Tuesday, August 30, 2011

Which is worse: curriculum or instruction?

As the US continues to fall behind other industrialized nations in math education, there is no shortage of frantic finger-pointing to help us out. But isn't there a simple solution? Japan is scoring higher on the TIMSS assessment, so perhaps we would do well to nationalize education, get students in class 20% longer, and somehow reconfigure our popular culture to value and encourage academic excellence. If our students' test results directly determined their quality of life, they'd probably study harder.

Looking over my friend Dr. Wai's response to a recent opinion piece by Garfunkel and Mumford in the New York Times, I wonder to what extent the traditional math sequence could be tweaked (rather than overhauled) to achieve the financial, statistical, and programming competencies suggested by the authors of the NYT piece. If we agree the goal is "quantitative literacy" (as has been called "numeracy" in the past), or competence in tackling real-life quantitative application problems, then all we have to do is decide on the best way to get students there. Simple.

As the pendulum swings back from integrated to traditional math sequence in my own district, I find myself feeling underwhelmed. Aren't there some meaningful changes that could be made rather than rearranging the furniture again? For a start, it would be nice if schools would teach the same stuff. I don't know how many millions of dollars are spent on new and different textbooks every few years (which are then to be criticized), but I'd guess it's more than ideal. Or how much money goes into "alignment" between textbooks and state assessments. Why not have the people doing the assessing also make the books? And while we're at it, why not have those books be public domain? Then take the money saved and double teacher salaries.

We're a long way from a national (or even state) curriculum, but efforts are being made. I take issue with Garfunkel and Mumford's contention that the Common Core State Standards Initiative are too abstract and "simply not the best way to prepare a vast majority of high school students for life". The beauty of math is in its ability (through abstraction) to apply to seemingly disparate areas.

For example, the authors contend that replacing the "algebra" course with "finance" could work because students would still encounter the exponential function (I'm paraphrasing rather crudely). But would they appreciate that the exponential function also models radioactive decay, or the cooling of a corpse, or the growth of the fennel plant I just found in my yard?



Incidentally, the first Common Core standard to address exponentials is "F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions"- this strikes me as entirely reasonable, and conducive to any number of instructional methods.

I don't know of a high school instructor who is "teaching 'pure' math, with no context," which Garfunkel and Mumford set up as a straw man. Engaging applications play a huge role in good teaching, but the abstraction of mathematics is what makes it functional. Haven't we progressed from the days of the Rhind Papyrus?

But then, we're not just teaching math; we're teaching students.

Aside from the immense effects that culture and economics have on math achievement, I doubt the solution lies in what we teach so much as how we teach. The TIMSS 1999 Video Study found that we spend twice as long reviewing material as Japanese teachers. Students formulate procedures in 44% of Japanese lessons but only 1% of US lessons. In a recent NCTM publication, Smith and Stein remind us that "...curriculum provides a set of instructional possibilities; what actually happens in the classroom depends on the teacher's view of what students need to know and do and her capacity to support the enactment of curricular tasks that are most likely to achieve those competencies."

What's that line about best-laid plans?

Thursday, August 18, 2011

Numberism

At the Portland Saturday Market the other day I happened across an interesting stall.


I poked my head in and found Sienna Morris, creator of images created with numbers...quite literally. Just as the pointillists used small daubs of paint to create coherent pictures, Morris uses numbers and calls the technique "numberism". She explained that the numbers she chooses to construct her drawings are significant; for example, in the piece called "A Cello", each string of the cello is drawn using the frequency for its particular pitch. The body of the cello contains the speed at which sound propagates through the particular type of wood. Even the 12th root of 2, which makes our modern musical scale possible, occurs in the image. Pretty cool!