Proof construction and in-process validation – Validation activities of undergraduates in constructing mathematical proofs

Kirsten, K.; Greefrath, G.

Forschungsartikel (Zeitschrift) | Peer reviewed

Zusammenfassung

Proof construction and proof validation are two situations of high importance in mathematical teaching and research. While both situations have usually been studied separately, the current study focuses on possible intersections. Based on research on acceptance criteria and validation strategies, 11 undergraduates’ proof construction processes are investigated in terms of the effective and non-effective validation activities that occur. By conducting a qualitative content analysis with subsequent type construction, we identified six different validation activities, namely reviewing, rating, correcting errors, reassuring, expressing doubts, and improving. Although some of these activities tend to be associated with successful or unsuccessful proving processes, their effectiveness depends primarily on their specific implementation. For example, reviewing is effective when accompanied by a knowledge-generating approach and based on structure- or meaning-oriented criteria to provide deeper understanding. Thus, the results suggest that difficulties in proof construction could be partly attributed to inadequate validation strategies or their poor implementation.

Details zur Publikation

FachzeitschriftJournal of Mathematical Behavior
Jahrgang / Bandnr. / Volume70
Seitenbereich101064null
StatusVeröffentlicht
Veröffentlichungsjahr2023
Sprache, in der die Publikation verfasst istEnglisch
DOI10.1016/j.jmathb.2023.101064
StichwörterAcceptance criteria; Mathematical proof; Proving process; Validation strategies

Autor*innen der Universität Münster

Greefrath, Gilbert
Professur für Mathematikdidaktik mit dem Schwerpunkt Sekundarstufen (Prof. Greefrath)
Kirsten, Katharina
Professur für Mathematikdidaktik mit dem Schwerpunkt Sekundarstufen (Prof. Greefrath)