that comment is from last summer. I entirely missed it. Priceless indeed.

priceless.

I think most mathematical skills take time to ’set.’ I would expect that skills taught a few years back are solid when kids reach me, and that the previous year’s needs refreshing and practice.

The application comes. But this is not social studies, where it comes the same day. Or where almost everything is application and it is the rarer occasion where the class steps back and notes more abstract phenomenon at play behind the details being studied.

Ultimate – I ask questions backwards from time to time. I ask students to explain answers. I like the ideas you mention, and use them. But I use them as well as, not instead of the old fashioned regular stuff. They complement each other.

performance standards would stretch strong students – perhaps appropriate for an algebra exam – but harder algebra problems and canning the 50% stats and probability would be better.

But performance standards tend to crush weak or even average students – inappropriate for a high school exit exam.

“The challenge is to find problems where they can do this without needing other content knowledge that isn’t part of the course.”

I think traditional word problems do this, without being any more artificial than the A and B style questions.

Within that, I do agree that more depth and fewer topics would make sense.

First, at the risk of lapsing into “back in my day” (the early 70’s) rose-colored glasses, I remember one of the strengths of the Regents exams being that they covered the range of abilities pretty well. They were also wonderfully predictable — you got the Baron’s guides, and worked your way through old exams, and you were prepared. In essence, the collection of old exams set the content standards for the course.

Second, I have mixed feeling about your dismissal of performance standards, for two reasons. One, mathematical skills aren’t very useful unless you have some sense of what they can be used for, and I think students do need to get some practice in figuring out how to dissect a problem and turn it into equations. The challenge is to find problems where they can do this without needing other content knowledge that isn’t part of the course. Two, careful thought about what students will use their math skills for will help shape a better curriculum. I spent a summer teaching summer school Algebra II, and focusing primarily on skills so that my students could at least pass a “local” exam, and what was frustrating was that the skills seemed pretty meaningless without any context (I drew the line at teaching them to interpolate log tables). I think the kids would have been better served by a course than didn’t try to cover quite so many skills, but took the time to provide the context for them.