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• Herschel's heritage and today's technology integration: a postulated parallel

  419-430

  Kenneth Ruthven

  Views:

  26

  During the early 20th century, advocacy of a range of mathematical technologies played a central part in movements for the reform of mathematical education which emphasised ‘practical mathematics' and the ‘mathematical laboratory'. However, as these movements faltered, few of the associated technologies were able to gain and maintain a place in school mathematics. One conspicuous exception was a technology, originally championed by the mathematician Herschel, which successfully permeated the school mathematics curriculum because of its:
  • Disciplinary congruence with influential contemporary trends in mathematics.
  • External currency in wider mathematical practice beyond the school.
  • Adoptive facility of incorporation in classroom practice and curricular activity.
  • Educational advantage of perceived benefits outweighing costs and concerns.
  An analogous perspective is applied to the situation of new technologies in school mathematics in the early 21st century. At a general level, the cases of calculators and computers are contrasted. At a more specific level, the educational prospects of CAS and DGS are assessed.

• Proof step analysis for proof tutoring - a learning approach to granularity

  325-343

  Marvin Schiller

  Dominik Dietrich

  Christoph Benzmüller

  Views:

  31

  We present a proof step diagnosis module based on the mathematical assistant system Ωmega. The task of this module is to evaluate proof steps as typically uttered by students in tutoring sessions on mathematical proofs. In particular, we categorise the step size of proof steps performed by the student, in order to recognise if they are appropriate with respect to the student model. We propose an approach which builds on reconstructions of the proof in question via automated proof search using a cognitively motivated proof calculus. Our approach employs learning techniques and incorporates a student model, and our diagnosis module can be adjusted to different domains and users. We present a first evaluation based on empirical data.

• Mathematical Laboratory: Semiotic mediation and cultural artefacts in the mathematics classroom

  183-195

  Maria G. Bartolini Bussi

  Views:

  91

  Aim of this presentation is to summarize the influence of Tamas Varga on the Italian research and practice concerning didactics of mathematics since the 70s of the 20th centuries. While being in Budapest for the Conference I noticed that this influence was not known by most Hungarian mathematics educators. I guess that also in Italy, only the teacher educators of my generation know Varga’s influence on the teaching and learning of mathematics in primary school. Hence I start from a brief summary of development of mathematics curriculum in Italy (mainly in primary school) in the last decades of the 20th century. I focus some elements that may be connected with Varga’s influence and, later, some recent development of them.

  Subject Classification: 97G20, 97-U6, 97A40