\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2012f.00537}
\itemau{Arzarello, Ferdinando; Dreyfus, Tommy; Gueudet, Ghislaine; Hoyles, Celia; Krainer, Konrad; Niss, Mogens; Novotn\'a, Jarmila; Oikonnen, Juha; Planas, N\'uria; Potari, Despina; Sossinsky, Alexei; Sullivan, Peter; T\"orner, G\"unter; Verschaffel, Lieven}
\itemti{Do theorems admit exceptions? Solid findings in mathematics education on empirical proof schemes.}
\itemso{Eur. Math. Soc. Newsl. 82, 50-53 (2011).}
\itemab
From the text: One of the goals of teaching mathematics is to communicate the purpose and nature of mathematical proof. {\it H. N. Jahnke} [ZDM 40, No. 3, 363-371 (2008; ME 2009f.00383)] pointed out that, in everyday thinking, the domain of objects to which a general statement refers is not completely and definitely determined. Thus the very notion of a ``universally valid statement" is not as obvious as it might seem. The phenomenon of a statement with an indefinite domain of reference can also be found in the history of mathematics when authors speak of ``theorems that admit exceptions". This discrepancy between everyday thinking and mathematical thinking lies at the origin of problems that many mathematics teachers encounter in their classrooms when dealing with a universal claim and its proof. The solid finding (the term ``solid finding" was explained in the previous issue of this newsletter) to be discussed in this article emerged from results of many empirical studies on students' conceptions of proof. In a simplified formulation, the finding is that many students provide examples when asked to prove a universal statement. Here we elaborate on this phenomenon.
\itemrv{~}
\itemcc{E50}
\itemut{mathematical education; mathematical thinking; theorems; proofs; empirical proof schemes; concept of formal proof}
\itemli{}
\end