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Cultural analysis of mathematical content in teacher education: the case of Elementary Arithmetic Theorems

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Abstract

This paper deals with the competence of Cultural (epistemological, historical and anthropological) Analysis of the Content (CAC), which is important for teachers’ awareness and autonomy when dealing with educational choices in a changing cultural and institutional context. We report on an 18-hour intervention in a teacher education course at the undergraduate level attended by 12 participants during the fall of 2013. The goal of the intervention was to enhance participants’ CAC in the case of Elementary Arithmetic Theorems by using the rationality construct derived from Habermas’ work. Qualitative analyses of participants’ discussions showed how the construct was gradually appropriated by them and contributed to their CAC. Trends emerging from quantitative comparisons with previous implementations of the same course provided some evidence regarding the effects of the intervention on the quality of participants’ CAC performances at the end of the course. The method chosen for participants’ assessment and their cultural background will be discussed as conditions for the success of the intervention.

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Notes

  1. These are courses for the master’s degree in mathematics at Genoa University, attended by those students who, according to the local organization of the 5-year MD curricula in the decade 2005–2015, choose the Mathematics Education option at the end of the second year.

  2. In Italy, the curriculum of master’s students in mathematics who choose the mathematics education option usually includes at least 8 credits of History of Mathematics and 8 credits of Logic and Foundations of Mathematics.

  3. After the master’s program, professional preparation takes place in a one-year closed number course (with internship in school).

  4. Anna and the other secondary school students, whose texts are analyzed during the sequence, belong to 6th to 9th grade classes involved in teaching experiments on Elementary Arithmetic Theorems.

  5. It is possible to build a formal proof in combinatorics and in modular arithmetic.

  6. Euclid’s text is proposed as translated by T. L. Heath, a current reference for translation in English but then also in Italian.

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  1. DIMA Università, Via Dodecaneso 35, 16146, Genova, Italy

    Elda Guala & Paolo Boero

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  1. Elda Guala
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  2. Paolo Boero
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Correspondence to Elda Guala.

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Guala, E., Boero, P. Cultural analysis of mathematical content in teacher education: the case of Elementary Arithmetic Theorems. Educ Stud Math 96, 207–227 (2017). https://doi.org/10.1007/s10649-017-9767-2

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