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Why learn algebra?

August 2, 2012

Much has been written about the recent editorial by Andrew Hacker in the New York Times. Prof. Hacker asks if we really should by demanding that proficiency in algebra be a condition for graduating from high school, or even college. This seems to fly in the face of accepted wisdom. Accordingly, the reaction from the scientific community has been overwhelmingly negative (some interesting examples are here, here  and here).

I believe that Hacker asks a reasonable question. I do not agree with his answer, but this is more a matter of belief than solid evidence. Unfortunately, I don’t think there are any definitive studies that quantify the impact that learning algebra has on our lives. The supposed benefits of learning abstract reasoning are many. Being able to reason abstractly may help in landing a better job and a better management of your private life. Understanding complex issues may also help in being a better citizen.

However, there are numerous confounding factors in trying to relate the teaching of abstract reasoning in schools to any of these purported benefits. I don’t see any way to causally link the study of algebra to any of these effects in a controlled way. For instance, being able to master algebra may be related to other factors that also affect its supposed benefits. These factors could be something we call intelligence, persistence, or parental guidance. Even more likely, they are a combination of all of these and many others. I cannot speak with any certainty about how the capacity to reason abstractly affects people outside academia. Few in this debate have pointed out how poorly we understand the issues involved (but see Carson Chow’s interesting take on the issue).

I do want to point out one reason to teach algebra as broadly as possible. This is related to a point I made in an earlier post that addressed the question of why we are getting better at everything. Part of the reason that world records are continuously broken is certainly better science and better training. However, the number of people that participates in sports also keeps growing. As I wrote earlier:

Today, athletes and artists are recruited from a much wider base, and there are more resources available to train them from an early age. Therefore the number of exceptionally talented people identified early is much greater… In mathematical terms, if you choose a sample from a distribution, then the number of picks far from the mean increases with sample size.

We do need talented engineers, scientists and programmers, perhaps more than ever before. And learinng abstract reasoning and algebra is fundamental in each of these vocations. All of us know outstanding individuals in all of these fields who did not do well in school (again, this is something I can’t quantify). I am convinced that we are not very good at identifying such talent early on. By not teaching algebra to a broad group of students, we would therefore narrow the pool from which future innovators will emerge. And this would have a negative impact on society as a whole in the long run.


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  1. The question is not whether we should teach everyone algebra. Of course we should. The question is whether that should be the filter on whom gets to proceed. This is a different question entirely. Should we have systematic mechanisms in place for those that simply can’t do it.

  2. josic permalink

    I read Hacker’s article again, and it is unclear what he actually advocates. However, the tone, title, and several suggestions in the article leave the impression that he proposes we seek alternatives to algebra, not only as a tool for assessment, but as a complete replacement of the subject. I agree that there should be ways to graduate from high school that do not involve passing some arbitrary tests, whether in algebra or other disciplines. This goes far beyond the original question, and is an issue that is perhaps far more pressing (see here for instance:

  3. The foundations of algebraic thinking are fundamental to general problem solving and frankly should be within the grasp of anyone pursuing a higher education. Letting graduates go out into the world “logically illiterate” is a disservice to them and society.

    Math is not for everyone, I get that, but College Algebra is not that hard if one puts aside the irrational anxiety, tries different approaches to learning and practices.


    • josic permalink

      I agree – but the key word here is higher education. I think Hacker’s argument is that this is only 30-40% of the population. He asks whether we should hold back the rest from graduating high school because they cannot or do not want to master algebra. As pointed out in a previous comment, part of the problem is the arbitrary testing system that is currently imposed.

  4. I think Hacker’s argument has a fundamental fallacy by not considering that educational practices may also be a significant cause of the failure rate. Biddle’s article does a reasonable job of addressing educational reform ( – thanks for providing that link. It’s a failure of educational philosophy to expect students to appreciate a topic by simply telling them it will be important in their lives many years later. Clearly that is even hard to justify in math! Even for other subjects, there is much more that is necessary to get a student excited. There are many angles to consider: the teacher’s enthusiasm level, the parents’ interest, homework support in the home, individual learning styles, etc. As evidence of poor math education, look at all the comments from people who claim to have a math-phobia of some sort. No student – I repeat – NO STUDENT should EVER come out of ANY class with a phobia for the subject. That is a failure on the part of the teacher. I’m not saying that teaching algebra or any other subject successfully is easy. It’s not. Like math aptitude, I think there’s a misunderstanding about aptitudes for teaching. People are not simply born as either good or bad teachers. Good teaching is a skill that can be learned.

  5. josic permalink

    Yes – that’s an important point that is given insufficient attention by Hacker. However, I do believe that there are students who will not be able to master algebra. Moreover, there is also the question of allocating effort – do you use the best and most motivated teachers to try to engage the students who are doing poorly? Or is it better to have them teach the best students? Certainly, increasing the quality of education is crucial. But our resources are limited, and will remain so.

Trackbacks & Pingbacks

  1. Best of Dropout Nation: The Moral Imperative of Literacy | Dropout Nation: Coverage of the Reform of American Public Education Edited by RiShawn Biddle

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