# Some thoughts on math

From Roger Schank at *The Pulse*:

[T]there is no evidence whatsoever, that accumulation of facts and background knowledge are the same thing. In fact, there is plenty of evidence to the contrary. Facts learned out of context and apart from actual real world experience that is repeated over and over are not retained. . . .

[K]ids don’t like math much and it is clear why. They find it boring and irrelevant to anything they care about doing. If you think math is so important, then why not teach it within a meaningful context, like business, or running a school doing the kind of math you had to do to do that – which certainly wasn’t algebra II. There is plenty of evidence that shows that teaching math within a real and meaningful context works a whole lot better than shoving it down their throats and following that with a multiple choice test. . . .

[T]here is no evidence whosoever that says that a nation that is trailing in math test scores will somehow trail in GDP or whatever it is you really care about. This is just plain silly, but we keep repeating the

mantrathatwe are behind Korea in mathas if it has been proven that this matters in some way. . . .[N]early every grown adult has forgotten whatever algebra he or she ever learned to pass those silly tests, so it is clear that algebra is meaningless for adult life. I ask every important person in public life that I meet to tell me

The Quadratic Formula.No one has ever been able to do so.

From David Thornburg at *The Pulse*:

Recent pronouncements from Washington regarding math education have suggested that pedagogical points of view don’t matter in the teaching of mathematics. For example: "There is no basis in research for favoring teacher-based or student-centered instruction," Dr. Larry R. Faulkner, the chairman of the panel, said at a briefing last Wednesday. "People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other."

Well, actually, Larry, if you read the “Rising Above the Gathering Storm” document (National Academies Press, 2007) you will likely be shocked to learn that, in fact, there are two methodologies proven to improve math proficiency: Statewide specialty high schools (e.g., IMSA) and inquiry-driven project-based learning (e.g., constructionism.) Now it may well be that Dr. Faulkner has more reliable sources than those at the National Academy of Science and other groups that contributed to this 591 page report on the challenge faced by the US in the areas of science and math education. However, let’s assume for the moment that the National Academies tend to use fairly reliable folks to generate their reports. In this case, then Faulkner is simply flat out wrong. There IS research showing that one methodology is better than another, and I just cited it. The fact that this research was reported by the same government that claims it does not exist is a puzzlement at best, and an example of the “big lie” at worst. Faulkner’s strategy seems to be that, if you lie to the American public loudly enough, it will believe you.

There seems to be a dearth of links/quotes that represent the other side of the debate. Let me know if you need any.

Matthew, absolutely. I just thought these two were interesting. Send ’em my way (or, better yet, blog about them and link to this post)!

Wow!

Apparently Mr. Tabor is an expert on all subjects, mathematics learning as well.

Perhaps he should disagree with Dr. Thornburg or Dr. Schank on The Pulse where their original articles reside.

I look forward to his proof that algebra is connected to GDP.

Gary,

Thanks for the kind words – I’m pleased that you’ve recognized all that I have to offer. I lament that it came so late in the education debate, but I’ll let bygones be bygones. Let’s move forward.

When I made my comment, I meant that I’d cull some of the better relevant bits so we could see the arguments on both sides. I didn’t suggest that I’d write them myself.

Swing-and-a-miss, Gary.

Swing-and-a-miss, indeed, Gary.

I think that he is missing a lot of what the basis of mathematics gives students. A lot of students don’t realize how much math they do on a daily basis; just because they don’t specifically need or remember everything they do in Algebra II, doesn’t mean its not going to help them latter on in life. It is merely the building a foundation of mathematics, which they will use throughout their entire life.

I’m perhaps not the best to counterargue — I use quite a bit of constructivism in my teaching, and work with an all-constructivism program in the summer. Two points though:

1. “Connections with work” is not the only way to make grab students — presenting a piece as an exploratory puzzle rather than some raw procedure can work just as well. Many attempts at incorporation of real-life context are very forced, and frustrate more than interest the students who have to deal with a “word problem”.

2. Some topics are scaffolds. Today in my class we are throwing around wads of paper and timing them, then using parametric equations with the quadratic formula to work out their velocity. While this is a “real-life” use of the quadratic formula, it can’t really be taught simultaneously — the lesson is simply using what was already learned. It’s like the Karate Kid not understanding wax-on, wax-off; eventually there *is* a payoff, and it can’t always be rushed in.

Very interesting discussion I am a inspiring math major at GVSU and I headed towards an education degree. When I go to ask for help from my friends or from other educators (friends) and math is not their majors. They look at me as if I was speaking Spanish! So I agree with your statement that nobody knows/cares about math in their adult life.