Why learn algebra?
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.