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Scheiner, Thorsten; Pinto, Marcia M. F. – For the Learning of Mathematics, 2022
Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Learning Processes
Ana Patricia García-Amado; Maythe García-Rivero; José Luis Cruz-Canales; Rubén Abraham Moreno Segura; Asuman Oktaç – For the Learning of Mathematics, 2024
The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…
Descriptors: Mathematics Instruction, Teaching Methods, High School Students, Student Attitudes
Swidan, Osama; Cusi, Annalisa; Robutti, Ornella; Arzarello, Ferdinando – For the Learning of Mathematics, 2023
This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…
Descriptors: Teaching Methods, Mathematics Instruction, Inquiry, Active Learning
Peck, Frederick A. – For the Learning of Mathematics, 2022
In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…
Descriptors: Mathematics Instruction, Secondary School Students, Learning Processes, Personal Autonomy
Lewis, Gareth – For the Learning of Mathematics, 2015
In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
Descriptors: Mathematics Education, Learning Processes, Ethnography, Learning Theories
Ulrich, Catherine – For the Learning of Mathematics, 2015
This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…
Descriptors: Mathematics Education, Secondary School Mathematics, High School Students, Constructivism (Learning)

Bouvier, Alain – For the Learning of Mathematics, 1987
Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Elementary School Mathematics