Ronald, thank you for your reply to my plaint about students' problem solving skills. I will reprint it at the end of this for others to consider. My first reaction when I read it was "Here's another suggestion from someone in an ivory tower." However, that reaction assumes that all students will refuse to do the work this approach requires and if ignore it, I am depriving them of a CHANCE to get better. Whether or not they take it is out of my control. I think all of us try to teach a similar approach to this, but I have never seen it so well formalized before. I plan to make a poster of it and put it on my classroom wall!
To quote: I think Katherine might like her students to use a Metacognitive Checklist such as the one below [attributed to Fortunato, Hecht, Tittle, & Alvarez by John Van De Walle in his 1994 text "Elementary School Mathematics"--Longman Press]:
"Before you began to solve the problem--what did you do? 1. I read the problem more than once. 2. I tried to find everything out about the problem that I could. 3. I asked myself, 'Do I really understand what the problem is asking me?' 4. I thought about what information I needed to solve this problem. 5. I asked myself, 'Have I ever worked a problem like this before?' 6. I asked myself, 'Is there information in this problem I do not need?'
As you worked the problem--what did you do? 7. I kept looking back at the problem as I worked. 8. I had to stop and rethink what I was doing and why. 9. I checked my work as I went along step by step. 10. I had to start over and do it differently. 11. I asked myself, 'Is what I am doing getting me closer to the answer?'
After you finished working the problem--what did you do? 12. I checked to see if all my calculations were correct. 13. I went over my work to see if it still seemed like a good way to do the problem. 14. I looked at the problem to see if my answer made sense. 15. I thought about a different way to solve the problem. 16. I tried to see if I could tell more than what the problem asked for."
Van De Walle included this checklist because, as he says, "If children are to become responsible for their own actions in problem solving, they must also learn to develop the metacognitive habits of monitoring and regulating their own thought processes." This seems particularly applicable to what Katherine said. [Van De Walle has a really good chapter on Developing Problem-Solving Processes. In it he also includes some good suggestions for teacher actions before students begin, while students are working, and after the problem is solved.]
Ron Ward/Western Washington U/Bellingham, WA 98225 firstname.lastname@example.org