TY - JOUR
T1 - How to Frame Understanding in Mathematics
T2 - A Case Study Using Extremal Proofs
AU - Carl, Merlin
AU - Cramer, Marcos
AU - Fisseni, Bernhard
AU - Sarikaya, Deniz
AU - Schröder, Bernhard
N1 - Funding Information: The fourth author is thankful for ideal and financial support by the Claussen-Simon-Stiftung (DE) and Studienstiftung des Deutschen Volkes. All authors are thankful for the support via the DEAL project to cover OA fees. Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/10
Y1 - 2021/10
N2 - The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding.
AB - The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding.
U2 - 10.1007/s10516-021-09552-9
DO - 10.1007/s10516-021-09552-9
M3 - Zeitschriftenaufsätze
SN - 1122-1151
VL - 31
SP - 649
EP - 676
JO - Axiomathes
JF - Axiomathes
IS - 5
ER -