TY - JOUR

T1 - Comparative analysis on the nature of proof to be taught in geometry

T2 - the cases of French and Japanese lower secondary schools

AU - Miyakawa, Takeshi

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by the notion of Mathematical Theorem showed differences in these aspects and also differences in the three functions of proof—justification, systematization, and communication—that are seemingly commonly performed in these countries. The results of analyses imply two major elements that form the nature of proof: (a) the nature of the geometrical theory that is chosen to teach and (b) the principal function of proof related to that theory. This paper suggests alternative approaches to teach proof and proving and shows that these approaches are deeply related to the way geometry is taught.

AB - This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by the notion of Mathematical Theorem showed differences in these aspects and also differences in the three functions of proof—justification, systematization, and communication—that are seemingly commonly performed in these countries. The results of analyses imply two major elements that form the nature of proof: (a) the nature of the geometrical theory that is chosen to teach and (b) the principal function of proof related to that theory. This paper suggests alternative approaches to teach proof and proving and shows that these approaches are deeply related to the way geometry is taught.

KW - Curriculum

KW - Functions of proof

KW - Mathematical Theorem

KW - Proof and proving

KW - Textbooks

UR - http://www.scopus.com/inward/record.url?scp=84976332616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976332616&partnerID=8YFLogxK

U2 - 10.1007/s10649-016-9711-x

DO - 10.1007/s10649-016-9711-x

M3 - Article

AN - SCOPUS:84976332616

VL - 94

SP - 37

EP - 54

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 1

ER -