
06643709
a
2016f.00809
Shinno, Yusuke
Fujita, Taro
An analysis of the essential difficulties with mathematical induction: in the case of prospective teachers.
Adams, G. (ed.), Proceedings of the British Society for Research into Learning Mathematics (BSRLM). Vol. 35, No. 3. Proceedings of the day conference, University of Reading, UK, November 7, 2015. London: British Society for Research into Learning Mathematics (BSRLM). 102107 (2016).
2016
London: British Society for Research into Learning Mathematics (BSRLM)
EN
E59
D79
proving
mathematical induction
learning problems
educational research
student errors
understanding
prospective teachers
preservice teacher education
mathematical theorems
theoretical modelling of proof by mathematical induction
subtheorems
metatheorems
metastatements
metaproofs
metatheory
http://www.bsrlm.org.uk/IPs/ip353/BSRLMIP35318.pdf
Summary: Although proof by mathematical induction (MI) is one of the important methods of mathematical proof, gaps and difficulties have been reported in mathematics education research so far. This study provides an analysis of the essential difficulties with mathematical induction that are experienced by prospective mathematics teachers. We take the notion of ``mathematical theorem" proposed by an Italian research group, and use this to describe in more detail the structural understanding of MI from a theoretical standpoint. Data are collected by a set of questions based on the idea of ``proof script" method. The results suggest that the difficulties of MI are concerned with prospective teachers' understanding of logical relations which we call ``subtheorem" or ``metatheorem".