All teacher education programs I am familiar with require students to attend courses. In our case, courses in mathematics, courses in general pedagogy, courses in practicing teaching, courses in ethics, courses in research methods, and courses in mathematics education. A lot of the sequencing of the content in the mathematics courses is given by the nature of the content. For sure, one can learn differentiation before integration, or integration before differentiation, but one needs to first have an understanding of what a function is in both cases.
That is not so for mathematics education, as I see it. What then could be viable principle(s) for the sequencing of content?
In a recent workgroup revising one of the programs at my institution, we considered this. And came up with these suggestions:
(a) We work from students working with part of a lesson, to a lesson, to a sequence of lessons, to term or year.
(b) We work from students working with teaching strongly classified mathematics to students working with teaching more interdisciplinary.
(c) We work from the elements that research identifies as easier for students to apply (such as exemplifying using variation theory) to the elements they find more difficult (such as engaging learners in reasoning).
(d) We consider carefully which "eye-openers" can be engaged when, so that we meet the students where they are in this respect. It does not make sense, for instance, to wait to challenge the idea that the teacher is one that must explain procedures to learners.
This resulted in us sequencing the content into four parts:
(1) Noticing learner thinking
(2) Making mathematical objects/concepts available to learners
(3) Giving everyone access to the world of mathematics (inclusion)
(4) Furthering mathematical thinking.
We would love to hear the views of others on these ideas.
/Iben
