Abstract
It can be often observed that some school students can use taught knowledge in new contexts, while others although familiar with the taught algorithms are not able to apply their knowledge in new contexts. The chapter starts from this observation. The main focus is consideration of these inter-personal differences as an effect of the teachers’ didactical variability (Sarrazy 2002) in the domain of word problems. Students of teachers with weak didactical variability in the domain of word problems are strong in standard problems, while those of teachers with advanced didactical variability may be weaker in them but better performing when solving non-standard, non-algorithmic problems (see e.g. Novotná, J., & Sarrazy, B. (2009). Teacher’s didactical variability and its role in mathematics education. In: Proceedings of CERME 6. Lyon, in print). The text deals with the crucial question how to increase teachers’ didactical variability.
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Notes
- 1.
In the text the word student refers to school students and teacher trainees to pre-service teachers.
- 2.
The following terminology is used: Coding of word problem assignment is the transformation of the word problem text into a suitable system (reference language) in which data, conditions and unknowns can be recorded in a more clearly organized and/or more economical form. The result of this process is called a model (in both cases—models taught by teachers or models as results of the inner need of the solver). The reference language contains basic symbols and rules for creating a model. There exist different reference languages for any one type of word problem.
- 3.
Topaze effect . When the teacher wants the pupils to be active (find themselves an answer) and when they can’t, then the teacher suggests disguises the expected answer or performance by different behaviours or attitudes without providing it directly. Example: Teacher: 6 × 7? Pupils: 56. Teacher: Are you sure?
- 4.
The course was originally designed for teacher training of prospective teachers of mathematics and English language. It is run in English. Regardless of this fact, also students who are prospective teachers of other non-language subjects and foreign languages (and moreover, not only language specialists) participate. This feature enriches the course in the multilingual perspective. It is easily adaptable for the practicing teacher training.
- 5.
See e.g. Martel (1999). Culturally colored didactics: The sociopolitical at the heart of second/foreign language teaching in Francophone geolinguistic spaces. Instructional Science, Vol. 27, Numbers 1–2, pp. 73–96. or http://www.e-learning-baltics.de.
- 6.
Translation from French by J. Novotná. Original text: « non pas seulement à passer au stade opératoire formel mais à construire un clavier de registres cognitifs. Ce clavier permet à la demande, et en cas de besoin, d’examiner un problème et de le résoudre au niveau fonctionnel, c’est-à-dire pratique et objectif, ou d’en extraire la quintessence opératoire et de construire ainsi un modèle plus général de l’activité. »
- 7.
Original text: « Un élève a des connaissances en mathématiques s’il est capable d’en provoquer le fonctionnement comme outils explicites dans des problèmes qu’il doit résoudre […] s’il est capable de les adapter lorsque les conditions habituelles d’emploi ne sont pas exactement satisfaites pour interpréter des problèmes ou poser des questions à leurs propos ».
- 8.
Hyperadaptation is a term which refers to features overly well adapted to their present function (Rudnick, D., Burian, R.: Hyperadaptation—Another Missing Term in the Science of Form. http://scholar.lib.vt.edu/theses/available/etd-6797-111852/unrestricted/etd.pdf)
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This research was supported by the project MEB 020904 in the programme Partenariat Hubert-Curien (PHC) Barrande.
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Novotná, J., Sarrazy, B. (2011). Didactical Variability in Teacher Education. In: Zaslavsky, O., Sullivan, P. (eds) Constructing Knowledge for Teaching Secondary Mathematics. Mathematics Teacher Education, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09812-8_7
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