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Heyd-Metzuyanim, Einat – For the Learning of Mathematics, 2019

In this theoretical paper, I examine the similarities and incommensurabilties between studies using the term "beliefs", and discursive frameworks studying "identity". I start by reviewing critiques against beliefs research voiced from discourse and socio-culturally oriented researchers in the field of mathematics education. I…

Descriptors: Self Concept, Mathematics Education, Beliefs, Sociocultural Patterns

Wasserman, Nicholas – For the Learning of Mathematics, 2019

In combinatorics, combinatorial notation, e.g., C(n, r), is explicitly defined as a numerical value, a cardinality. Yet, we do not use another symbol to signify the set of outcomes--the collection of objects being referenced, whose cardinality is, for example, C(n, r). For an expert, this duality in notation, of signifying both cardinality and…

Descriptors: Mathematics Education, Mathematical Concepts, Symbols (Mathematics), Equations (Mathematics)

Dimmel, Justin; Milewski, Amanda – For the Learning of Mathematics, 2019

We describe how a group of secondary mathematics teachers posed and solved a real-world problem. The problem was posed by teachers on a sandbar off the coast of an island in the Bahamas, where panoramic views of water meeting sky spurred the teachers to wonder how far away they could see. We analyze how the teachers translated the natural…

Descriptors: Secondary School Teachers, Mathematics Teachers, Problem Solving, Relevance (Education)

Coles, Alf – For the Learning of Mathematics, 2018

This article brings an enactivist perspective to the question of what can be said about mathematics teacher learning from observations of talk (including transcript, interview and questionnaire data). From an enactivist stance, doing and knowing are equivalent and learning is a change in knowing/doing. Through an analysis of transcript data, four…

Descriptors: Mathematics Teachers, Mathematics Instruction, Teacher Behavior, Knowledge Level

Tomaz, Vanessa Sena; David, Maria Manuela – For the Learning of Mathematics, 2018

Our aim is to discuss some choices of communicational artifacts made by Maxakali Brazilian Indigenous students to register and operate with numbers in a mathematics education course, and how these choices reflect in the ongoing classroom activity. We rely on Activity Theory to analyze an activity involving them and discuss how the choice of…

Descriptors: Foreign Countries, Indigenous Populations, Minority Group Students, Mathematics Education

Davis, Brent – For the Learning of Mathematics, 2018

Based on input from several scholars, Gascón and Nicolás (2017) attempted "to start a dialogue aimed at laying the foundations for a better understanding and a scientific cooperation between different theories in Didactics." Consistent with that goal, I examine uninterrogated assumptions that shaped their analysis. I assert that such…

Descriptors: Mathematics Education, Educational Research, Educational Theories, Ideology

Paoletti, Teo; Moore, Kevin C. – For the Learning of Mathematics, 2018

Supporting students developing understandings of function has been a notoriously elusive task in mathematics education. We present Thompson and Carlson's (2017) description of a covariational meaning of function and provide an example of a student who maintains meanings compatible with this description. We use this student's activity to illustrate…

Descriptors: Mathematics Education, Mathematical Concepts, Knowledge Level, Comprehension

Larsen, Sean – For the Learning of Mathematics, 2018

The purpose of this article is to explore the use of didactical phenomenology as an instructional design heuristic. In doing so, I will articulate ways in which didactical phenomenology can be used in conjunction with the guided reinvention and emergent models heuristics to support instructional design. This discussion will be supported by…

Descriptors: Phenomenology, Instructional Design, Heuristics, Algebra

Bussi, Maria G. Bartolini – For the Learning of Mathematics, 2018

In this paper, I wish to reply to the questions posed by Gascón & Nicolás (2017) about the (possibly) prescriptive nature of the research results in didactics of mathematics: To what extent, how, under which conditions can (or must), didactics set value judgments and normative prescriptions in order to provide criteria about how to organize…

Descriptors: Mathematics, Mathematics Instruction, Research

Maffia, Andrea; Mariotti, Maria Alessandra – For the Learning of Mathematics, 2018

Multiplication can be presented to students through different models, each one with its pros and cons. In this contribution we focus on the repeated sum and the array model to investigate the relations between the two models and those between them and multiplication properties. Formal counterparts are presented. Taking both a mathematical and…

Descriptors: Models, Numbers, Multiplication, Correlation

Lai, Yvonne; Jacobson, Erik – For the Learning of Mathematics, 2018

This paper focuses on the design of tasks that situate teachers in the work of mathematics teaching. We examine a simple, yet fundamental feature of pedagogical content knowledge tasks: the extent to which pedagogical warrants are necessitated by the pedagogical context. We argue that this feature has implications for the design of tasks, as well…

Descriptors: Mathematics Instruction, Pedagogical Content Knowledge, Instructional Design, Mathematics Teachers

Boggs, George; Whitacre, Ian; Schellinger, Jennifer; Champagn, Zachary; Schoen, Robert – For the Learning of Mathematics, 2018

The literature concerning students' understanding of the equal sign has focused narrowly within the context of formal mathematics. Researchers have put forth a hierarchy of conceptions of the equal sign with only the top level regarded as correct. Meanwhile, we find that the equal sign is used widely and in a variety of ways in advertising and…

Descriptors: Symbols (Mathematics), Mathematical Concepts, Concept Formation, Teaching Methods

Culligan, Karla; Wagner, David – For the Learning of Mathematics, 2018

When deciding what constitutes students' "on task" or "off task" mathematical communication, teachers and researchers are also making judgements about what is, and what is not, mathematics. In this paper, we question our ability to separate the mathematical from the nonmathematical. We explore intersecting storylines in Grade…

Descriptors: Mathematics Activities, Mathematics Instruction, Relevance (Education), Grade 10

Alshwaikh, Jehad – For the Learning of Mathematics, 2018

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

Descriptors: Mathematics Education, Visual Aids, Semiotics, Grammar

Staats, Susan – For the Learning of Mathematics, 2018

A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause,…

Descriptors: Algebra, Mathematics Activities, Persuasive Discourse, Poetry