Should Students Learn Algebra? Two Views
An article in yesterday’s New York Times has sparked a lot of conversation about how students learn math. Written by political science professor Andrew Hacker and titled “Is Algebra Necessary?”, the article begins:
“A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.” Instead of teaching algebra, Hacker argues, we should teach them real-world math skills, like how to understand the Consumer Price Index.
Here are two intelligent responses to Hacker’s article, the first from blogger and New America Foundation fellow Dana Goldstein:
“There’s a strong argument to be made that math is taught poorly in many schools, with little attention paid to how most people are likely to use numbers in the real world, or how math is applicable to economics, the sciences, and government. But this argument also has a disturbing slippery slope quality; if teenagers find any somewhat obscure task difficult (like reading Shakespeare or doing library research), should they be allowed, or even be encouraged, to avoid learning it? A great teacher can often spark interest in a subject a student thought she would never enjoy. One reason to have more rigorous academic standards is to leave open the possibility of that magic happening more often for more young people, and to make sure unfair streotypes about who is ‘academic’ don’t prevent kids from discovering unexpected passions.” Read more of Dana’s post here.
The second response is from UVA psychologist Daniel Willingham:
“The difficulty students have in applying math to everyday problems they encounter is not particular to math. Transfer is hard. New learning tends to cling to the examples used to explain the concept. That’s as true of literary forms, scientific method, and techniques of historical analysis as it is of mathematical formulas.
The problem is that if you try to meet this challenge by teaching the specific skills that people need, you had better be confident that you’re going to cover all those skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won’t transfer.
The best bet for knowledge that can apply to new situations is an abstract understanding—seeing that apparently different problems have a similar underlying structure. And the best bet for students to gain this abstract understanding is to teach it explicitly.
But the explicit teaching of abstractions is not enough. You also need practice in putting the abstractions into concrete situations.
Hacker overlooks the need for practice, even for the everyday math he wants students to know. One of the important side benefits of higher math is that it makes you proficient at the other math that you had learned earlier, because those topics are embedded in the new stuff.” Read more of Dan’s post here.
I’m persuaded by Dana and Dan’s arguments that we should continue to teach algebra. What do you think?