I just “learned” last week in a graduate course that I’m taking, that some researchers believe that it is impossible to teach problem-solving. They say that it is an innate quality that students either have or don’t have. Well, what the hell…I better give up now.

I also “learned” that comprehension has to procede production..so does this mean that in order to produce a valid solution to a problem you have to understand how to do it first? Hmm, well, I have students every day coming up with ideas that I don’t necessary teach them and they have pretty good production, I think.

I just read in a chapter of a book by Collins, Brown and Newman (see below for citing) that the reason why teaching problem-solving is hard is because it “requires the externalization of processes that are usually carried out internally”. You can imagine how tough that is. It’s tough enough for a teacher to make adjustments to a skill like knowing how to write the equation of a line that they can see and observe. At the same time, students can have a hard time seeing an example of what they should be doing to problem-solve as opposed to seeing how to write the equation of a line. Collins, Brown and Newman say that “this externalization (can be) accomplished through discussion, alternation of teacher and learner roles and group problem solving” (p.458).

This makes me reflect on how I might be modeling problem-solving in class. In order for the kids to be able to follow a model, there has to be something there for them to watch and mimic, right? I think what I try to do sometimes is ask questions of the kids, and try to get them to answer me in moments when I really know what to do next, but want someone to help out. I know that I am not always right, so that at least models it. I also think that I do not hesitate to attack a difficult problem. I tell them, do like Ed Burger tells you to do. He came to our school last year and told the students “Do you know what to do when you get a math problem you can’t do? (Pause) Don’t do it!” (Cheers from the audience) “No, no, not what I meant, you do an easier one.” His message was that when presented with a problem that you can’t do, make it simpler by seeing what you CAN do. I thought this was a hugely important message for him to send to the students. It really speak to the message of empowerment and prior knowledge. This is something I’m still working on how to convey to students.

Collins, Brown & Newman, (1989). Cognitive apprenticeship: Teaching the crafts of reading,writing, and mathematics. In Resnick, L & GLaser, R (Eds). Knowing, learning, and instruction: Essays in honor of Robert Glaser. (pp/453-494), Hillsdale, NJ:Lawrence Erlbaum Associates, Inc.