On Sat. 6-24, Bill Schuth wrote: >Regardless of how well developed the reading skills of one's students >are, it would not be possible to spend time on all of the significant works >in the human experience. For that reason, the literature teacher should: > > 1) provide students with experiences which prove to them that > literature is valuable and enjoyable. > 2) teach students the skills necessary to successfully analyze > and criticize others' works. > 3) give students the opportunity to attempt to generate and > experiment with various styles of writing. > >Are these not similar to what a mathematics teacher should be doing?
I sincerely hope the analogy holds. I just finished "teaching" a course in Mathematics for Elemetary School Teachers. Eleven weeks, four contact hours per week, in ONE dose, Mondays, 4:30-8:30 pm. If anyone expected the course to "cover" all of elementary school mathematics (whatever that means), disappointment was certain. Yet the students had experiences that persuaded them that mathematics was interesting and valuable, and that they could engage in it successfully. They often worked in cooperative groups and made great strides in their ability to ask questions that elicited explanations of reasoning and to explain their own reasoning to others. They engaged in solving problems that ranged from examining the question "when you change a fraction to a decimal, and you know it will not terminate, what is the maximimum number of decimal places you might have to carry out the division steps before the repeating pattern begins?" to non-routine problems like the "Locker Problem," to real-world problems like those in "PACKETS" for middle school grades. They made and investigated conjectures, argued about their solutions (e.g., to the "Monty's Dilemma" problem), made connections within mathematics (e.g., the triangular numbers popped up every few weeks) and to other domains of knowledge, and did a lot of writing.
My goal was to get them started on lifelong learning in mathematics and for them to have some experiences as students to give them a feel for what it might be like to implement the Standards.
Many (unfortunately, not all) of the students were amazed at how much their attitudes and beliefs about mathematics could change in one term. They found it liberating to discover that math is not an ability one must be born with, that mathematics can be understood, that they are entitled to ask "why?" when a math teacher shows and tells "how to," that math is about patterns and relationships more than it is about getting the one right answer by executing the one right computational algorithm.
When these students go on to their "Elementary Math Methods" course, I don't think they will have any trouble seeing the potential value of implementing the NCTM Standards in their classrooms. Unlike some of the "math smarties" on this list, they were the casualties of traditional math teaching in the past. It didn't work for them. Hopefully, they will build on their recent positive experiences, not get completely discouraged watching traditional stuff again as student teachers, and become competent instructional leaders in math in their own classrooms over the next several years.
Standards-based improvements will take time.
Marsha Landau firstname.lastname@example.org Associate Professor, Mathematics Education National-Louis University 2840 Sheridan Rd Evanston, IL 60201