Sunday, November 11, 2012

True Math

A few words about middle school math at Summers-Knoll.

Our objective is to graduate students who are numerate. This is precisely analogous to literate. A literate person can read, but that isn't the whole picture. A truly literate person can use words precisely, practically, powerfully, and with an exciting sense of possibility. 

A truly numerate person can do all that with numbers. This is a critically, even criminally undervalued skill. It is why Tom Magliozzi of Car Talk fame--he of the PhD in from MIT--wrote, chagrined:

The purpose of learning math . . . . . is only to prepare us for further math courses.

In 2011, journalist, author and social entrepreneur David Bornstein opined, in The New York Times:

Imagine if someone at a dinner party casually announced, “I’m illiterate.” It would never happen, of course; the shame would be too great. But it’s not unusual to hear a successful adult say, “I can’t do math.” That’s because we think of math ability as something we’re born with, as if there’s a “math gene” that you either inherit or you don’t.
It’s hard to imagine what society might look like if we could undermine the math hierarchies that get solidified in grade school. These patterns tend to play out across society, often in negative ways. Wasn’t it the whiz kids who invented financial derivatives and subprime mortgages? And how many adults got themselves into hot water with their mortgages because, at bottom, they didn’t really understand the risks?

How will we produce thoughtful, numerate graduates at SK? There are three corners to this program: math in the world; math on the page; and project-based math.

Math in the world asks real questions. Why was the 2012 Presidential election primarily fought in seven states? Why is zero a revolutionary concept? How much money should an adult save per paycheck? How does one build a safe playground structure? How much mulch is enough mulch underneath a set of monkey bars? Michael Paul Goldenberg has been posing such questions with students of all ages for three decades, and we are fortunate to have him driving these questions in the SK middle school. Answering them requires hard-core, gory, flat-out arithmetical axioms, theorems, operations, and principles. But answering them also requires the ability to identify which skills and operations are relevant. 

Those skills have historically been practiced at SK via Singapore Math, an innovative approach to basic skills that gained global credibility and popularity approximately a decade ago, after it prompted rapid advances in test results from that Asian city-state's elementary students. Singapore has been joined in recent years by the uber-viral website Khan Academy.

Khan and Singapore are terrific practice, and we expect our students to spend fifteen minutes per day with their noses in the book or screen, because, in mathematics, as in second-language study, there is no substitute for exercise. Not for nothing do our students attend math on a regular basis, even in a project-based curriculum. Jason DePasquale is masterminding our students' work in these programs, and in a school the size of SK, we are able to individualize these work programs and goals to an unusual degree.

In keeping with the theme of Ancient Civilizations, students in my section of math have been divided into Mesopotamians and Egyptians. Each will build a pyramid in the style of its civilization. The math will emerge as necessary as each group decides what materials it will use, the dimensions of its building, the geometry required, the physics of architectural design. These projects should be on display at the performances of 'Gilgamesh' in mid-December. Other projects will evolve as our school service and theme-based work in Global Citizenship and Circle of Life develops over the course of the academic year.

We have settled upon the work of an innovative scholar, teacher, mentor, and gamer, Henri Picciotto of Beirut and San Francisco, to help shape the direction of our seventh and eighth grade students. Henri is the author of a highly regarded algebra textbook--after whose publication, he founded a professional organization called Escape the Textbook. For more on his approach, and more of his plentiful materials, go to http://www.mathedpage.org/. Henri is also a former colleague of mine from the Urban School of San Francisco. His vision of math education, in part:

Mathematics education is not just about preparing students for "practical" matters and helping the economy. It is an important part of human culture of sense-making, and should be introduced as such to all students from a young age. In addition to being useful, math is fun and beautiful. We should not lose sight of this as we attempt to make the curriculum more relevant through greater reliance on applications.

Finally, another word from David Bornstein.
Even deeper, for children, math looms large; there’s something about doing well in math that makes kids feel they are smart in everything. In that sense, math can be a powerful tool to promote social justice. “When you have all the kids in a class succeeding in a subject, you see that they’re competing against the problem, not one another,” says [Canadian mathematician and teacher John] Mighton. “It’s like they’re climbing a mountain together. You see a very healthy kind of competition. And it makes kids more generous to one another. Math can save us.

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