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Prospective teachers often perceive a “double discontinuity” between school mathematics and university mathematics. The first discontinuity can be described as the belief that there is no coherence between school mathematics and university mathematics, which forms part of the notoriously problematic transition from school to university. The second discontinuity can be described as a belief about the lack of relevance of university mathematics for the later professional practice of prospective teachers. Beliefs about coherence and relevance have been known to impact prospective mathematics teachers’ interests and academic success. In this paper, we discuss an intervention involving 72 prospective secondary school mathematics teachers, aimed at influencing their beliefs about coherence and relevance. For this, we refer to the construct of beliefs as the main part of our theoretical framework, as well as the sub-constructs of beliefs regarding coherence and relevance. We then describe an intervention implemented within the first two years of mathematics courses, involving so-called “teacher-oriented” tasks that aim to trigger reflection on the benefit of university mathematics for teaching mathematics in school. The effect of the intervention was measured with a pretest-posttest experimental design using a questionnaire concerning teachers’ beliefs about coherence and relevance. Our results show that the prospective teachers’ beliefs about coherence and relevance generally decrease during the semester. However, statistically significant differences between the treatment group and a control group were found, especially regarding their beliefs about relevance.
Prospective teachers often perceive a “double discontinuity” between school mathematics and university mathematics. The first discontinuity can be described as the belief that there is no coherence between school mathematics and university mathematics, which forms part of the notoriously problematic transition from school to university. The second discontinuity can be described as a belief about the lack of relevance of university mathematics for the later professional practice of prospective teachers. Beliefs about coherence and relevance have been known to impact prospective mathematics teachers’ interests and academic success. In this paper, we discuss an intervention involving 72 prospective secondary school mathematics teachers, aimed at influencing their beliefs about coherence and relevance. For this, we refer to the construct of beliefs as the main part of our theoretical framework, as well as the sub-constructs of beliefs regarding coherence and relevance. We then describe an intervention implemented within the first two years of mathematics courses, involving so-called “teacher-oriented” tasks that aim to trigger reflection on the benefit of university mathematics for teaching mathematics in school. The effect of the intervention was measured with a pretest-posttest experimental design using a questionnaire concerning teachers’ beliefs about coherence and relevance. Our results show that the prospective teachers’ beliefs about coherence and relevance generally decrease during the semester. However, statistically significant differences between the treatment group and a control group were found, especially regarding their beliefs about relevance.
ZusammenfassungViele Lehramtsstudierende haben Schwierigkeiten, Verbindungen zwischen der Mathematik, die sie an der Hochschule lernen, und der Mathematik, die sie später in der Schule unterrichten sollen, zu erkennen. Dieses Phänomen wurde von Klein (1908) als doppelte Diskontinuität beschrieben und beschäftigt die Lehramtsausbildung noch heute. Mittlerweile haben verschiedene Hochschulen sogenannte Lehramtsaufgaben in ihre Lehre integriert, um diesem Problem entgegenzuwirken und Verbindungen zwischen Schul- und Hochschulmathematik explizit zu adressieren. Ergebnisse dazu, inwiefern Lehramtsaufgaben tatsächlich einer wahrgenommenen doppelten Diskontinuität entgegenwirken, gibt es bisher allerdings nur vereinzelt. Die in diesem Beitrag berichtete Fragebogen-Feldstudie mit 98 Studierenden in einer Treatmentgruppe von Gymnasiallehramtsstudierenden und Vergleichsgruppe Fachstudierender zielt daher darauf ab, erste Befunde zur Frage nach der Auswirkung von Lehramtsaufgaben auf die Wahrnehmung der doppelten Diskontinuität zu ergänzen. In der Studie bewirkten Lehramtsaufgaben keine Erhöhung der wahrgenommenen Relevanz von Hochschulmathematik für den Lehrberuf, konnten aber einem Absinken ebendieser vermutlich vorbeugen. Darüber hinaus zeigte sich in dieser Studie erwartungsgemäß, dass sich der Einsatz von Lehramtsaufgaben positiv auf die Wahrnehmung von Verbindungen zwischen Schul- und Hochschulmathematik auswirken kann. Ersteres bestärkt vorhandene Forschungsbefunde, Letzteres wurde in bisherigen Studien noch nicht einheitlich beobachtet. Es werden Ansatzpunkte für weiterführende Forschung zur hochschuldidaktischen Lehrinnovation der Lehramtsaufgaben abgeleitet.
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