Tim Rowland, Peter Huckstep and Anne Thwaites: Elementary teachers' mathematics subject knowledge: the knowledge quartet and the case of Naomi
This article is a precursor to the article Turner/Rowland treated a previous post
I've often discussed with Norwegian mathematics colleagues in teacher education the problem of how students are supervised in their school-based placements. Too often, the discussions with students concern only "administrative" and pedagogical issues, and too little attention is given to the mathematical parts of the lesson. This article is an attempt to help this situation.
The point of the research was to "develop an empirically based conceptual framework for the discussion of mathematics content knowledge, between teacher educators, trainees and teacher-mentors, in the context of school-based placements". The "Knowledge Quartet" is the result:
- Foundations (Propositional knowledge and beliefs)
- Transformations (How the content knowledge is transformed "into forms that are pedagogically powerful" (Shulman))
- Connection (between different parts of a lesson, between lessons or between different parts of the curriculum)
- Contingency (How "to respond to children's ideas")
The authors cite Ma citing Duckworth that intellectual "depth" and "breadth" "is a matter of making connections". This quite deep insight suddenly got very visual for me: isolated points of learning can hardly be have "depth" or "breadth". (My visual image/metaphor soon breaks down, however, so I think I'll stop thinking about it...)
The second part of the lesson, discussing Naomi's lesson, showed how her lesson could be analysed from the four "points of view" given above.
The article is highly recommended.
Labels: mathematics, teacher education