Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.

Ações colaborativas na formação de professores: investigação dos conceitos de padrão e generalização

Esse artigo traz reflexões sobre uma formação continuada, parte de uma pesquisa qualitativa, que teve por objetivo investigar os saberes docentes (re)construídos por professores do Ensino Fundamental, por meio do estudo de padrões e generalizações com enfoque de uma matemática para o ensino. Destaca-se nessa pesquisa o papel dos saberes que emergem da prática para construção de saberes próprios da profissão docente. O estudo baseou-se em teorias que valorizassem a apropriação de um saber matemático para o ensino, em um processo coletivo e colaborativo de formação. Os relatos dos professores nas discussões coletivas revelaram que eles, em sua maioria, se apropriaram de uma cultura matemática referente ao conteúdo de padrões e generalizações, pois conceitos relacionados a esses conteúdos e às ideias subjacentes surgiram das reflexões da prática docente e das discussões das problematizações propostas. Ao enfatizar processos de colaboração e investigação, essa formação continuada proporcionou, dentro de um contexto histórico, social e cultural, a (re)construção de novos saberes de uma Matemática para o ensino da Álgebra. This article brings reflections on continuing teacher training, part of a qualitative research that aimed to investigate the teaching knowledge (re) constructed by elementary school teachers through the study of patterns and generalizations focusing on mathematics for teaching. Stands out In this research, the role of the knowledges that emerge from practice, for the construction of specifics knowledges of teacher profession. The study based on theories that value a mathematics knowledge for teaching, in a colletive and colaborative process. The teachers reports in the colletive discussion revealed that them, in their majority, appropriated of a mathematics culture referring to the content of patterns and generalizations, since concepts related to these contents and the underlying ideas emerged from their teachers practice reflections and from proposed problematizations discussions. To emphasize collaboration and investigation this teacher training process provided, within a historical, social, cultural context, the (re) construction of new mathematics knowledge for teaching.

What mathematics knowledge for teaching is used by a Grade 2 teacher when teaching counting

Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting.Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their interconnectedness in the teaching of counting.Setting: The research was conducted in a former Model C school in the Eastern Cape province of South Africa.Method: Using a case study methodology, 15 Grade 2 mathematics lessons were observed, video recorded and transcribed. Two formal interviews based on two selected video-recorded lessons were conducted to understand this teacher’s practice. The data were analysed using Deborah Ball and colleagues’ MKfT framework.Results: The study found that Foundation Phase mathematics teaching requires the knowledge and tactful employment of all six knowledge domains as described in the work of Ball and colleagues. The Knowledge of Content and Teaching (KCT) domain, was found to be essential in teaching counting in Grade 2. The other five domains supported and informed the KCT domain.Conclusion: We suggest from the insights gained here that research examining the MKfT that competent teachers draw on in teaching Foundation Phase mathematics could assist in developing curricula for in-service and pre-service teacher education programs.