Mathematical Reasoning: The Learner, the Teacher, and the Teaching and Learning

Spinillo, Alina Galvão; Lautert, Síntria Labres; Borba, Rute Elizabete de Souza Rosa

doi:10.1007/978-3-030-69657-3_1

Cited by 1 publication

(1 citation statement)

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“…This investigation is part of an interdisciplinary field called psychology of mathematics education, which seeks to understand the epistemological, psychological, and didactic obstacles involved in the mathematics teaching and learning processes (Carraher et al, 1988;Carrião et al, 2018;Da Rocha Falcão, 2003;Lautert et al, 2020;Spinillo et al, 2021;Utsumi, 2020). Among the theoretical contributions used in the studies of this field of knowledge, attention is drawn to the theory of conceptual fields developed by Gérard Vergnaud, which seeks to understand the dynamics involved in the process of construction of knowledge that inexorably leads to the study of a variety of situations in close relationship with the operational invariants (as fundamental properties that characterise a given concept) and the linguistic and symbolic representations that allow the representation of concepts and their relationships.…”

Section: Introductionmentioning

confidence: 99%

Solving Double and Multiple Proportion Problems in the Final Years of Elementary School

2022

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Background: Many studies analysed solutions to simple proportionality problems, but few focused on double and multiple proportionality. Objectives: Analysis of students’ solutions to double and multiple proportionality problems. Design: Quantitative and qualitative analyses of empirical data. Setting and participants: Ninety students in grades 7 to 9 in Recife, Brazil. Data collection and analysis: Participants solved, in writing, double and multiple proportionality problems and orally explained their solutions. The analysis considers performance and solution strategies. Results: Percentage of correct answers per problem and school grade ranged from 67 to 97%, with no significant differences between types of problems or grades. Partipants used scalar, functional, and mixed strategies, with higher frequency of scalar strategies for double and of functional strategies for multiple proportionality problems. Conclusions: Double and multiple proportionality problems were equally accessible. Correct answers associated with the mixed strategy suggests that students considered multiple relationships in problems’ statements.

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Section: Introductionmentioning

confidence: 99%