Forms of mathematical interaction in different social settings: examples from students’, teachers’ and teacher–students’ communication about mathematics

The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’ joint professional discourse is about a combined learning and talking between two students before an intervention by their teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting 2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher and by the expectations of the students.

Automatic item generation of probability word problems

Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems based on templates that allow for the generation of word problems involving different topics from probability theory. It was tested in a pilot study with N = 146 German university students. The items show a good fit to the Rasch model. Item difficulties can be explained by the Linear Logistic Test Model (LLTM) and by the random-effects LLTM. The practical implications of these findings for future test development in the assessment of probability competencies are also discussed.     

Exploring the nature of divergent thinking: A multilevel analysis

In this study, a large sample with a clustered data structure from an educational context was utilized to analyze the relationship between cognitive abilities, school type, gender, and divergent thinking. The sample comprised 1098 students in 55 classrooms. A sequence of nested multilevel regression analyses revealed that processing capacity, as a core component of intelligence, as well as processing speed shared a significant amount of variance with divergent thinking. Additionally, school type affected divergent thinking even when controlling for intellectual abilities. Furthermore, a significant gender difference in divergent thinking favouring females was found. Gender differences as well as the effect of processing capacity and processing speed varied across classrooms, reflecting differences in the classroom environment. The nature of the relationships of cognitive and social factors to divergent thinking was considered.     

SIPP (The Siemens International Practical Programme): an international student exchange programme

The Siemens International Practical Programme was set up in 1975 by SIEMENS AG upon the recommendation of its national office in Sweden. The purpose of the programme is to give students of electrical engineering at technical universities the chance to gain experience related to their areas in a foreign country, an experience which they, in turn, can convey to their fellow students. Through their own observations in the Federal Republic of Germany the students also have the opportunity to learn more about Siemens — its history, its wide variety of electro-technical products, and its production facilities — than would otherwise be possible in their home countries.     

AEG-Telefunken TR 440: Unternehmensstrategie, Markterfolg und Nachfolger

Zusammenfassung  AEG-Telefunken entwickelte seit 1957 Rechner. Neben den Prozessrechnern spielten die Gro?rechner TR 4 und TR 440 eine wichtige Rolle. Von 1969 bis 1976 wurden 46 TR 440 installiert, bei einem Gesamtumsatz von 730 Mio. DM (370 Mio. Euro) [2]. In der Produktpolitik spielten die Rechner keine zentrale Rolle, obwohl eine ausgezeichnete technologische Ausgangsposition bestanden hatte und die Telefunkenrechner sp?ter nachdrückliche technologiepolitische Unterstützung erhielten. Die Entwicklung des Systems TR 440 hatte mit wesentlichen konzeptionellen und technologischen Schwierigkeiten zu k?mpfen, wozu der Mangel an qualifizierten Zulieferern und erfahrenen Mitabeitern kam. Trotzdem gelang es, bis 1970 den bislang schnellsten in Europa entwickelten Rechner [6] fertig zu stellen und Systemsoftware zu entwickeln [9], die den Produkten der Mitbewerber um Jahre voraus war. Von Anfang an hatte das Unternehmen nach geeigneten Kooperationspartnern gesucht. Mit dem Verkauf des Gro?rechnergesch?ftes an Siemens gingen die bereits laufenden Planungen für einen TR 440-Nachfolger zu Ende.

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AEG-Telefunken developed computers since 1957. Besides process control computers, the large scale computers, TR 4 and TR 440, played an important role. 46 TR 440 computers were installed from 1969 to 1976, summing up to a sales volume of 730 Mio. DM (370 Mio. Euro) [2]. AEG-Telefunken did not consider computers as a strategic part of its product policy, though the company had had an excellent technological position for this business and the Telefunken computers got vigorous political support. The development of the TR 440 system had to defeat essential conceptual and technological difficulties, besides lack of qualified suppliers and experienced personnel. Nevertheless, the company could, by 1970, develop the fastest European computer so far [6], with system software ahead of competitors by years [9]. From the beginning, the company had been looking for business partners. With the sale of the large scale computer business to Siemens, all activities on a TR 440 successor were stopped. AEG-Telefunken computer business strategy is also subject of a paper to appear in the IEEE Annals of the History of Computing.

     

‘I will do it but religion is a very personal thing’: teacher education applicants’ attitudes towards teaching religion in Ireland

There has been extensive research internationally describing teachers’ homogenous socio-demographic backgrounds and critiquing the associated equity and diversity issues, most especially with regard to ethnicity and gender, and to a lesser extent, social class and disability. Yet, teachers’ religious affiliations and/or convictions have rarely been explored. Since 96% of state primary schools in Ireland are denominational, considering religious diversity in teaching is both critically important and a complex undertaking. This paper examines primary initial teacher education (ITE) applicants’ religiosity, and views of teaching religion, in Ireland. Our data suggest low levels of religious practice and religiosity among ITE applicants, many of whom would prefer to teach religion using a non-confessional approach. The paper raises critical questions regarding the experiences, constitutional rights and professional practice of increasingly secular and/or non-practicing Catholic teacher cohorts in a predominantly Catholic primary education system that has survived the trend towards progressive ‘unchurching’ of Europe.