Caracterización del conocimiento matemático para la enseñanza del álgebra en edades tempranas en los futuros profesores de educación infantil y primaria

Pincheira Hauck, Nataly
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The purpose of this research is to characterise the mathematical knowledge mobilised by future early childhood and primary pre-service teachers for algebra instruction at an early age. To achieve this purpose, we use the perspective of Ball et al. (2008) and the Mathematical Knowledge for Teaching (MKT) model as an analytical tool. The research has adopted a mixed methodological approach and a sequential exploratory design. From this perspective, two instruments have been constructed: the MKT-Early Algebra Questionnaire (3-6) and the MKT-Early Algebra Questionnaire (6-12). We have examined empirical studies carried out in relation to the instruction of algebra at an early age and the mathematical knowledge of early childhood and primary education teachers. Likewise, we have analysed the treatment given to algebra in international curricular guidelines, the textbooks corresponding to both school stages, and the mathematical tasks designed by pre-service teachers to mobilise the beginnings of algebraic thinking and the mathematical knowledge for teaching involved in such tasks. This analysis has allowed us to establish the reference meaning of the research, which forms the basis by which we have constructed and validated the two questionnaires. The MKT-Early Algebra Questionnaire (3-6) was applied to a sample of 60 pre-service teachers of early childhood education and the MKT-Early Algebra Questionnaire (6-12) was applied to a sample of 76 pre-service teachers of primary education. The results show the limitations in the mathematical knowledge of pre-service teachers to instruct algebra at an early age. These limitations were apparent both in the domain of content knowledge (common knowledge of content; specialised knowledge of content; knowledge of the mathematical horizon) and in the pedagogical knowledge of content (knowledge of content and students; knowledge of content and teaching; knowledge of the curriculum). It is worth noting that the mathematical knowledge of both pre-primary and primary school teachers is characterised by fewer limitations with respect to common knowledge of the content and greater difficulties in the knowledge of the mathematical horizon. From the data obtained, it is concluded that it is necessary to offer training programmes for teachers to strengthen and develop the different subdomains of mathematical knowledge for the instruction of algebra at an early age ​
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