Mathematics for teaching: A form of applied mathematics

In this article we elaborate a conceptualisation of mathematics for teaching as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design and implementation of a special kind of mathematics tasks whose use in mathematics teacher education can support the development of knowledge of mathematics for teaching. Also, we discuss broader implications of the article for mathematics teacher education, including implications for mathematics teacher educators' knowledge for promoting mathematics for teaching.     

Intercultural learning in English as foreign language instruction: The importance of teachers’ intercultural experience and the usefulness of precise instructional directives

The development of intercultural competence, especially in foreign language instruction, is considered a key goal of teaching in German schools. The present article sheds light on the teaching of intercultural topics in the context of English as a foreign language (EFL). It presents the results of an analysis of data from a larger study (DESI study – Assessment of Student Achievements in German and English as a Foreign Language) bringing the intercultural experience of teachers and observable aspects of instruction into focus. Videotapes of EFL-classroom instruction of 9th and 10th grade students are analyzed in order to assess characteristic of the implementation of intercultural topics. The study reveals the impact of teachers’ intercultural experience on the quality of their intercultural instruction. Furthermore, the results indicate that precise external directives for particular lessons can help teachers put intercultural topics into practice.     

Exploiting Hierarchy in Text Categorization

With the recent dramatic increase in electronic access to documents, text categorization—the task of assigning topics to a given document—has moved to the center of the information sciences and knowledge management. This article uses the structure that is present in the semantic space of topics in order to improve performance in text categorization: according to their meaning, topics can be grouped together into meta-topics, e.g., gold, silver, and copper are all metals. The proposed architecture matches the hierarchical structure of the topic space, as opposed to a flat model that ignores the structure. It accommodates both single and multiple topic assignments for each document. Its probabilistic interpretation allows its predictions to be combined in a principled way with information from other sources. The first level of the architecture predicts the probabilities of the meta-topic groups. This allows the individual models for each topic on the second level to focus on finer discriminations within the group. Evaluating the performance of a two-level implementation on the Reuters-22173 testbed of newswire articles shows the most significant improvement for rare classes.     

What static and dynamic properties should slalom skis possess? Judgements by advanced and expert skiers

Flexural and torsional rigidity are important properties of skis. However, the flexural and torsional rigidity that lead to optimal performance remain to be established. In the present study, four pairs of slalom skis that differed in flexural and torsional rigidity were tested by advanced and expert skiers. Using a 10-item questionnaire, different aspects of the skis' performance were rated on a 9-point scale. For each pair of skis, physical measurements were compared with the ratings of the two groups of skiers. Correlations (Spearman) were then determined between (i) different mechanical properties of the skis (static and dynamic), (ii) subjective assessments of the participants, and (iii) properties of the skis and the participants' assessments. The latter showed that expert skiers rate the aspects of the skis more accurately than advanced skiers. Most importantly, expert skiers are particularly sensitive to torsion of the skis. These results suggest that such highly rated elements should be addressed in future ski designs.