What Do Prospective Mathematics Teachers Bring With Them to Their Professional Education?

What prospective teachers bring to teacher education programs is a critical influence on what they actually learn there. We do not know enough about what they bring nor, in preparing them to teach mathematics, what we should especially pay attention to about what they bring. These issues are necessarily prior to reconsideration's of the structure or curriculum of mathematics teacher education. This point would seem to be little more than an ordinary and self-evident caveat. After all, there is mounting evidence from cognitive science that children's prior knowledge powerfully affects the way they make sense of new ideas. This research has been influential in the curricula of both school mathematics and teacher education. Mathematics educators who develop innovative mathematics curriculum materials for classrooms design them to take into

account what we know about how children learn and the kinds of misconceptions they are likely to have. Some teacher educators talk about "constructivism" and student misconceptions in their courses. To make the same point about teacher learning should be trivial — it should seem obvious that teachers, like their pupils, may have ideas and understandings that influence their learning.

Ironically, however, this perspective on human learning rarely influences what university educators do with their students. University classes, whether in mathematics, history, or educational psychology, are typically "delivered," even when they are about the problems with delivering knowledge to children in schools. As one teacher remarked wryly, she had been in courses where she got lectures on constructivism. All too often the assumption in higher education is that teaching equals learning, that those who are capable enough and who want to learn the material will and will make sense of it correctly. And this assumption is made by the very persons who are raising these issues about lower education.  In order for teacher education to help prepare teachers to approach mathematics teaching from the perspective of mathematical pedagogy, we need to understand more about

(1) the students of mathematics teacher education — prospective teachers, and

 (2) what they learn from different approaches to professional preparation. Brown and Cooney (1982) argue

that

If . . . it is important to know how children learn mathematical knowledge in order to articulate effective instructional programs, then we are faced with the inescapable conclusion that it is important to know how teachers learn to teach mathematics in order to design effective teacher education programs. . .We have as a profession appreciated the naivete of assuming that it is possible to design a teacher-proof curriculum . . .but have we advanced beyond our initial naivete to realize that the teachers we train are far more than passive conduits through which intended curricula become learned curricula? 

Both foci of inquiry — what teachers bring and what they learn — are important to the improvement of mathematics teacher preparation, but this dissertation focuses on the first aspect: knowledge about what future math teachers bring to their formal preparation to teach mathematics. This work should also contribute conceptually to investigations of what teachers learn from different kinds of programs or experiences by offering a theoretical framework of what things to investigate and follow track about teachers' learning over time through a professional sequence.

My overarching research question is:

What do prospective elementary and secondary teachers bring with them to teacher education that is likely to affect their learning to teach mathematics?