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Mathematical proof is essential for mathematics as a discipline. Thus, mathematics students are expected to learn to handle proofs proficiently in multiple situations, for example, when constructing, comprehending, or validating proofs. However, there is only limited evidence on whether performances in proof construction, comprehension, and validation can better be described by one overall mathematical proof skill or multiple skills that may be highly related but are still separable. In particular, prior theoretical conceptions and empirical research provide no conclusive evidence in either direction. The present study empirically addresses this issue by comparing five different structural equation models (SEM), ranging from a 1-dimensional overall skill to 2-dimensional models to a 3-dimensional model with individual skills for each activity. Evidence from 153 undergraduate mathematics students showed that a 2-dimensional model corresponding to a skill for proof construction and a combined second skill for proof comprehension and validation matches the data best and is superior to the other models based on multiple criteria for SEM model fit and comparison. While both skills are highly related, data still suggests that they should be conceived as separate skills. The finding has implications for ways how validating and comprehending proofs could be incorporated into learning how to handle mathematical proofs.
Karriere Leichte Sprache Gebärdensprache EnglishDeutsch Startseite Forschen Alle
Mathematical proof is essential for mathematics as a discipline. Thus, mathematics students are expected to learn to handle proofs proficiently in multiple situations, for example, when constructing, comprehending, or validating proofs. However, there is only limited evidence on whether performances in proof construction, comprehension, and validation can better be described by one overall mathematical proof skill or multiple skills that may be highly related but are still separable. In particular, prior theoretical conceptions and empirical research provide no conclusive evidence in either direction. The present study empirically addresses this issue by comparing five different structural equation models (SEM), ranging from a 1-dimensional overall skill to 2-dimensional models to a 3-dimensional model with individual skills for each activity. Evidence from 153 undergraduate mathematics students showed that a 2-dimensional model corresponding to a skill for proof construction and a combined second skill for proof comprehension and validation matches the data best and is superior to the other models based on multiple criteria for SEM model fit and comparison. While both skills are highly related, data still suggests that they should be conceived as separate skills. The finding has implications for ways how validating and comprehending proofs could be incorporated into learning how to handle mathematical proofs.
Karriere Leichte Sprache Gebärdensprache EnglishDeutsch Startseite Forschen Alle
Der Science Day am 26. September ist der Höhepunkt des Festivaljahres „Science Summer 2025“. Unter dem Motto „Wissenschaft erleben“ laden die Hochschulen und wissenschaftlichen Institutionen der KielRegion an diesem Tag zum Entdecken, Experimentieren und Lernen an mehreren Standorten in Kiel ein.
September 2025, laden alle Hochschulen und wissenschaftliche Institutionen aus der
Karriere Leichte Sprache Gebärdensprache EnglishDeutsch Startseite Forschen Alle
Abteilungen Didaktik der Mathematik Weiterbildung Terminübersicht Terminübersicht Alle
Karriere Leichte Sprache Gebärdensprache EnglishDeutsch Startseite Forschen Alle
Karriere Leichte Sprache Gebärdensprache EnglishDeutsch Startseite Forschen Alle
Vertreterinnen und Vertreter aus Schulpraxis und Hochschulen erarbeiteten in Schleswig-Holstein gemeinsam einen Aufgabenkatalog für die mathematischen Voraussetzungen eines MINT-Studiums
Innerhalb Schleswig-Holsteins wird der Katalog an alle Schulen mit gymnasialer Oberstufe
Kieler Forschungswerkstatt: verschiedene Projekte und Citizen Science Aktionen Alle
