Algebraic thinking

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Connections between algebraic thinking and reasoning processes

International audienceThe aim of the present study is to investigate the relationship of algebraic thinking with different types of reasoning processes. Using regression analyses techniques to analyze data of 348 students between the ages of 10 to 13 years old, this study examined the associations between algebraic thinking and achievement in two tests, the Naglieri Non-Verbal Ability Test and a deductive reasoning test. The data provide support to the hypothesis that a corpus of reasoning processes, such as reasoning by analogy, serial reasoning, and deductive reasoning, significantly predict students' algebraic thinking

The effect of two intervention courses on students' early algebraic thinking

International audienceThe aim of this study is to investigate the nature and content of instruction that may facilitate the development of students' early algebraic thinking. 96 fifth-graders attended two different intervention courses. Both courses approached three basic content strands of algebra: generalized arithmetic, functional thinking, and modeling languages. The courses differed in respect to the characteristics of the tasks that were used. The first intervention included real life scenarios, and semi-structured tasks, with questions which were more exploratory in nature. The second intervention course involved mathematical investigations, and more structured tasks which were guided through supportive questions and scaffolding steps. The findings, yielded from the analysis of pre-test and post-test data, showed that the first course had better learning outcomes compared to the second, while controlling for preliminary differences regarding students' early algebraic thinking

Investigating early algebraic thinking abilities: a path model

International audienceThe introduction of algebra in the elementary school mathematics is expected to navigate students from concrete, arithmetical thinking to increasingly complex, abstract algebraic thinking required in secondary school mathematics and beyond. Yet, empirical studies exploring this idea are relatively scarce. Drawing on a sample of 684 students from grades 4, 5, 6, and 7, this study explored a path model which tested associations between students' abilities in solving different types of early algebraic tasks: generalized arithmetic, functional thinking, and modeling languages. Results emerging from latent path analysis showed that students were more successful in generalized arithmetic tasks and only when this was achieved they were able to solve functional thinking tasks; once these were achieved, they could proceed to solve modeling languages tasks. Qualitative analysis of students' solutions provided further insight into these findings

The role of generalized arithmetic in the development of early algebraic thinking

International audienceThe purpose of this study is to characterize early algebraic thinking in relation to students' understanding of generalized arithmetic concepts and procedures. The participants of the study were 203 Grade 6 students. Data were collected from two tests which focused on number, operations, equivalence, and equality properties. The first test included arithmetic tasks which could be solved by either strategies based on calculations or strategies based on arithmetic structure, while the second test included algebraic tasks which involved letters-symbolic representations. The results indicate that students who were able to solve arithmetic tasks using arithmetic structure were also able to solve algebraic tasks. The findings imply that generalized arithmetic abilities underpin the syntactical manipulation of algebraic expressions and exemplify why seeing structure is a highly important process of early algebraic thinking

Algebraic Thinking

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Algebraic Thinking

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Introduction to the papers of TWG03: Algebraic Thinking

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Algebraic thinking

In CERME12, the Thematic Working Group 3, ‘Algebraic Thinking’, continued its work from previous CERME conferences. We had a total of 27 papers and three posters with a total of 39 people in the group. Participants represented countries from Europe and other continents: Canada, Cyprus, Denmark, Finland, France, Germany, Greece, Hungary, Italy, Norway, Spain, Sweden, The Netherlands, United Kingdom, and the United States of America. The papers loosely centred around six themes. These were: Generalisation and Pattern, Structure, Equations and Variables, Theoretical, Functional Thinking, and Algebraic Thinking. We discuss each of these themes [in this paper].</p