Typische Teilprozesse beim Lösen hochschulmathematischer Aufgaben: Kategorienbildung und Ankerbeispiele

Ableitinger, Christoph

doi:10.1007/s13138-012-0033-y

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…As a consequence, typical exercises in university mathematics education include the development of own proofs (Liebendörfer 2018). Students typically encounter manifold challenges with such university mathematics exercises, such as a missing understanding of the exact problem to be solved or a missing understanding of possible options how to handle the problem (Ableitinger 2012). As developing own proofs is not the focus of school mathematics education, mathematics freshmen usually are poorly skilled in proving and thus feel overtaxed by such exercises (Brandell et al 2008;Ko and Knuth 2009;Rach and Heinze 2011;Schwarz et al 2008).…”

Section: Challenges Of Mathematics Freshmenmentioning

confidence: 99%

First Year Students’ Resilience to Cope with Mathematics Exercises in the University Mathematics Studies

2020

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University mathematics studies are known for high dropout especially in the freshmen year. This dropout is often traced back to the excessive demands freshmen have to face. Research aimed at identifying students’ characteristics that enable them to overcome the demands, for example through cognitive abilities, motivational constructs or self-beliefs. In this paper, we take a different perspective and suggest to include a construct that has not been considered in university mathematics education so far: mathematical resilience. Mathematical resilience is a well-established construct in school education to describe students’ attitude in handling everyday educational challenges like setbacks or frustration. We aim to transfer the construct to university mathematics education. Based on a literature review, we argue that the weekly mathematics assignments (i.e., compulsory exercises) pose a major emotional challenge for freshmen as they require advanced mathematical skills like proving, which students only scarcely learn at school. Failing at those mathematics exercises can lead to lasting frustration and, eventually, dropout. Mathematical resilience may thus be a relevant construct to consider when investigating dropout. We present a novel instrument measuring mathematical resilience against mathematics exercises. Findings of an empirical study with 424 mathematics freshmen confirm that mathematics assignments are in fact viewed as the most frustrating everyday challenge. Moreover, the data provide evidence on the validity and reliability of the novel instrument. The results show that mathematical resilience and the corresponding instrument contribute to research on academic success and failure of mathematics freshmen considering the specific conditions of university mathematics studies.

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Section: Challenges Of Mathematics Freshmenmentioning

confidence: 99%

First Year Students’ Resilience to Cope with Mathematics Exercises in the University Mathematics Studies

2020

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Demonstrationsaufgaben im Projekt „Mathematik besser verstehen“

Ableitinger

2013

Zur Doppelten Diskontinuität in Der Gymnasiallehrerbildung

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Welche mathematischen Anforderungen erwarten Studierende im ersten Semester des Mathematikstudiums?

2014

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Zusammenfassung Mit dem Übergang von der Schule in ein Hochschulstudium mit Hauptfach Mathematik verändern sich nicht nur die Rahmenbedingungen des Lernens, sondern auch der Lerngegenstand selbst. Insbesondere in der Studieneingangsphase steht der wissenschaftliche Charakter der Mathematik und dabei vor allem das mathematische Beweisen im Vordergrund, wohingegen zentrale Tätigkei-ten für den Schulunterricht wie das Ausführen von Berechnungen und das Lösen realitätsbezogener Anwendungsprobleme eine untergeordnete Rolle spielen. Dieses kann zu inadäquaten Erwartungen der Studienanfängerinnen und Studienanfänger bezüglich der inhaltlichen Anforderungen im Mathematikstudium führen, welche den individuellen Lernprozess möglicherweise behindern. In einer Studie mit 309 Mathematikstudierenden haben wir die Entwicklung dieser Erwartungen in den ersten Studienwochen nachgezeichnet und den Einfluss der Erwartungen auf den Studienerfolg am Ende des ersten Semesters untersucht. Schon zu Studienbeginn zeigten sich größtenteils Erwartungen, die als realistisch beurteilt werden können und die sich im ersten Semester adäquat weiterentwickelten. Der Einfluss von als realistisch eingestuften Erwartungen auf den Studienerfolg im ersten Semester war signifikant, aber gering. Aufgrund dieser Ergebnisse diskutieren wir kritisch, inwiefern das Eingehen auf Erwartungen der Lernenden in Unterstützungsmaßnahmen zu Studienbeginn sinnvoll ist. 206 S. Rach et al. 3Schlüsselwörter Inhaltliche Anforderungen · Erwartungen · Mathematische Studieneingangsphase · Studienerfolg · Individueller Lernprozess Mathematics Subject Classification C25 · C35 · C75 Which Mathematical Demands do Students Expect in the First Semester of Their Study?Summary As a result of the transition from school to university for students majoring in mathematics, changes become evident in both the formal organization of learning and in the character of the subject itself. Especially in the first year of university, the character of mathematics as a scientific discipline and in particular mathematical proving prevails, whereas key school activities such as arithmetic and algebraic manipulation and modeling real-world problems have little relevance. This can lead to students' unrealistic expectations about the mathematical demands at university level which may hinder their individual learning processes. In the first weeks of study, we analyzed the development of these expectations in a survey comprised of 309 students with a major in mathematics. Then at the end of the first semester, we investigated the influence of these expectations on students' success. We established that when entering university, students' expectations can be judged as being mostly realistic. Furthermore, students successfully adapted their expectations during the first semester. Additionally, the influence of realistic expectations on the students' success during this timespan was significant, but small. Based on these results, we discuss whether talking about learners' expectations at the beginning of ...

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Typische Teilprozesse beim Lösen hochschulmathematischer Aufgaben: Kategorienbildung und Ankerbeispiele

Cited by 3 publications

References 12 publications

First Year Students’ Resilience to Cope with Mathematics Exercises in the University Mathematics Studies

First Year Students’ Resilience to Cope with Mathematics Exercises in the University Mathematics Studies

Demonstrationsaufgaben im Projekt „Mathematik besser verstehen“

Welche mathematischen Anforderungen erwarten Studierende im ersten Semester des Mathematikstudiums?

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