id: 06163114
dt: j
an: 2013c.00348
au: Leung, Issic K. C.; Lew, Hee-chan
ti: The ability of students and teachers to use counter-examples to justify
mathematical propositions: a pilot study in south Korea and Hong Kong.
so: ZDM, Int. J. Math. Educ. 45, No. 1, 91-105 (2013).
py: 2013
pu: Springer, Berlin/Heidelberg
la: EN
cc: E50 C40 C60
ut: counter-examples; refutation of propositions; logically deductive reasoning
ci:
li: doi:10.1007/s11858-012-0450-x
ab: Summary: Counter-examples, which are a distinct kind of example, have a
functional role in inducing logically deductive reasoning skills in the
learning process. In this investigation, we compare the ability of
students and prospective teachers in South Korea and Hong Kong to use
counter-examples to justify mathematical propositions. The results
highlight that South Korean students performed better than Hong Kong
students at justifying propositions using counter-examples in algebra
problems, but both did equally well in geometry problems. In terms of
the prospective teachersâ€™ ability to justify propositions using
counter-examples in two particular topics, properties of the absolute
value function and parallelogram, Hong Kong prospective teachers
performed relatively weakly in the absolute value problem but better in
the parallelogram problem compared with South Korean prospective
teachers. The weaknesses and strengths of students and prospective
teachers in generating counter-examples associated with logical
reasoning in mathematical contexts in the two regions indicate ways of
improving the effectiveness of learning and teaching mathematics
through the use of counter-examples.
rv: