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Issues about individual teacher subject knowledge: details
- Teachers at FH resisted one teacher's suggestions. However, it became clear that they thought they were being offered merely an alternative way of presenting one topic, not grasping that the teacher concerned was offering a research-based way to have a different effect on learning throughout one aspect of mathematics. If teachers are in the habit of topic-based or task-based discussion, then new ideas will be seen in this light and are likely to be rejected if their deeper worth is not appreciated.
- There were several incidents in which we felt that a teacher's own mathematics was limited, but nothing happened in the public forum to address this. For example, one teacher said that labelling the vertices of a triangle with letters was an aspect of algebra.
- In a discussion about how trial and error doesn't feel like a robust argument, someone said that exploring number bonds systematically does feel OK to him. No one suggested that in number theory sometimes this is a method to prove by exhaustion, or that the mathematical context influences the choice of 'proof' technique.
- On another occasion a teacher said 'putting the torn corners of a triangle together to show 180 degrees is not a proof, it is a demonstration'. It was unclear why she said this and no one responded. We wondered if this had been directed at teachers whose understanding of proof was limited, but we question whether this kind of announcement is effective.
