id: 06454510
dt: j
an: 2015d.00508
au: Dawkins, Paul Christian
ti: When proofs reflect more on assumptions than conclusions.
so: Learn. Math. 34, No. 2, 17-23 (2014).
py: 2014
pu: FLM Publishing Association, c/o University of New Brunswick, Faculty of
Education, Fredericton, NB; Canadian mathematics education study group
- CMESG (Groupe Canadien d’étude en didactique des mathématiques -
GCEDM), [s. l.]
la: EN
cc: E55
ut: proof; assumptions; proving; mathematical logic; mathematical concepts;
geometry: provability
ci:
li: http://flm-journal.org/index.php?do=details&lang=en&vol=34&num=2&pages=17-23
ab: Summary: This paper demonstrates how questions of “provability" can help
students engaged in reinvention of mathematical theory to understand
the axiomatic game. While proof demonstrates how conclusions follow
from assumptions, “provability" characterizes the dual relation that
assumptions are “justified" when they afford proof of appropriate
results. I provide examples of students’ learning in teaching
experiments connected to an advanced, undergraduate, neutral axiomatic
geometry course. Students used “provability" relations to choose
definitions, develop the notion of independence, and understand the
relationship between axioms and theorems. I argue that provability
promotes cognitive need for systematization, allaying concerns that
geometric proof lacks illuminative value.
rv: