TY - JOUR

T1 - Secondary teachers' knowledge of elementary number theory proofs

T2 - The case of general-cover proofs

AU - Tabach, Michal

AU - Levenson, Esther

AU - Barkai, Ruthi

AU - Tsamir, Pessia

AU - Tirosh, Dina

AU - Dreyfus, Tommy

N1 - Funding Information:
The research was supported by THE ISRAEL SCIENCE FOUNDATION (Grant no.

PY - 2011/12

Y1 - 2011/12

N2 - In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine the validity of an argument made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and more difficult to understand.

AB - In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine the validity of an argument made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and more difficult to understand.

KW - Elementary number theory

KW - High school teachers

KW - Proof

UR - http://www.scopus.com/inward/record.url?scp=81155128600&partnerID=8YFLogxK

U2 - 10.1007/s10857-011-9185-9

DO - 10.1007/s10857-011-9185-9

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AN - SCOPUS:81155128600

VL - 14

SP - 465

EP - 481

JO - Journal of Mathematics Teacher Education

JF - Journal of Mathematics Teacher Education

SN - 1386-4416

IS - 6

ER -