The final report of the National Math Panel is finally out, and I have to admit that, overall, I really like it. I completely agree with their conclusion that the tension between conceptual understanding and procedural fluency is a false battle. It isn't the standard algorithm OR flexibility in solving problems. Conceptual understanding, fluency, and problem-solving all work together. Quick recall of basic math facts is very important, but it isn't everything. The opposing sides in the Reading Wars eventually accepted a truce; kids need to know how to decode, and they should love and understand what they read. Let's hope the antagonists in the Math Wars have reached a similar accord.
One area noted in the report should readily be embraced by everyone. Effort and attitude matter. They summarize the research of Carol Dweck (see one of my previous blogs) about shifting the learner's attitude from one focused on innate ability to one that recognizes growth through effort. It's critical for students and teachers to acknowledge incremental improvement and the effort it takes to achieve it. I wouldn't be surprised to find a relationship between these attitudes and math anxiety. The panel recognizes the reality of math anxiety and recommends more research to uncover its source. Indeed, the report makes many recommendations for further research. We need it.
The panel's report did, though, leave me wanting in a couple of areas. While the report talks about the importance of problem solving, it never describes what "problem solving" means or how it should be developed. Maybe the research isn't robust enough to illuminate clear directions. I would also have liked more clarity about why the panel members singled out particular areas in measurement and geometry for instructional focus. I don't disagree with the importance of the selected areas of content, but I would welcome more elaboration about how they fit into an algebra trajectory.
Hopefully, NCTM's Curriculum Focal Points and this report of the National Math Panel provide enough guidance for states to review and revise their curriculum standards in math. The list of learning objectives on state curriculum frameworks tend to be long and without emphasis on what's really important. The objectives get treated as separate, isolated teaching and learning events. Fitting them all into a school year inevitably leads to shallow coverage trumping real mastery. Let's concentrate on what's important and make sure kids really get it before moving on. Now, if only we can get the testing establishment to reflect this focus, but that's the topic of another blog.