On the Development of Early Algebraic Thinking. 'Sobre el desarrollo del pensamiento algebraico temprano'.

Resumen basado en el de la publicación

Primary teachers’ algebraic thinking: example from lesson study

Previous studies have reported on primary children’s algebraic thinking and generalising in a range of problem settings but there is little evidence of primary teachers’ knowledge of algebraic thinking. In this paper the development in algebraic thinking of one primary teacher who taught a research lesson in a Japanese Lesson Study project involving teachers from three primary schools is presented. The findings suggest the need for professional learning in algebra and reasoning and indicate the value of Lesson Study.

Deepening teachers' understanding of content and students' thinking : the case of Japanese lesson study in Australian primary classrooms

Japanese Lesson Study has been adapted in many countries as a platform of professional development (Groves & Doig, 2010; Lewism Perry & Hurd, 2004). One of the critical elements of Japanese Lesson Study is detailed and careful planning of the research lesson with an explicit focus on the mathematics and students' mathematical thinking (Doig, Groves, & Fujii, 2011; Murata, 2011; Watanabe, Takahashi, & Yoshida, 2008). This presentation will share some findings from a small scale research project of the implementation of Japanese Lesson Study in three Victorian primary schools in 2012.It will focus on the way in which teachers used Japanese lesson Study to plan a structured problem solving rsearch lesson on algebraic thinking for students in Year 3 and Year 4. Insights into the two teachers' planning journey and their developing understanding of anticipated student responses and the mathematics of the problem to be used in the research lesson will be discussed. Implications regarding the implementation of Japanese Lesson Study - into Australian schools for teachers' professional learning will be drawn. 

Two of everything: developing functional thinking in the primary grades through children's literature

Traditionally algebra has been regarded as the domain of the secondary school years in Australia and many other countries. Non-mathematics teachers, parents and students often narrowly regard algebra as the manipulation of symbols adhering to tightly prescribed rules (Serow, Callingham & Muir, 2013). It is now recognised, however, that foundational ideas associated with algebraic thinking can, and should be, included in mathematics curricula in the pre-school and primary years (Bobis, Mulligan & Lowrie, 2009). This stance is reflected in the Australian Curriculum: Mathematics (Australian Curriculum Assessment & Reporting Authority, 2012) which extends key algebraic ideas to patterns and generalisations, and acknowledges that number and algebra are developed together as each enriches the study of the other. This article explores the concept of functional thinking and demonstrates how the story, ‘Two of Everything’ (Hong, 1993) is employed as a springboard for developing functional thinking with students from the early years through to upper primary schooling.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Equações de 1.º grau : estratégias e erros na resolução e simplificação de equações de 1.º grau

Relatório da prática de ensino supervisionada, Mestrado em Ensino da Matemática, Universidade de Lisboa, 2011

O desenvolvimento do pensamento algébrico de alunos do 4º ano de escolaridade : uma experiência de ensino

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014

Lendo e explorando histórias: a emergência do pensamento algébrico em crianças de 4 anos

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1º e 2º Ciclos do Ensino Básico

Desenvolvendo o pensamento algébrico no 2.º ciclo do ensino básico: o sentido dos símbolos e da generalização

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Understanding and developing structure - its importance for mathematics learning

This issue comes at a time when mathematics education research is becoming more intently focused on the development of "structure" as salient to generalised mathematics learning. Not surprisingly the attention on structure creates particular synergies with the increasingly rich field of research on algebraic thinking and arithmetic processes, particularly in the early years. In many ways, this special issue is concerned with describing the process of "structuring" that enables abstraction and generalisation. A recent MERJ special issue, Abstraction in Mathematics Education (Mitchelmore & White, 2007), illustrated theories of abstraction aligning these to notions of underlying structure. The importance of structure in the transition from school to university was also highlighted by Godfrey and Thomas (2008), and Novotna and Hoch (2008) in the previous special issue of MERJ (Thomas, 2008). In this special issue we present six papers that provide evidence of developing structure as critical for all learners of mathematics throughout schooling.

Introdução a álgebra no ensino fundamental: o “X” da questão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A análise de sequências pictóricas por alunos do 4.º ano

Relatório de estágio apresentado para a obtenção do grau de mestre em Educação Pré-Escolar e ensino do 1.º ciclo do ensino básico.

A análise de sequências pictóricas por alunos do 4.º ano

Relatório de estágio apresentado para a obtenção do grau de mestre em Educação Pré-Escolar e ensino do 1.º ciclo do ensino básico.

Influência da tecnologia no desenvolvimento do pensamento algébrico : um estudo no 1º CEB

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico.