Clara Einfeldt wrote: << I have come to believe that our own students do not need more math courses to make them better teachers, but they need math couses taught in a different way. They need to attend math courses that have professors model the STANDARDS way of teaching. We need to start thinking of these pre-service teachers as constructivist learners. The context that students learn math is directly dependent on the beliefs and attititudes that acquire about not only the mathematics itself, but also the way math should be taught. Those of us working with pre-service teachers have to start integrating math content and pedagogy. If we truly believe that teachers teach the way they are taught, then we need to take a close look at not only the math classes they are taking, but the WAY those math classes are being taught.>>
I am currently teaching a course called Topics in Mathematics which is attempting to do what you recommend. NYS has recently required that all students entering teaching certification programs must have had at least one undergraduate college math course. Our graduate school of education had to decide whether to send our students to another college to meet this pre-requisite or to offer them a course which we could teach to meet this requirement in a manner consistent with the Standards. The students who come into this course (I have had three consecutive sessions to date) are generally mathphobic. As they describe their math histories, it is very clear to me that something we have been doing in math education in this country is not working. These people are the math throw-aways that we have produced. My challenge is to teach college math to people who think they can never learn mathematics-who avowedly hate mathematics and they want to be teachers of children.
There are many challenges to teaching this course as you can imagine,but it has been one of my most rewarding teaching experiences. We do mathematics. They begin a process of empowerment to continue learning math, to appreciate the need for understanding mathematics in our culture and they learn that math is a creative, enjoyable, useful part of their lives.
I have to hold at bay all the fears I have that I am not teaching them enough of a traditional college math content, constantly reassuring myself that the change of mindset about math is uppermost; constantly reevaluating what it means to be a mathematician, no matter what the math topic under study. I emphasize strategies of problem solving, discerning patterns, describing patterns in general terms, connecting math to their own areas of expertise, seeing the mathematics in the world they live in, making sense of the things that turned them away from math whether it was trig or quadratics or Euclid. I try to design experiences that help them put into place the role of the algorithm in math, the role of definition in math, the role of proof. They generate algorithms. They define terms. They learn to deal with frustration in math as a normal part of the creative process: a natural part of real problem solving. They stop looking for someone to give them the exact way to get the exact answer. They stop asking me if the answer is right. They begin to trust their own power to reason. They use materials that visually expose mathematical relationships. They begin to write their own theorems as they discern thesel relationships. They read math books (not traditional math textbooks) and find that they can build their own understandings through reading about math. They write truly extensively about their understandings and I respond extensively in writing-guiding them in the direction they need to go as individuals. . I ask them questions; they ask me questions. It's a personal dialogue of math learning.
I find I must tailor the course to the individual class and until I meet the members of the class I cannot design the exact course I will follow with them. The class evolves as their needs are exposed. I have the above goals in mind but how I'll achieve them depends on who the students are and what they come with. It's overwhelming at times. I worry that some of them know so little math but I think of the alternative: another math course like the high school courses they had that produced the problems to begin with. Another course to tell them how stupid they are in math, another course clipping along at a rapid pace covering a pre-determined curriculum, another course that perpetuates the belief that someone else has to tell them mathematics and that they are incapable of generating mathematical understanding independently. I feel better for about a day and then I start worrying again.
I would love to hear from anyone who also teaches this population. I'm interested in maximizing the mathematics learned without losing the embryonic mathematician in the process.
Lucille L. Peterson Math Leadership Program Bank Street Graduate School of Education Tel: 212-875-4665 610 West 112th Street Fax: 212-875-4753 New York, NY 10025 E-mail: firstname.lastname@example.org