\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015d.00508}
\itemau{Dawkins, Paul Christian}
\itemti{When proofs reflect more on assumptions than conclusions.}
\itemso{Learn. Math. 34, No. 2, 17-23 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{E55}
\itemut{proof; assumptions; proving; mathematical logic; mathematical concepts; geometry: provability}
\itemli{http://flm-journal.org/index.php?do=details&lang=en&vol=34&num=2&pages=17-23}
\end