
06163114
j
2013c.00348
Leung, Issic K. C.
Lew, Heechan
The ability of students and teachers to use counterexamples to justify mathematical propositions: a pilot study in south Korea and Hong Kong.
ZDM, Int. J. Math. Educ. 45, No. 1, 91105 (2013).
2013
Springer, Berlin/Heidelberg
EN
E50
C40
C60
counterexamples
refutation of propositions
logically deductive reasoning
doi:10.1007/s118580120450x
Summary: Counterexamples, 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 counterexamples to justify mathematical propositions. The results highlight that South Korean students performed better than Hong Kong students at justifying propositions using counterexamples in algebra problems, but both did equally well in geometry problems. In terms of the prospective teachers' ability to justify propositions using counterexamples 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 counterexamples 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 counterexamples.