Volume 38 (October 2006) Number 5


Zentralblatt für Didaktik der Mathematik

Articles • Electronic-Only Publication • ISSN 1615-679X

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Practice makes perfect on the blackboard: A cultural analysis of mathematics instructional patterns in Taiwan

Bih-jen Fwu, National Taiwan University (Taiwan)

Hsiou-huai Wang, National Taiwan University (Taiwan)

Abstract: Studies show a sharp difference in math achievement between students in the U.S. and students in several East Asian countries, amongst them Taiwan. It is suggested that the patterns of math instruction applied by teachers may have contributed to these differences. This study intends to investigate the patterns of math instruction applied by the Taiwanese teachers and to delve into the cultural roots of these patterns. Data source includes videotaping of instruction by three middle school math teachers and a questionnaire survey of 297 eighth-graders. It was found that the Taiwanese math instruction pattern may be summarized as a cultural activity of “practice makes perfect, on the blackboard.” The underlying cultural beliefs are further explored, including the incremental view of human intelligence, self-improvement through diligent effort, and the teacher’s role as an authority figure.
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Using International Research to Contest Prevalent Oppositional Dichotomies
David ClarkeUniversity of Melbourne (Australia)

Abstract: International comparative research has the capacity to problematise our most basic assumptions. Dichotomies such as teacher-centred versus student-centred classrooms, telling versus not-telling, speaking versus listening, and even teaching versus learning can restrict educators and educational theorists to a fragmented view of the classroom. Constructing such dichotomies as oppositional creates a set of false choices, sanctifying one alternative, while demonising the other. International research offers insight into possible explanatory frameworks within which such dichotomies are no longer oppositional, but instead can be seen as complementary and fundamentally interrelated. The acceptance of such complementarities is a first step towards an inclusive theory of classroom practice and learning
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How much time do students have to think about teacher questions? An investigation of the quick succession of teacher questions and student responses in the German mathematics classroom
Aiso Heinze, University of Munich (Germany), Markus Erhard, Krumbach (Germany)

Abstract: Several studies have shown that the style of the German mathematics classroom at secondary level is mostly based on the so called “fragend-entwickelnde” teaching style which means develop­ing the lesson content by a teacher directed sequence of teacher questions and student responses. In this article we describe a study on the time the students have for thinking about a teacher question in the public classroom interaction. Our investigation is based on a re-analysis of 22 geome­try lessons from grade 8 classes which mainly deal with a challenging proving content. The results show that the average time between a teacher question and a student response is 2.5 seconds. There are no remarkable differences between different phases of the lessons like comparing homework, repetition of content or working on new content. Moreover, for 75% of the teacher questions the first student was called to answer within a three second time interval.
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Cognitive level in problem segments and theory segments
University of Zurich (Switzerland)
Frank Lipowsky, University of Kassel (Germany)
Christine Pauli, University of Zurich (Switzerland)
Kurt Reusser,
University of Zurich (Switzerland)
Eckhard Klieme, German Institute for International Educational Research, Frankfurt (Germany)

Abstract: Problems play an important role in mathematics instruction and are therefore frequently seen as central points of application for measures of instructional development.The research project “Quality of instruction and mathematical understanding in different cultures” examines the cognitive level of practice problems and theory problems in a three-lesson unit on the Introduction to Pythagorean theorem: Analogously to the TIMSS 1999 video study, a differentiation was made between the cognitive level of problem statement and the cognitive level of problem implementation. Additionally, the lesson time was also divided into practice and theory segments. The results show that teachers with a high proportion of connection activities in practice segments do not necessarily also spend a greater proportion of time on an analogous level for theory.
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Video technology in the assessment of an in-service teacher learning program –Differences in mathematics teachers’ judgements on instructional quality
Sebastian Kuntze,
University of Munich (Germany)

Abstract: Video technology offers the possibility to make instructional situations available for discussion in teacher learning projects. For the confrontation with videotaped instructional situations, the teachers’ rating of characteristics for instructional quality plays an imminent role. As criteria for instructional quality are often linked to the goals of the teacher learning project, the teachers’ views offer possibilities to evaluate these projects. For the example of instructional situations in German classrooms concerning geometrical proof, differences in judgements on instructional quality are analysed. The study focuses on data of a cluster analysis showing initial divergencies in the rating of videotaped instructional situations and it describes how the teachers’ views evolve.
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Learning with Classroom Videos: Conception and first results of an online teacher-training program
Kathrin Krammer, University of Zurich (Switzerland)
Nadja Ratzka, German Institute for International Educational Research (Germany)
Eckhard Klieme,
German Institute for International Educational Research (Germany)
Frank Lipowsky, University of Kassel (Germany)
Christine Pauli, University of Zurich (Switzerland)
Kurt Reusser, University of Zurich (Switzerland)

Abstract: Within the framework of a yearlong teacher education program we examined the conditions and effectiveness of learning with classroom videos. In online phases and face-to-face sessions (blended learning), 20 teachers from two different countries (Germany and Switzerland) analyzed videos of their own math-lessons and math-lessons of other teachers. Using different instruments, the training program was evaluated from a scientific perspective. The evaluation aimed to obtain information about processes within the training, about the acceptance of the training by the teachers and about changes of the professional knowledge and the patterns of perception of teaching processes of the teachers.
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