id: 02074058
dt: j
an: 2011a.00505
au: Epp, Susanna S.
ti: The role of logic in teaching proof.
so: Am. Math. Mon. 110, No. 10, 886-899 (2003).
py: 2003
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: E30 E50
ut:
ci:
li: doi:10.2307/3647960
ab: Summary: Even simple mathematical proofs and disproofs are more logically
complex than most mathematicians realize. Research by mathematics
educators and cognitive psychologists supports the claim that the
logical reasoning abilities needed to discover them are not widely
present in the population. Two hypotheses are proposed to explain some
of the reasons why so many students have difficulty with proof and
disproof: differences between mathematical language and the language of
everyday discourse, and the kinds of shortcuts and simplifications that
have been part of studentsâ€™ previous mathematical instruction. The
article describes research about whether instruction can help students
develop formal reasoning skills and suggests that such instruction can
be successful when done with appropriate parallel development of
transfer skills. The final sections discuss at what point the
principles of logic should be introduced and give a variety of
suggestions about how to teach them.
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