Assessing the didactic - mathematical knowledge of prospective primary school teachers on elementary algebraic reasoning

Different studies suggest the need to introduce elementary algebraic reasoning at an early age, which in current curricular proposals is only taught in Secondary Education. In this paper, the responses to a questionnaire evaluating prospective primary school teachers' didactic-mathematical knowledge regarding elementary algebraic reasoning are analysed. The aim is to provide a diagnosis of prospective primary school teachers' knowledge regarding elementary algebra and its teaching. The results will be used to develop a training programme for teachers, which ultimately ensures an effective study process in primary education. The sample consisted of 597 students from the Universities of Granada, Jaen, Public University of Navarra, Santiago de Compostela in Spain, and the University of Aveiro in Portugal. The questionnaire comprises 25 items that assess algebraic and pedagogical content knowledge in primary education. Taking into account that in these universities the groups are ad extra homogeneous and ad intro heterogeneous, entire groups were intentionally selected at each university. The quantitative analysis of the results enabled the estimation of the instrument psychometric properties (difficulty and discrimination indexes, reliability and validity). The comparison of the training programmes in mathematics and the way in which the subject is taught in the different universities reveals that current curriculum emphasizes on the psycho-pedagogical area. It also reveals an unsatisfactory disciplinary training that does not include algebraic reasoning. Results show significant differences among universities in the participants' level of knowledge in the various didactic - mathematical knowledge components. We conclude that it is necessary to improve the teachers' education programmes so they can progressively foster their pupils' algebraic reasoning. To achieve this goal these programmes should include specific training activities on elementary algebraic reasoning.