Developing Algebraic Thinking in the Context of Arithmetic

Russell, Susan Jo; Schifter, Deborah; Bastable, Virginia

doi:10.1007/978-3-642-17735-4_4

Cited by 39 publications

(28 citation statements)

References 6 publications

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“…Representative of such mathematical convergence, early algebraic reasoning comprises and intertwines several mathematical domains including properties of operations, patterning, symbolic representation, and functions (Kaput, Carraher, & Blanton, ; Russell, Schifter, & Bastable, ; Warren, ). As with other domains such as counting and arithmetic reasoning (Steffe, ; Thomas & Tabor, ), each of the converging domains of early algebraic reasoning may be thought to have some manner of developmental progression.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms

Fisher

Thomas

Jong

et al. 2019

School Sci & Mathematics

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This paper examines the implementation of an instructional module on preservice elementary teachers’ professional noticing of children’s mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic elementary mathematics classrooms. Findings indicated that two of the three components of professional noticing (attending and interpreting) showed statistically significant increases in a treatment group that did not occur in a comparison group. The deciding component remains a challenge that warrants further research.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms

Fisher

Thomas

Jong

et al. 2019

School Sci & Mathematics

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“…Alguns autores vêm questionando essa separação entre Álgebra e Aritmética (e.g., Canavarro, 2007;Lins & Gimenez, 2001;Russell et al, 2011), argumentando que os alunos não necessitam aprender primeiramente Aritmética para só depois aprender Álgebra, pois existe uma relação intrínseca entre esses dois âmbitos da Matemática.…”

Section: O Ensino Da áLgebra Nos Anos Iniciais E Sua Problemáticaunclassified

“…Pesquisas têm demonstrado que o desenvolvimento do Pensamento Algébrico nos alunos requer que o professor prepare e implemente tarefas com objetivo de discutir, argumentar e comparar ideias matemáticas, além de buscar generalizações a partir de tarefas advindas da própria Aritmética (Canavarro, 2007;Russell et al, 2011). Porém, desenvolver tais atividades, coordenar debates nos quais os alunos explicitem suas ideias matemáticas, explorar qualquer oportunidade que surja em sala de aula para rever ou aprofundar conceitos matemáticos, depende em grande parte da profunda compreensão dos conceitos matemáticos pelo próprio professor, segundo explicita Ma 2009).…”

Section: Considerações Finaisunclassified

Conhecimento matemático para ensinar Álgebra nos Anos Iniciais do Ensino Fundamental

Ferreira

Ribeiro

2017

Zetetike

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ResumoVárias são as pesquisas, sobretudo realizadas no exterior, que evidenciam a importância do trabalho com o Pensamento Algébrico nos Anos Iniciais do Ensino Fundamental, porém elas vêm focando essencialmente o aluno e o que ele aprende, deixando o professor à margem dessa discussão. Em razão da importância, para a aprendizagem dos alunos, do conhecimento matemático para ensinar e também da potencialidade do trabalho com o Pensamento Algébrico nos Anos Iniciais, este artigo tem por objetivo debater o conhecimento matemático revelado por um grupo de professores dos Anos Iniciais, ao discutir tarefas com potencial algébrico. Os dados foram coletados no contexto de um curso de extensão de 32 horas, e os resultados evidenciam a ainda pouca familiaridade dos participantes com as questões centrais que envolvem a caracterização e o trabalho com o Pensamento Algébrico. Palavras-chave:Álgebra nos Anos Iniciais, Pensamento Algébrico, Conhecimento matemático dos professores. AbstractSeveral researches bring to front the important of Algebraic Thinking at early years (mainly at international level). But such researches focus mainly on students and their learning, leaving aside the teachers and their knowledge. Considering, in an intertwined manner, the importance and role of teachers' knowledge in students learning and the potentialities of Algebraic Thinking at early grades, this paper aims at identify and discuss the mathematical knowledge for teaching revealed by a group of teachers when discussing tasks aimed at enhancing the Algebraic Thinking. Data has been gathered in a professional development course and the results reveal some problematic issues concerning the core aspects related with Algebraic Thinking.

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“…While studying the research done on generalization (like Russel et al, 2011;Van de Walle et al, 2012;Rivera & Becker, 2005, 2007Blanton, 2008, etc) we found out that tasks requiring generalization are included in the curriculum in several countries. This is not the case with the Slovak curriculum.…”

Section: Introductionmentioning

confidence: 99%

Types of Generalization Made by Pupils Aged 12–13 and by Their Future Mathematics Teachers

Slavíčková¹

2021

sciED

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This paper seeks to establish what kind of arguments pupils (aged 12–13) use and how they make their assumptions and generalizations. Our research also explored the same phenomenon in the case of graduate mathematics teachers studying for their masters’ degrees in our faculty at that time. The main focus was on algebraic reasoning, in particular pattern exploring and expressing regularities in numbers. In this paper, we introduce the necessary concepts and notations used in the study, briefly characterize the theoretical levels of cognitive development and terms from the Theory of Didactical Situations. We set out to answer three research questions. To collect the research data, we worked with a group of 32 pupils aged 12–13 and 19 university students (all prospective mathematics teachers in the first year of their master’s). We assigned them two flexible tasks to and asked them to explain their findings/formulas. Besides that, we collected additional (supportive) data using a short questionnaire. The supporting data concerned their opinions on the tasks and the explanations. The results and limited scope of the research indicated what should be changed in preparing future mathematics teachers. These changes could positively influence the pupils’ strategies of solving not only flexible tasks but also their ability to generalize.

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Developing Algebraic Thinking in the Context of Arithmetic

Cited by 39 publications

References 6 publications

Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms

Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms

Conhecimento matemático para ensinar Álgebra nos Anos Iniciais do Ensino Fundamental

Types of Generalization Made by Pupils Aged 12–13 and by Their Future Mathematics Teachers

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