The only solution, I think, is to keep issuing those challenges until, by the second term, no one thinks any less of them and everyone is comfortable with failure, even the kids who never fail.

I just wrote a post concerning two activities we did in class today. In my mind, both leaned to the “green knowlege” side of the spectrum. What absolutely shocked me in the two activities was the reaction of two of my most intelligent students. They HATED the activities. They weren’t comfortable with the trial and error involved in the two games.

Now, I understand high achieving students like being successful. Most of the time this success comes easy to the intelligent students. Today, it took a little work. This took some being wrong. Has our emphasis on grades (even in elementary school where grades are more or less determined on whether or not a student turned in their work) ruined the students of even attempting to answer a problem where they might be wrong?

Also, not all types of “green knowledge” can be tested this way. You cannot design a multiple-choice test that can effectively evaluate a student’s ability to write. For that matter, a multiple-choice test will never tell you whether or not a student “knows” how to swim … only the lake will prove that.

If we make a distinction between “knowing” and “doing” (i.e., knowledge and skills), then I think we just push the issue further back. If I answer all the right questions about swimming, but can’t actually do it, do I “know” it? And which part of that is red vs. green? Isn’t it more effective to just ask me to swim? And how do you get at my cognitive abilities if all I have to do is select someone else’s cognitive conclusions from a list?

But I agree with your last point: more focus on “green knowledge” can’t help but spill over into improved testing of “red knowledge.”

[And, to repeat what I’ve said elsewhere, I’m not against red knowledge or the testing of it through multiple choice tests. I’m against seeing both as the definitive assessment of a student’s education and of the educational system as a whole … which is the generic public view.]

I’m conflicted on your first point, though. It is possible to test green knowledge through multiple choice examinations. California does.

I think the gravitational pull of standardized testing though is toward red knowledge, which is unfortunate. I think if I taught more green knowledge my students would do better on these exams ’cause they wouldn’t shut down on problems whose solutions weren’t immediately apparent.

H., thanks for the positive feedback. When Richardson says that he doesn’t read people who post too much, I get all self-conscious about my post volume. And sorry, haven’t seen a camera yet.

Anyway, thanks for writing these great summaries! I may need to look up some writings by this Mr. Sallee.

This distinction, and its importance, is THE main problem I have with the over-reliance on standardized tests. Typical multiple-choice testing does little to nothing to encourage (to say nothing of “help to assess”) whether any “green knowledge” has been mastered by the student.

This distinction is also a helpful doorway, I think, for bringing writing and reflection into the math classroom. (Same could be said for other disciplines that are not traditionally writing-centered.)