The issue of what we need to include in a mathematics teacher education and how to sequence it is something I have grabbled with for some time now. It is all good to say that all the aspects in Ball et al.’s famous egg are justified content components. But few programs last long enough to cover this in a reasonable sense. My standard response to the selection question is that we must select content that is in some way exemplary – by which I mean that the content deals with a specific aspect that reflects and exemplifies greater issues.
But in what ways? Exemplary to the main ‘knowledge of students and content’ (KSC) components? Exemplary to various pedagogies? Exemplary to the mathematical content? The challenge becomes to select content and related activities that illustrate several aspects of the complexity of mathematics teaching. But also to decide that some aspects are so overarching or so important that they need to become a main idea, running through courses. Which, then, are these?
Five years ago, I moved from a university in South Africa, to a university in Sweden. Fascinating to me was that the issue of KSC received relatively little attention at my new institution. What in the contexts made it so different what teacher educators thought their students needed? Horizon content knowledge was not widely engaged either, but all students had to learn to engage with research both as consumers of published research and as producers of small research studies, and curriculum theory was addressed within mathematics education courses as well. On the other hand, the psychological perspectives that had been included in the mathematics education courses at my South African institution are here mostly addressed in generic pedagogical courses.
The ’flower’ in an earlier blog was an attempt to identify a main idea, namely that teachers must utilize professional judgement. But the various ‘petals’ in the flower are of such different nature that they cannot guide selection of content.
One possible starting point could be the main professionally informed tasks or activities in which mathematics teachers engage. Then noticing, identifying key mathematical ideas, and guiding mathematical explorations are perhaps focal points?
Another potential starting point is to use a particular view of mathematics. To choose the perhaps most current, commognition. What would that mean to what happens in a classroom and what a teacher needs to know and be able to do?
Yet another way would be to use a particular mathematics education theory as a way to select content. The best candidate for this is perhaps ATD with its ecology, both for mathematical content and for education. The main challenge here is that each mathematics education task does not neatly correspond to one or a few techniques.
Add to this the issue of different competencies being more or less difficult to acquire. For instance, a recent paper in a special issue of ZDM suggests five levels of difficulties, where differentiation of instruction first comes in at level 4, and more explorative learner activities only became more dominant at level 5 (Kyriakides, Creemers, & Panayiotou, 2018). How does our ideal teacher then fit with what it is reasonable to expect from all our students? And what does this mean to the sequencing of content?
Kyriakides, L., Creemers, B. P., & Panayiotou, A. (2018). Using educational effectiveness research to promote quality of teaching: The contribution of the dynamic model. ZDM, 50(3), 381-393.
