Success?

Hear that change jingling in my pocket? Good. I have two little questions for you.

1. I have a quarter, a dime and a nickel. How much money DO I have?
2. I have three coins. How much money COULD I have?

The first question is a basic arithmetic problem with one and only one right answer. You might find it on a multiple-choice test.

The second is an open-ended question with a number of different possible correct answers. It would lend itself to a wide-ranging debate over the details: Are these all American coins? Are any of them counterfeit? Do you have any bills?

Frankly, it’s a lot more interesting than the first.

Andrew Hacker is professor emeritus of political science at Queens College, City University of New York, and the author of several more-or-less contrarian books about education, some of them bestsellers.

His latest is called The Math Myth: And Other STEM Delusions. It poses many nagging, open-ended questions like the second example above, without a lot of neat, tied-up-with-a-bow answers like No. 1.

Hacker’s central argument is that advanced mathematics requirements, like algebra, trigonometry and calculus, are “a harsh and senseless hurdle” keeping far too many Americans from completing their educations and leading productive lives.

He also maintains that there is no proof for a STEM shortage or a skills gap; and that we should pursue “numeracy” in education rather than mathematics knowledge. And, furthermore, that we should teach numeracy in an active, engaged, social way, with more questions like No. 2.

How do you define numeracy?

Being agile with numbers. Regarding numbers as a second language. Reading a corporate report or a federal budget. This is not rocket science–it’s easy to do. Kids become numerate up through 5th or 6th grade.

And what is the difference between numeracy and mathematics?

There’s a firm line between arithmetic and mathematics. When we talk of quantitative skills, 97 percent of that is arithmetic. Mathematics is what starts in middle school or high school, with geometry, algebra, trigonometry, precalculus and calculus.

Why are Americans apparently so bad at teaching and learning math?

When I say most of it is badly taught, what I really mean is that most teachers just can’t really rouse enthusiasm for math among 90 percent of the students. Surely you’ve had such teachers.

No comment. But lots of people have raised the alarm about this. Why isn’t the solution just to have math teachers, and students, work harder and do a better job?

I’m saying: No, we don’t need that many people studying mathematics. We’re shooting ourselves in the foot. One in five people don’t graduate high school — this is one of the worst records of developed countries. And the chief academic reason is that they fail algebra — of course there are other nonacademic reasons, like prison and pregnancies. In our community colleges, 80 percent don’t get a college degree. The chief reason is that 70 percent fail remedial math. And even in our four-year colleges, 40 percent don’t get B.A.s [after 6 years]. And the biggest reason is they fail freshman math. We’re killing our kids. We’re destroying their futures because of this requirement. I think it’s outrageous and we’re doing a lot of harm.

But what’s the alternative? Simply dumbing down the curriculum so everyone can pass?

When I first wrote the article “Is Algebra Necessary?” in the New York Times, most of the letters I got were from people who love math, are good at math and believe everybody should have to do it whether they like it or not. And again and again they talk about how mathematics teaches rigor, it’s tough. There’s this whole discipline thing. It’s like as if math is an enforced number of pushups.

I’m not anti-math. It’s a grand human achievement up there with chess and crossword puzzles.

But you don’t want everyone to have to master chess to get a high school diploma.

I’m going to be very careful about what Andrew Hacker wants to be compulsory. What I would like is for math teachers starting in high school to make the subject so fascinating that kids will want to take it. In writing the book, I went out and sat in on two dozen math classes from Virginia to Michigan to Mississippi. In some of them — not too many — the teachers were so infectiously enthusiastic that the kids joined in. And I wish we could bottle what they do and spread it around.

What about the need for more people with STEM skills?

Well, we certainly need people who know how to do coding. When it comes to engineers, according to the Bureau of Labor Statistics, we’re producing all the engineers we need. The skills shortage is a myth. The chief shortage is getting people who will work for low wages. That’s why companies in California want to bring people in on H-1B visas who will live eight in a room and do coding for a small amount above minimum wage.

What impact do you think the Common Core State Standards are having on math learning and teaching?

They’re expecting everybody to get almost up to the SAT level in high school. Either there’s going to be massive failures, or the states will ratchet down the requirements.

You taught your own alternative numeracy course at Queens College designed to make students more agile with numbers. How did you make the topic more appealing?

I had 19 students. I broke them up in groups of three or four. Math is always highly individualized, but in the world of work we want people to work in teams. I’d give them exercises, like, ‘How would you decimalize time?’ It’s really cumbersome the way we do it — we have a 60-minute hour, a 24-hour day, a seven-day week. How would you make a 10-day week or a 10-month year? Six different teams can come up with six different answers to that question.

Copyright 2016 NPR. To see more, visit http://www.npr.org/.
Does Algebra Get in the Way of Student Success? 2 March,2016

• DaveMontrose

Yes, yes, and more yes. At the very least, states need to remove the End of Course Exam requirements for Algebra courses. All they accomplish (other than lining Pearson’s pockets) is a boost to the dropout rate.

• I loved math in school. I was in pre-algebra in 6th grade and just kept going till a high school Geometry teacher bored me to tears. I have used geometry and algebra throughout my adult life. However, I am on your side about the way we teach this subject in isolation. And not just for those who do not “get” math—I see too many students in advanced math classes who cannot comprehend graduated income taxes or how to look at a score of 48/50 and figure their percentage in their head. They have years of math classes but no comfort at all using mathematics. Math is mostly a tool used to accomplish something else—teach its usefulness or simply do not bother!

• Benjamin Andre

Though it is nice to think that general numeracy would be a greater skill to learn than specific mathematical skills due to increased practicality, the reality is that knowledge transfer is so difficult for us to handle that learning general mathematical skills may not be entirely plausible. But at the same time, just teaching children how to use formulas isn’t the solution either. The real root of the algebra problem is located in early childhood when children learn the fundamentals of math. Children are born with innate mathematical functions, such as an approximate number system and relations of numbers, and it is upon these functions that we must build. However, children usually aren’t excited to learn math, despite how important it is. Therefore I suggest teaching children mathematical concepts in an interesting way instead of just instructing them on formulas. A study done by Ramani and Siegler (2008) utilized a number line based board game to teach children mathematics. Their study suggested that children are more likely to learn numerical skills when playing the number line based board game as compared to a board game based entirely on colors. Other studies have dealt with teaching math based on models. One example of the model method in action is Singapore. Singapore consistently ranks near the top of international mathematical literacy charts, suggesting that the model system that they use is very effective in instructing students. All of the previously stated evidence suggests that in order to fix the underachievement of students in algebra, changes need to be made at a much lower level rather than changing algebra instruction all together. And even then, it is incredibly hard to teach extremely generalized skills that can be utilized in all situations. But the only way to even have a chance at allowing skills to be generalized is if they are taught early.

• john

To be fair out of a cohort of 115 students who were aged 16 I posted the following question:

I am 25 you are 16 how far apart in age are we

At 16 years old, I had less than 60% answer correctly. That day literally mind crushed me , how can a child fail k-8 and then be forced/expected to complete high school let alone be allowed into the high school. I do not think the problem is Algebra but something far more systemic and actually dangerous

In my experience most high school drop outs ( in this area at least) are not even at the 8th grade competency level, of course they will drop out I am asking them to multiple and divide when they have never been taught how to find the difference between two numbers .

• Robert Clegg

I hate to tell everyone, but in 2004 we solved how to teach algebra. No, not some ivory tower research study; although there is peer reviewed journal research validating the results- doubled classroom performance, 2-3 grade level improvement on state exams, and 87% student approval rating. School districts in NYC, Chicago, Florida, and Texas public schools implemented it over 2.5 million times through 2008. And the product won Macworld Editors’ Choice Award in 2006.

Why aren’t educators banging down the doors to understand this? Why do pundits fail to research and know about this?

If you want the whole story, KQED, you’ll have to contact me.