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Walkoe, Janet; Levin, Mariana – For the Learning of Mathematics, 2020

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

Descriptors: Algebra, Thinking Skills, Mathematics Education, Definitions

Büscher, Christian – For the Learning of Mathematics, 2020

New Artificial Intelligence methods hold the potential to transform qualitative research in mathematics education. This study introduces and uses the machine learning technology of simple neural networks to automatically analyse transcript data. This serves as the basis to reflect on the use of machine learning technology in order to uncover some…

Descriptors: Mathematics Education, Educational Research, Artificial Intelligence, Networks

Adiredja, Aditya P.; Louie, Nicole – For the Learning of Mathematics, 2020

Despite advances toward equity, mathematics education continues to be entangled with deficit discourses at every level. Here, we analyze the webs of meaning that comprise deficit discourses. We show how these discourses are supported by seemingly neutral narratives about what counts as mathematics and narratives about students from marginalized…

Descriptors: Mathematics Education, Equal Education, Social Bias, At Risk Students

Skovsmose, Ole – For the Learning of Mathematics, 2020

The article identifies three narratives about mathematics education. The first claims that mathematics is a wonderful subject, which provides a true foundation for human knowledge and progress. The second presents mathematics as a suspicious subject, which serves functions of oppression. The third highlights that mathematics has critical…

Descriptors: Mathematics Education, Social Influences, Mathematics, Political Issues

Mirin, Alison; Zazkis, Dov – For the Learning of Mathematics, 2020

Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

Descriptors: Calculus, Mathematics Education, Mathematical Concepts, Problem Sets

Ferrari, Giulia – For the Learning of Mathematics, 2020

The article discusses the role of body movement, perception and kinaesthesia in mathematical thinking and accounts for the virtuality of mathematical concepts. A first person experience with a graphing motion software (WiiGraph), which involves ample body movements and is used to draw a circle, is presented. To study the unfolding of the…

Descriptors: Mathematical Concepts, Movement Education, Perception, Mathematics Education

Sümmermann, Moritz L.; Rott, Benjamin – For the Learning of Mathematics, 2020

While design of artefacts plays a large role in mathematics education, in this paper we argue that this is not reflected in mathematics education research. Design may only be considered for publication as an appendix for or as a result of empirical research. We argue that this development, which is in line with the fading of subject-matter…

Descriptors: Mathematics Education, Educational Research, Research Design, Technology Integration

Norton, Anderson – For the Learning of Mathematics, 2019

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Descriptors: Mathematics Education, Mathematics Instruction, Instructional Effectiveness, Geometry

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)

Staats, Susan; Laster, Lori Ann – For the Learning of Mathematics, 2019

This comment on Gascón & Nicolás (2017) explores relationships between mathematics education research and conceptualizations of time. Using Fabian's critique of temporal perspectives in anthropological research (1983) and Lemke's framework of timescales (2000), we consider ways in which implicit attitudes towards time in research can position…

Descriptors: Time Perspective, Time, Teaching Methods, Mathematical Concepts

Niss, Mogens – For the Learning of Mathematics, 2019

The purpose of this paper is to discuss a phenomenon that has evolved in mathematics education research journal articles during the last three decades, namely the 'ideal-typical' research paper. By not reflecting today's multi-faceted reality of the field, the ideal-typical research paper represents a far too narrow and rigid understanding of…

Descriptors: Mathematics Education, Educational Research, Journal Articles, Text Structure

Thouless, Helen; Gifford, Sue – For the Learning of Mathematics, 2019

In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

Descriptors: Preschool Children, Pattern Recognition, Geometric Concepts, Disadvantaged Youth

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