"An interesting example of this concept comes from my sister, who is a seventh-grade English teacher. Her feeling is that it might be better for her to be a math teacher, since she has long struggled to understand mathematics herself. ... it does make me think that sometimes the best things for people to teach are the ones that did not come easily for them, where the learning process has been a struggle of which they are constantly aware."
I just wanted to comment that it was my struggle with mathematics that led me to pursue it as a major in college. My struggle also caused me to be reflective about the learning and teaching processes as they relate to mathematics and eventually led me to become a mathematics teacher. I feel that my struggle with the subject has made me a better math teacher: it has made me more intent to respect learning differences, more willing to try new ideas, and more reflective about what occurs in the classroom.
And, David Wecksler writes:
"I think making teachers models of learning and problem-solving IS one of the "most imporant parts" of any curriculum, and that this modelling plays an especially crucial role in mathematics instruction. . . this teacher-as-learner model becomes crucial in defining classrooms as __resources for__ constructing understanding rather than just sources for receiving knowledge, and in creating a "classroom culture" in which learning, understanding and instruction play equally important roles."
I think that this is one of the areas that packaged mathematics programs designed to address the NCTM standards fail to acknowledge. Many of the packaged programs offer a lot of exciting, mathematically-rich content, but fail to address the mode of presentation or teaching method adequately. In fact, many of the packaged programs include lessons plans that tend to be dominated by teacher-directed activities and do little to empower students in their own learning. The programs also do little to establish the teacher-as-learner model that David discusses. At best, many of the programs only pay lip-service to the most recent pedagogical findings.
By maintaining traditional teaching methods, the programs may be made more palatable to school districts and teachers; however, I think they are also setting those districts and teachers up for failure. Most of the goals and desired outcomes outlined in the NCTM standards can not be accomplished without the implementation of less-traditional teaching methods: student-directed learning, group discussions, writing about mathematics, 'unstructured' mathematics explorations, integrating mathematics with other areas, etc. Because of this problem with the teaching methods in packaged programs, the frustration that many teachers feel about new math programs is more understandable. Of course, this problem could be addressed with adequate in-service traning about mathematics teaching methodology; unfortunately, school districts often neglect this component.