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Pier Luigi Ferrari – For the Learning of Mathematics, 2024
The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…
Descriptors: Persuasive Discourse, Mathematics Instruction, Teaching Methods, Language Usage
Dave Hewitt – For the Learning of Mathematics, 2024
The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…
Descriptors: Mathematics Instruction, Teaching Methods, Memory, Mathematics Education
Francesco Beccuti – For the Learning of Mathematics, 2025
Research in mathematics education has long identified the ideology of certainty as central to mathematical instruction and to the way in which mathematics is (mis)used in social and political discourses. As we will see, this ideology is not merely a matter of individual beliefs, but is deeply embedded in the material practices and power structures…
Descriptors: Ideology, Mathematics Education, Mathematics Instruction, Politics of Education
Anna Wallin; Paola Valero; Eva Norén – For the Learning of Mathematics, 2025
Drawing on research in the context of Swedish school-age educare and adopting a post-humanist theoretical--methodological approach, we put forward the notion of mathemat-ing to conceptualise mathematical events that emerge in out-of-school configurations of practice. In them, ethical sensibilities as affects of engagement and rejection may be…
Descriptors: Ethics, Mathematics Instruction, Child Care, Foreign Countries
Sian Zelbo – For the Learning of Mathematics, 2025
This essay examines how line graphs functioned as markers of status and authority in early 20th-century America, distinguishing intellectual elites from ordinary citizens. Despite education reformers' efforts to democratize functional thinking and graphical representation in the first decades of the century, line graphs retained their position as…
Descriptors: Mathematics Instruction, Graphs, Mathematics Skills, Educational Change
Oi-Lam Ng – For the Learning of Mathematics, 2025
This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…
Descriptors: Thinking Skills, Computation, Problem Solving, Mathematics Education
Federica Ferretti; Chiara Giberti; Sara Bagossi; Eugenia Taranto; Ferdinando Arzarello – For the Learning of Mathematics, 2024
Covariational reasoning, essential for understanding functions and modeling dynamic situations, is traditionally introduced in secondary education. This paper proposes introducing covariational reasoning in primary school settings through an artifact, the Tracer. Previous studies investigate a covariational approach to functions with younger…
Descriptors: Mathematics Instruction, Elementary School Students, Thinking Skills, Teaching Methods
Jørgen Sjaastad – For the Learning of Mathematics, 2024
Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…
Descriptors: Creative Activities, Mathematics Instruction, Teaching Methods, Learner Engagement
Gaya Jayakody; Shelton Perera – For the Learning of Mathematics, 2024
It is widely accepted that the classroom teaching practices of in-service secondary mathematics teachers can benefit from the advanced mathematics they learned during their university education. However, pinpointing explicit instances of how this advanced knowledge informs teaching practices has proven challenging for both teachers and…
Descriptors: Mathematics Instruction, Secondary School Teachers, Knowledge Level, Calculus
Sheena Tan – For the Learning of Mathematics, 2025
The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…
Descriptors: Dialogs (Language), Mathematics Instruction, Mathematics Skills, Persuasive Discourse
Shai Olsher; Aehsan Haj-Yahya – For the Learning of Mathematics, 2025
Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Geometry
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