2 Algebra From a Symbolization Point of View

Kaput, James J.; Blanton, Maria; Moreno, Luis Felipe Romero

doi:10.4324/9781315097435-3

Cited by 58 publications

(131 citation statements)

References 1 publication

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“…A qualitative distinction between these two ways of conceptualizing the relationship-that is, having either a particular or a general view of the relationshipmight be understood in terms of one's capacity for symbolization. Kaput, Blanton, and Moreno (2008) argued that generalizing and symbolizing are inherently linked in that generalizing requires one to use an expression-either a conventional or unconventional representation-to symbolize multiple instances in a unitary way. We suggest that although children who conceptualized a relationship as a particular sequence of cases (i.e., Levels 2 or 4) perceived an underlying relationship, they did not yet have a representational means to compress multiple instances into a unitary form that could symbolize these instances.…”

Section: Discussionmentioning

confidence: 99%

“…In perhaps the same way a child might not yet view "5" as a composed object and instead see it as a partitioned set of 5 units (ones), we maintain that at this level, children had not yet composed the underlying recursive pattern as a generalization over a class of instances. In other words, children did not yet understand-or "see"-the sameness in each instance in a way that allowed them to articulate the pattern as a generality in a unitary form (Kaput, Blanton, & Moreno, 2008).…”

Section: Maggiementioning

confidence: 99%

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A Learning Trajectory in 6-Year-Olds' Thinking About Generalizing Functional Relationships

Blanton¹,

Brizuela

Gardiner³

et al. 2015

JRME

109

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The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional relationships. We employed design research and analyzed data qualitatively to characterize the levels of sophistication in children's thinking about functional relationships. Findings suggest that children can learn to think in quite sophisticated and generalized ways about relationships in function data, thus challenging the typical curricular approach in the lower elementary grades in which children consider only variation in a single sequence of values.

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Section: Discussionmentioning

confidence: 99%

Section: Maggiementioning

confidence: 99%

A Learning Trajectory in 6-Year-Olds' Thinking About Generalizing Functional Relationships

Blanton¹,

Brizuela

Gardiner³

et al. 2015

JRME

109

View full text Add to dashboard Cite

show abstract

“…One of the pattern materials is generalization of linear patterns. Generalization is defined as the process of finding similarities in each example or case, so that it applies in general (Brief, 2003;Kaput, 2008;Kaput, Blanton, & Moreno, 2008). While the linear pattern is a pattern that has the first difference that is constant and the terms are formulated with = + (Stacey, 1989).…”

mentioning

confidence: 99%

Generalization Strategy of Linear Patterns From Field-Dependent Cognitive Style

et al. 2019

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Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students’ failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors’ components such as the experience of field-dependent type students. For this reason, this study was carried out to explore the thinking process of students who fail and investigate the thinking processes of students who succeed in generalizing linear patterns. The results of this study provide an effective learning strategy solution for field-dependent students in generalizing linear patterns. This study employed a qualitative approach with a case study design to junior high school students. The results indicated that students in the field-dependent cognitive style looked at pattern questions represented in the form of geometric images globally without looking at the structure of the image. Two strategies for generalizing linear patterns used by field-dependent students were examined, namely recursive and different strategies.

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“…Citamos como exemplo o 12º ICMI Study 2 em 2001, que foi dedicado ao ensino de Álgebra e falou da necessidade de desenvolver nos estudantes a capacidade de abstração (Stacey;Chick, 2004). Encontramos pesquisadores que discutem e investigam sobre as deficiências no ensino e aprendizagem da Álgebra Kaput, 2005;Moreno, 2008;Ribeiro;Cury, 2015;Wasserman, 2016).…”

Section: A áLgebra Sob O âMbito Escolarunclassified

A história da álgebra e o pensamento algébrico: correlações com o ensino

Coelho

Aguiar

2018

Estud. av.

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RESUMO O ensino de Álgebra tem se restringido a questões técnicas e operacionais, deixando de lado, muitas vezes, o desenvolvimento de conceitos e do pensamento algébrico. Acreditamos que esse enfoque está por trás das deficiências diagnosticadas em várias pesquisas e avaliações governamentais. Neste texto, apresentamos como os conceitos que foram relevantes para o desenvolvimento da álgebra ao longo dos séculos podem e devem participar do processo de ensino da álgebra.

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2 Algebra From a Symbolization Point of View

Cited by 58 publications

References 1 publication

A Learning Trajectory in 6-Year-Olds' Thinking About Generalizing Functional Relationships

A Learning Trajectory in 6-Year-Olds' Thinking About Generalizing Functional Relationships

Generalization Strategy of Linear Patterns From Field-Dependent Cognitive Style

A história da álgebra e o pensamento algébrico: correlações com o ensino

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