I’ve been living with this question for a long time – starting with my own son when he attended Middle School (he is now 45, a Managing Director in Greenwich Capital, with his own Middle School aged children).
On Sunday, July 29, the question got a renewed focus with an article titled “Is Algebra Necessary?” in the cover Op-Ed of the New York Times, written by Prof. Andrew Hacker, a colleague of mine from the City University of New York.
I am spending my time trying to democratize the issue of Climate Change by writing a book that I have designated as a textbook for the general public; writing this weekly blog; teaching General Education courses on the topic and founding an undergraduate program designed to lower the communication barriers between the Natural Sciences and the Social Sciences.
The common thread in all these activities is an attempt to democratize the necessary decision making process required to address these climate issues that are so essential to continued human existence. I make the point that the main stumbling block we face is the need to expand science education to the general public, so that decisions that are based on interactions between humans and the physical environment will adhere to a common set of principles.
Suddenly, Professor Hacker tells me in his opinion piece that I must do this without algebra. Here are his arguments:
My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
According to the data in the article, one quarter of ninth graders fail to finish high school. In South Carolina, it is 34% and in Nevada 45%. Algebra, according to this account (based on chats with educators) is the main culprit. Furthermore, he states:
Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: ‘failing math at all levels affects retention more than any other academic factor.’ A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.
The article makes an argument that not teaching algebra to everybody does not mean not teaching quantitative reasoning:
Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
He suggests that we replace algebra with “citizen statistics” that will include topics such as personal finance and how to compute the “Consumer Price Index.” The notion is that we should teach skills to students that will be useful in the job market and should not teach difficult abstract concepts that make them want to drop out of school.
Hacker is talking about the heart of elementary algebra: variables that represent numbers and the rules that apply to these variables. To use a relevant example – any estimate of environmental impact requires an estimate of future growth of quantities such as population and economic activities. With a constant growth rate, this is calculated as exponential growth, and involves calculation with exponential functions related to logarithmic functions. These functions are usually taught in schools in pre-calculus, a level that is more advanced than elementary algebra and only selectively required, depending on the track that students are taking. Many students that take environmental courses have never taken pre-calculus. One can teach exponential growth without relying on exponential functions by instead using the concept of doubling time. However, one needs to manipulate simple one variable equations in order to be able to estimate the needed information. The simplest graphing requires ability to work with slopes, intercept and scale – you cannot do that without elementary algebra.
Even simple things such as unit conversion and percentage calculations need elementary algebra.
Political decisions will need to be made based on interactions with the physical environment. These will require a kind of literacy test for the ability to understand the data on which the decisions are being made. To exclude anybody from mastery of these skills means to give up on them. We don’t want to go in this direction.
There is no question that the teaching of mathematics, perhaps more than any other subject, can be improved. But the “improvement” cannot be done by excluding students that have difficulties. No, we have to redouble our efforts so as to reach these students.