I just read this article: http://www.washingtonpost.com/blogs/answer-sheet/post/to-students-its-all-about-the-boring-content/2011/08/14/gIQAjvzAFJ_blog.html
I would agree with the author that, when trying to improve schooling, it is necessary but not sufficient to focus on the “who,” the “where,” and the “how” and, indeed, that it is also important to consider the “what” (the actual content being taught). I think sometimes schools forget the original reasons why people thought it would be important to teach people certain things in the first place.
Indeed, this sometimes means that there are things that are taught as part of a typical math curriculum that probably don’t really need to be there. However, there are also lots of things that actually are there for good reason, but are just presented in a way that doesn’t let their value come through (this actually goes back to the “who,” “where,” and “how” that the author of that article referred to).
Then again, lots of what happens in math classes really seems to be designed to get students to eventually be able to understand calculus (which lots of people never actually take). Maybe we could cut out some of Algebra II/pre-calc and teach statistics, basic game theory, basic graph theory, and logic instead. (Don’t get me wrong, calculus is clearly important, but not necessarily more important than all of those other interesting things). I’d guess that the vast majority of people who have taken math through high school or college have the false assumption that proofs only exist in geometry class.
If you have some time, read this: http://www.maa.org/devlin/LockhartsLament.pdf
So, yes, some content is actually boring and unnecessary, just as the author of the original article claims. However, I think most of what people would claim is boring and unnecessary is actually just framed in a way that masks the interestingness.
For example, the textbook problem given in the article asks students to use the distributive property to calculate 5 x 215 without using the 2-button on a calculator. Ok, split up the 215 into two pieces such as 100 and 115, then multiply each of those by 5 and add them together.
I think a better way of asking that question is to cut out the part about the distributive property and instead just ask: “How can we multiply 5 x 215 without using the 2-button?” With some experience, number sense, and guidance from the teacher, students might come up with this method (or some entirely different method, which could also be pretty cool). If they come up with this method, then they can think about why it works (and convince themselves that it actually does) and then actually go through and calculate and see if they get the same answer as they would when just multiplying 5 x 215. Then, with some guidance, they can try to formalize this trick they just created: 5 x 215 = 5 x (100 + 115) = 5 x 100 + 5 x 115. And then, guess what, wow, that works with variables, too! Now, we’ve just learned 1/3 of algebra!
The point the original article misses is that a topic doesn’t need to be readily applicable to a student’s life to be interesting or valuable.
Along these lines, I’m a big fan of Dan Meyer’s work. Among other things, he argues that a math problem is most engaging (and thus most valuable) when the math question posed is obvious based on the context of the problem (that is, you could delete the last sentence of the word problem where it actually asks the question, but still know what you need to figure out) and then the answer should be checkable in a satisfying way that doesn’t just involve checking the answer in the back of the book. For example: http://blog.mrmeyer.com/?p=8483 (the rest of the stuff he posts to his blog is also pretty cool, too).
Here’s his TED talk, too: http://www.youtube.com/watch?v=BlvKWEvKSi8
On the other hand, the author’s point about new teachers not having time to actually do the work to improve content is well-taken. There are so many other things I need to be figuring out how to do as a new teacher. Depending on existing text-book stuff (not all of which is bad) is entirely necessary, particularly for a first-year teacher. The trick is just remembering that there is math beyond the textbook and not just getting in the habit of depending on that forever….