By Tim Rowland
This e-book is helping readers to develop into larger, extra convinced academics of arithmetic via allowing them to concentration severely on what they comprehend and what they do within the lecture room. construction on their shut commentary of fundamental arithmetic school rooms, the authors offer these beginning out within the educating career with a four-stage framework which acts as a device of help for constructing their instructing: making feel of origin wisdom, remodeling wisdom, connection, and contingency.
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Extra info for Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet
Four of these are generic in nature: • general pedagogical knowledge; • knowledge of learners; • knowledge of context; • knowledge of the purposes of teaching and learning. The other three relate to content-specific knowledge, and it is these that we are most interested in here: • subject-matter knowledge; • pedagogical content knowledge; • curriculum knowledge. In the case of mathematics, subject-matter knowledge is concerned with both substantive and syntactic knowledge. qxp 10/8/2008 12:51 PM Page 21 KNOWLEDGE FOR TEACHING MATHEMATICS 21 them – such as knowing the properties of an isosceles triangle, understanding what is meant by a fraction, knowing how to multiply by 10, and knowing that division undoes multiplication.
This book is about ways of building up your knowledge about mathematics and mathematics teaching. It is structured around reflection on classroom situations, and in this way we are trying to complement, not to duplicate, what other primary mathematics books for teachers already do very well. We mention some of them at the end of this chapter. As we have already said, Naomi needs knowledge about subtraction and how to teach subtraction. These are two different kinds of knowledge, although sometimes it is difficult to separate teachers’ own ‘learner knowledge’ – what they needed to pass school exams – from the ‘teacher knowledge’ that they need to help someone else to learn.
In her study of four early years teachers, Carole Aubrey (1997a, 1997b) demonstrated how the interaction of teachers’ subject-matter knowledge, pedagogical content knowledge and knowledge of learners affected their teaching. Though Shulman (1986) included ‘knowledge of learners’ as a separate category of generic teacher knowledge, Deborah Ball et al. (2005) saw such knowledge as an aspect of specialised content knowledge. Aubrey’s use of ‘knowledge of learners’ follows Ball et al. in focusing on knowledge of children as learners of mathematics.