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- W2185909358 abstract "For the purpose of the study reported here we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about the ways in which they implement their AMK in teaching. We find an apparent confusion between what teachers perceive as difficult or challenging for their students and what is ‘advanced’ according to our working definition. We conclude with a call for a more articulated relationship between AMK and mathematical knowledge for teaching. Research reported here is the beginning of our journey aimed at identifying explicit relationships between school mathematics and university mathematics, as perceived by secondary school teachers. We first describe the relationship (or lack thereof) between teachers’ knowledge of mathematics and the achievements of their students, which led researchers to posit a need for ‘specialized’ mathematical knowledge for teaching. Then we describe different kinds of teachers’ knowledge and provide a working definition of advanced mathematical knowledge (AMK) and its relation to advanced mathematical thinking (AMT). Acknowledging the existing gap between secondary and undergraduate mathematics we illustrate suggestions for reducing this gap. We then describe the views of several secondary school mathematics teachers about their usage of AMK in their teacher practice. SUBJECT MATTER KNOWLEDGE AND TEACHING While teaching is unimaginable without teachers knowing the subject matter, it is unclear how “knowledge for teaching” can be measured. The most used measure, the number of mathematics courses taken by a teacher, did not lead to conclusive results. Begle (1979) found that students’ mathematical performance was not related neither to the number of university courses their teachers had taken, nor to teachers’ achievement in these courses. However, Monk (1994) found a minor increase in secondary students’ achievement associated with the number of college courses in mathematics taken by mathematics teachers. Further, “researchers at the National Centre for research on teacher education found that teachers who majored in the subject they were teaching often were not more able than other teachers to explain fundamental concepts in their discipline” (NCRTE, 1991, quoted in CBMS, 2001, p." @default.
- W2185909358 created "2016-06-24" @default.
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- W2185909358 date "2010-01-01" @default.
- W2185909358 modified "2023-09-27" @default.
- W2185909358 title "ADVANCED MATHEMATICAL KNOWLEDGE: HOW IS IT USED IN TEACHING?" @default.
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