In September, I walked into a classroom with 16 preservice elementary school teachers wanting to learn how to teach mathematics. It is now December, and they are excited and concerned about their student teaching assignments next semester. As I look at these preservice teachers with whom I spent the last 12 weeks, I wonder if I had done my job. Then, another question comes to my mind: What is my job? Or, what is (are) the primary goal(s) of a preservice mathematics methods course?
The Professional Standards gives us a fairly comprehensive picture of what good mathematics teaching is. A good mathematics teacher poses worthwhile mathematical tasks. A good mathematics teacher orchestrates classroom discourse, using appropriate instructional tools and by creating a productive learning environment. Furthermore, a good mathematics teacher is a "reflective practitioner," engaged in "ongoing analysis of teaching and learning."
The Professional Standards then goes on to discuss the standards for mathematics teachers' professional development, which directly relates to our task. According to the Standards, we are to provide opportunities:
I agree with all of these ideas, but I ask myself, "How am I going to do all of these in just 15 weeks?" It's true that many of my students take 2 mathematics content courses where "good mathematics teaching" is practiced (so we think). They take other professional courses where ideas like students as learners, classroom management, teacher as professional are discussed (and hopefully learned). Yet, I also know that mathematics content instructors cannot be reasonably expected to help all students gain conceptual understanding of (most of) school mathematics. There are many ideas about learning and teaching that is peculiar to mathematics (mathematical pedagogical content knowledge). There is so much to do in such a short time. We talk about "less is more" but what are the big ideas in a mathematics methods course? What should the student at the end of a mathematics methods course be like? Surely we cannot expect her/him to be an expert mathematics teacher. But, s/he will be in charge of a room-full of students in a few months. Can we spend 5 weeks talking about teaching and learning of geometry while not discussing anything about teaching and learning of whole number computation? Could we expect her/him to project what s/he learned in teaching and learning of geometry into teaching and learning of whole number computation? I know that each student must construct her/his own knowledge, including knowledge about teaching and learning of mathematics, but if s/he is going to be the mathematics teacher for a group of students, what are the minimum ideas I want her/him to know? (I haven't even mentioned anything about these teachers' beliefs and attitudes toward mathematics.)
These are just a few of questions I have in my mind as I reflect back. They are somewhat uncomfortable to ask because I am expected to know the answers, but, honestly, I am not sure if I do. So, I want to pose them to my colleagues who are engaged in the same task of preparing future mathematics teachers.
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