id: 06643709
dt: a
an: 2016f.00809
au: Shinno, Yusuke; Fujita, Taro
ti: An analysis of the essential difficulties with mathematical induction: in
the case of prospective teachers.
so: 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). 102-107
(2016).
py: 2016
pu: London: British Society for Research into Learning Mathematics (BSRLM)
la: EN
cc: E59 D79
ut: proving; mathematical induction; learning problems; educational research;
student errors; understanding; prospective teachers; preservice teacher
education; mathematical theorems; theoretical modelling of proof by
mathematical induction; sub-theorems; meta-theorems; meta-statements;
meta-proofs; meta-theory
ci:
li: http://www.bsrlm.org.uk/IPs/ip35-3/BSRLM-IP-35-3-18.pdf
ab: 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 “sub-theorem" or “meta-theorem".
rv: