Dr. Mazur’s “work” is on peer collaboration. And his data speak to that work. I’m not sure “those that understand the concepts fully can virtually always do the computations as well” is an appropriate take-away from that presentation. I could be wrong, of course. I’ll have to watch his present again.

The standardized tests I took as a kid in elementary/middle/high school measured my ability to perform a series of unrelated 30 second problems. The problems I solve now are not in any way related to this skill I learned precollege. I simply have something I need to create or improve, and I need to figure out how to do that. For anybody who will use mathematics in their career, they are not simply given a hundred word problems and paid money to solve them.

That is what school was meant to prepare a student for wasn’t it? So why do we put so much weight on the measurement of such a minor skill?

Incidentally, with reference to Michell Bullard’s comment: she’s absolutely right, and if you check out Eric Mazur’s work (at the college level, in physics), he’s got the data to back it up. Specifically, he’s shown that students may understand the rote mechanics of very elaborate processes without understanding the concept, but those that understand the concepts fully can virtually always do the computations as well. He’s got a nice talk here: http://www.youtube.com/watch?v=WwslBPj8GgI.

In am idealistic world, by all means, scrap testing, give everyone a job they love and a good future, and everyones happy. But this isn’t the reality.

Our students not only rely on us to educate them in way which makes them see world in a different light, but also to help them pass any tests with flying colours, so that doors to their future stay open. In theory though, if the teaching is good enough, and your formative-y type assessment is good enough, then the tests should be no problem. But, whichever way we look at it, the test scores should matter to some degree.

I must admit that the bottom circle “what improves our test scores” does not strike me as terribly important. What do we do when that circle does not overlap with “what is valuable”?

A rich diagram.

Dan, I’ve read some of the criticism sent your way and part of it comes from a lack of distinction between “curriculum design” and comprehensive, point A-to-Z teaching and learning. When I see someone on the Math Forum ask “Where’s the math?” after seeing one of your WCYDWT posts (because you don’t show how a problem would be actually be solved), I can’t help but feel they’ve misunderstood what you’re trying to do (and not do). I wish more math teachers and mathematicians would as quickly criticize an equation and its solution by asking “Where’s the context?” Curriculum design is just part of the puzzle – an important piece for which you have considerable talent. I’m anxious to see how those talents develop in grad school. (Check out Freudenthal’s design work – there’s good stuff there!)