The following notes are from the literature review of Tim Burgess in his paper Statistical Knowledge for Teaching: Exploring It in the Classroom published in For the Learning of Mathematics, Vol.29, No.3. Knowing and Using Mathematics in Teaching (Nov., 2009), pp. 18-21.
- Teacher’s knowledge is organized in a content-specific way, rather than around the generic tasks of teaching such as lesson planning, and so on.
- Significant mathematical reasoning and thinking occurs as teachers go about ‘figuring out what students know; choosing and managing representations of mathematical ideas; appraising, selecting, and modifying textbooks; deciding among alternative courses of action; and steering a productive discussion”
- There are two categories of teacher’s knowledge according to Hill, Schilling,and Ball (2004) and further clarified by Ball, Thames, and Phelps (2005, 2008): (1) Common knowledge of content (CKC), and (2) specialized knowledge of content (SKC).
- CKC includes the ability to recognize wrong answer, spot inaccurate definitions in textbooks, use mathematical notation correctly, etc.
- SKC includes the ability to analyze students’ errors, evaluate students’ alternative ideas, give mathematical explanations, and use mathematical representations.
- Ball et al (2005) also subdivided Shulman’s PCK (1986) in two categories: (1) knowledge of content and students (KCS) and (2) knowledge of content and teaching (KCT).
- KCS includes the ability to anticipate students errors and common misconceptions, interpret students’ incomplete thinking, and predict what students are likely to do with specific tasks and what they will find interesting and challenging.
- KCT deals with the teacher’s ability to sequence the content for instruction, recognize the instructional disadvantages of different representations, and weigh up the mathematical issues in responding to students’ novel approaches
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