Benjamin Rott

Inductive and Deductive Justification of Knowledge: Flexible Judgments Underneath Stable Beliefs in Teacher Education

ABSTRACT Personal epistemological beliefs are considered to play an important role for processes of learning and teaching. However, research on personal epistemology is confronted with theoretical issues as there is conflicting evidence regarding the structure, stability, and context-dependence of epistemological beliefs. We give evidence how theoretical and methodological issues can partly be resolved by distinguishing between relatively stable “epistemological beliefs” and situation-specific “epistemological judgments.” A qualitative content analysis of a series of semistructured interviews (study 1) with pre-service teachers, teachers, and teacher educators as well as a statistical analysis of pre-service teachers’ extensive answers in questionnaires (study 2), both on the topic of “mathematical discovery,” reveal not only beliefs of the participants but also different qualities of judgments. Therefore, in further research both aspects of beliefs should be considered in a more differentiated manner when categorizing belief structures.

Mathematical Creativity and Its Subdomain-Specificity. Investigating the Appropriateness of Solutions in Multiple Solution Tasks

In mathematics education, researchers often talk about mathematical creativity. However, we see a lack of research on the question of whether such an ability exists for mathematics in general; or whether mathematical creativity should rather be viewed subdomain-specifically; for instance, in the contexts of geometry, algebra, or arithmetic separately. In this paper, we present results of an empirical study investigating upper secondary school students’ performances in Multiple Solution Tasks (MSTs). First, we elaborate on the notion of appropriateness and its influence on the investigation of creativity; and illustrate implications based on the given data. Second, we give an insight into students’ performances along three different MSTs from different mathematical domains and point out correlations between students’ performances in two domains: geometry and algebra. Our results do not support the construct of domain-specific or subdomain-specific creativity, but indicate that mathematical creativity should be considered task-specifically.

Mathematische Begabung in den Sekundarstufen erkennen und angemessen aufgreifen

Es wird eine Konzeption fur Fortbildungen vorgestellt, die fur Workshop‐Slots von 2–3 Stunden Lange gedacht ist. Dabei wird das Thema mathematische Begabung aus verschiedenen Blickwinkeln beleuchtet. Neben grundsatzlichen Uberlegungen zum Begabungsbegriff wird das Erkennen mathematisch begabten Handelns im Unterricht ebenso thematisiert wie Moglichkeiten der Forderung innerhalb und auserhalb des Klassenunterrichts.

Bericht des Arbeitskreises „Problemlösen“

Problemlösen gewinnt zunehmend an Bedeutung in der Schule. Dies spiegelt sich in den Bildungsstandards und Bildungsplänen wider. Entsprechend bedarf es der Entwicklung geeigneter Unterrichtskonzepte und Aufgaben einerseits, andererseits aber auch Programme für die Lehramtsausbildung und nicht zuletzt für die Lehrerfortbildung. Anhand konkreter Beispiele werden zentrale Aspekte des Problemlösens dargelegt und Erfahrungen aus der Arbeit mit Studierenden und aus der Lehrerfortbildung berichtet. Dabei werden auch Daten aus Forschungsprojekten vorgestellt.

Epistemological Judgments in Mathematics: An Interview Study Regarding the Certainty of Mathematical Knowledge

Research on personal epistemology is confronted with theoretical issues as there exist conflicting data regarding its coherence, discipline-relation and contextdependence as well as methodological issues regarding the often used questionnaires to measure epistemological beliefs. We claim that it is necessary to distinguish between relatively stable “epistemological beliefs” and situationspecific “epistemological judgments”. In a sequence of interviews with regard to the topic of “certainty of mathematical knowledge”, we show that the usual categories used in questionnaires to measure epistemological beliefs have to be differentiated. We argue that epistemological judgments provide a promising framework to interpret the statements of the interviewees.