Monday, July 30, 2012

We May Not Need Algebra: The Horror!

In the future, I can see a math teacher sadly proclaiming, "First, they cut ancient history from the curriculum, but I didn't care because I didn't teach history. Then they came after Shakespeare, but I didn't care because I didn't teach English. When they came after algebra, the precedent was set and I was totally screwed."

The algebra teachers who smugly watched their social studies and literature counterparts try to justify their curriculum may soon face the same battle.  Writing in the New York Times, Andrew Hacker opines:
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.
Surely Hacker is wrong. STEM is allegedly America's salvation, and algebra is a key component of STEM. Hacker has an answer:
Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college, which has tailored classes in “machine tool mathematics.”
That sort of collaboration has long undergirded German apprenticeship programs. I fully concur that high-tech knowledge is needed to sustain an advanced industrial economy. But we’re deluding ourselves if we believe the solution is largely academic.
 Hacker offers at least one possible alternative to algebra:
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.
He also suggests that math and other disciplines combine analyses:
I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet.
One could also examine the poetry or music of mathematics  instead of the math of poetry. Hacker's conclusion shows why that sort of inversion might be necessary:
Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.
If only a literary allusion to some guy pushing a boulder up a hill existed. Hacker could have referenced such a story to help make his mathematical point.


David Newquist said...

As old teacher, I have noted that the most successful students have been those who benefited from general education in the arts, humanities, sciences, and (with some reservation) the social sciences. When we started eliminating foreign language requirements for baccalaureates, and cut back on the study of literature and rhetoric, and the fine arts, we deprived students of the essential tools for critical and creative thinking. In so doing, we have relinquished our top place in education.

Math is a particular case in point in how curriculum is weakened. In the 1950s, math educators introduced an approach to teaching math they called the "New Math." The name was a mistake because it caused many people to assume that the New Math came up with new rules and properties. In fact, what it attempted to do was meet the problems that Hacker refers to. The New Math intended to ground students in understanding its principles, such as number theory, and statistical inference as applied in probability, and the like. The biggest opponents to the New Math were engineers, who could not grasp that the procedures and principles of mathematics were not being reinvented, but were being explained so that people who would not be working complex equations would have an understanding of how math worked, and to give that knowledge also to those would be manipulating mathematical formulas.

Much of education has been taken up by disciplinary turf battles rather than in processes for integrating the facets by which students come to understand knowledge. The state of our education system is the product of that competitive approach.

caheidelberger said...

One phrase keeps this math major from flipping his lid at this proposal: "citizen statistics." Stats gets short shrift in the standard Alg1-Geometry-Alg2-PreCalc SD HS sequence, yet it is the most important math we can give our graduates. Give the kids the CPI, unemployment figures, state budgets, and make them interpret all that data, tell us what that data says about how legislators or citizens should vote. And teach that math with spreadsheets. ;-)

But I also want a unit on Pascal's triangle... and fractals. Let's do that liberal arts thing, the poetry of math!

LK said...

In hindsight, I may have been a bit too flippant in the original post. The sight of STEM folk acting as cannibals did give me a bit of perverse joy.

On the particulars, I certainly agree that turf wars hurt education.

I was serious about the poetry of math. I teach a Pascal unit with the triangle in my world lit class.