A recent opinion essay in The New York Times by Andrew Hacker, asking the question “Is Algebra Necessary?”, drew hundreds of comments. Some of SchoolBook’s contributors went further and have written their own essays in response. What’s your opinion? Respond to our query below. (We would especially love to hear from students or recent graduates.)
As a parent with three children rising through New York City public schools, I’m sympathetic to the argument by the Queens College professor Andrew Hacker that “elite” colleges often saddle students with large debts for little discernible benefit in salaries or social status over their less-prestigious brethren.
Whether or not my kids earn 3.8 GPAs and score 2,200 on their SATs, Dr. Hacker’s claim that they can obtain an excellent college education for less than $200,000 resonates.
Regardless of where my children attend college, I know they will need a well-rounded preparation in their primary and secondary schools. They might become doctors or engineers, poets or professors. But wherever life leads them, they’ll need to be able to appreciate Shakespeare, understand standard deviation, and explain the laws governing the conservation of energy.
Thus I was taken aback by Dr. Hacker’s recent essay in The New York Times asserting that algebra is meaningless and should be dropped in favor of more practical math.
There are many ways to succeed in college, but none of them require algebra? It was important for Andrew Hacker in the late 1940s and when I attended junior high in the late 1970s, but now my son doesn’t need it? He’ll just look up the answer on the Internet?
If my child was accepted at Yale, a friend once assured me, I would not turn it down and I’d find a way to pay for it. But whether he attends a “top 25” school or a community college, he will have to work, participate in the life of his community, and understand complex questions like the healthcare and defense dilemmas we’re intent on burdening him with.
To meet these challenges he’ll need a solid grounding in the critical theories under-girding our world, including the abstractions one learns in algebra.
Using set theory, Sesame Street offers a brilliant example of why abstraction matters. After repeating the word “fish” six times to take a room service order from a group of penguins, the hapless hotel clerk learns he can just say “six fish” and it means the same thing.
“Does it work on other stuff?” he asks. “Say cinnamon rolls, cream pies and spark plugs?”
This leap, the ability to appropriately generalize from a specific example, is at the core of a high quality education, be it in literature, art, history or math.
But to generalize well, children need a solid grounding in the facts. In the case of math, this means both strong computational fluency and a good understanding of the underlying critical theories. Some students will gain this insight faster; others will have to work harder. Either way, I’m not willing to let my children’s schools off the hook for teaching this effectively.
Dr. Hacker is certainly correct when he observes we do a mediocre job teaching math; over the last decade in New York City our children have shown modest progress on national math tests like the NAEP. But as a parent and taxpayer, I’m disappointed that he thinks the solution is to stop teaching foundational math like algebra.
Clearly the first step is to improve instruction. The University of California-Berkley professor Hung-Hsi Wu has long criticized the “textbook standard math” that we use in New York City (and across most of the U.S.).
Dr. Wu’s 30-year analysis shows that we teach math “as a jumbled collection of tasks.”
“It would be reasonable,” he says “to attribute a good deal of students’ non-learning of mathematics to their being fed such jumbled information all the way from kindergarten to grade 12.”
Like many educators, Dr. Wu hopes the Common Core will lead to a more coherent approach to math instruction, but he does not suggest dropping algebra.
We also need improved assessment. It’s hard to tell how instruction is working when the tests don’t tell you what the students are (or are not) learning.
SchoolBook readers learned about the faulty polygon that disgraced this spring’s fifth-grade math test. I’ve found other basic errors in previous state math exams.
More significantly, a Brooklyn Technical High School math teacher Patrick Honner notes both the 2011 and 2012 Regents exams contained “mathematical errors, poorly constructed questions, underrepresented topics, and 9th-grade questions on 11th-grade exams.”
If the New York State Department of Education can’t even ask the right questions, is it any wonder students find algebra challenging? In the ‘no excuses’ culture that dominates education reform these days, it is simply shameful that Albany can’t produce higher quality tests.
Before dropping algebra in favor of more ‘useful’ mathematics, we would do well to first examine how we deliver and assess the most fundamental aspects of math education.
If we can get these basics right, we’ll discover that algebra isn’t so tough after all, and that our students are better equipped to contemplate, and contribute to, the world around them.