As you may recall, my first post briefly discussed the California Board of Education’s mandate that every 8th grader in the state must take Algebra. My purpose here is not to discuss the ruling further, but rather to point out the response article published last month in the San Francisco Chronicle.
The article is well-researched and thoroughly written. Not only does it feature discussion of the pros and cons of such a mandate from a wide range of interviewees, but it also tries to address the question of why Algebra, and mathematics in general, is perceived so terribly by American kids and adults alike. It also attempts to paint a picture of what Algebra actually is, for those of us who fell by the wayside of mathematics long ago.
The current state of mathematics education is given quite a scathing review by the people mentioned in the article who actually know their mathematics. The harshest critic is former UC Santa Cruz mathematician Paul Lockhart, who wrote the following in a 2002 essay:
If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done … I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.
What is it about contemporary mathematics education that is so broken? There are three factors discussed in the article, and all of them are spot on: the failure of our curriculum to make math seem relevant, the educational system’s focus on testing, and the lack of qualified teachers.
Even though it is 2008, and technology surrounds us, many students have trouble seeing how math will help them later in life. Given the exponential growth in technological industries, not to mention reliance on data and statistics that is prevalent throughout the social sciences and other careers such as medicine, it is unlikely that this lack of foresight is due to the dwindling relevance of mathematics. If kids don’t see why math is useful, it’s because we’re not doing a good job showing them.
The article gives some examples of how math is used in unlikely places – from parking cops to delivery trucks to iPods. The main argument behind these examples is “Hey! Algebra is relevant – look at all this cool stuff that uses it!” On one hand, this may seem a bit deceptive. After all, saying that all you need is some Algebra to understand the machinery behind an iPod is a bit like saying that all you need to become a French pastry chef is knowledge of how an oven works – both make oversimplifications of the knowledge required. But on the other hand, algebra is a vital piece of foundation you will need in order to understand many modern technologies, even if a complete understanding requires a much deeper understanding of mathematics. It may be difficult to explain all the intricacies of how a circuit board works to a fourth grader, but saying something is better than nothing – especially when that fourth grader believes that studying math is essentially pointless.
The aforementioned Professor Lockhart advocates a less rigid approach to mathematics education, one in which the students can more freely explore mathematical ideas. Perhaps the reasoning here is to help guide the student down the same path of discovery that first led to the concept being taught. This is indeed a good way to teach mathematics, because it intertwines the concept with our own intuition, so that rather than seeming abstract and separate from reality, mathematics is seen as a way of interpreting the world in a rigorous, but natural way.
Unfortunately, such a pedagogical approach does not blend well with that pillar of American education: standardized testing. When teachers are forced to teach to a test, the motivation for studying mathematics is no longer to achieve a deeper and richer understanding of the world, it’s to fill in bubbles with a No. 2 pencil quickly and with minimal error. This brings up a slew of other issues: for example, how can we be sure that the tests are actually testing the mathematical knowledge we want the students to acquire? The article gives some examples of test questions at the end, but all of them can be solved by simply checking the given answers. While not an efficient test taking strategy for every question, it can certainly be used often enough to give the impression of mathematical competency.
Finally, the article pointed to a somewhat startling result: about a third of middle school Algebra I teachers do not have a math credential, and given the algebra mandate, that number is only expected to go up. Of course, there are probably good algebra teachers around who may not have a math credential, but at the same time, there are many math teachers in this country who are underqualified. Sadly, Jaime Escalante is but one man, and can only reach so many kids.
Given all this, the state of math education in this country may seem dismal. Perhaps it is. Will anything be done about it? I sure don’t know. But I am curious to see what effect, if any, this mandate will have. If nothing else, it should make for some interesting discussion.