This helped me figure out that all problem are not what you think and that the number you think is to big may actually be to small and this helps you think about all the pushup and points they did.

Bucky the badger did to many push ups even though he probably cheated.Bucky the badger was in pain when he left and when he came back out he was so refreshed and motivated.

I used this 3Act almost word for word from the task page and it was great. Students who normally were checked out were completely engaged.

My best two students disagreed on whether order mattered and I was able to convince (falsely) one of them that order didn’t matter. And sure enough one of my “average” students – who always works her butt off but is rarely rewarded publicly in class for that work – was the only one to figure out and show that order matters.

It was the perfect transition away from conic sections and graphing and into discrete math, permutations, and sequences/series.

And the cherry on top – I had asked a few weeks ago to be observed by our senior teacher and today was the day he came in!

Most of the time this is fine, but a couple of times there have been problems for which the theory necessary for any sort of reasonable solution had not been covered (one problem at the end of Chapter 8 was poorly worded, so that it could not be answered without a theory of blackbody radiation, which was not covered anywhere in the book).

Certainly many math problems can be done with incomplete information (resulting in a function of the missing variables, rather than a numeric answer). I don’t think that such word problems are done nearly often enough in math classes.

They have each been major players on the anti-progressive side of the Math Wars for a couple of decades and have no compunction about lying, distorting the truth, engaging in the most absurd sorts of straw man fallacies and hyperbole to convince as many careless people as possible that any approach to mathematics education that doesn’t look just like what they (as “math” types) received is a harbinger of the Four Horseman of the Educational and Economic Apocalypse.

As far as I know, Ze’ev has never taught, and I doubt Wilson has taught below the elite university level. What they know about teaching math to K-12 kids is essentially nothing.

Spend a day in math classrooms in any high-needs school (or, frankly, not-so-high-needs school) and tell me that it suffices to demonstrate solid mathematical competency and understanding to be able to calculate correctly some routine arithmetic, algebraic, or geometric exercise and “show your work.” Give some of the stronger-performing kids a contextualized problem, say one in which one computes various critical points of a quadratic equation for projectile motion and then ask what they mean IN THE CONTEXT of the problem. You’ll discover that the x-intercept at x = -3 means that the projectile was on the ground precisely at 3 seconds before launch and that it traveled smoothly and continuously along the same trajectory that the projectile follows from release to the second x-intercept. Apparently, no baseball player having a catch has ever juggled a ball for a few seconds before throwing it back.

That said, I don’t think that being able to communicate, using mathematical language or verbally, is essential to understanding mathematics. I have noticed a fairly common type of student that has good mathematical thinking, but gets destroyed by the communication piece. They have difficulty with both reading and writing, whether it is English or mathematical notation, but are much better than average thinkers in that they are able to apply prior ideas to new situations. Being able to communicate math and being good at math are both desirable, but they are two different things.

This idea also seems to tie into Devlin’s project of trying to make games that take all of the language out of the mathematical ideas. The mathematical thinking and mathematical communication are two different things.

Of course, all of the above depends on your definition of math and communication.