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Faustino, Ana Carolina; Skovsmose, Ole – For the Learning of Mathematics, 2020

Dialogue has been characterised as a communicative pattern that supports critical learning in education. Seeking to analyse this relationship, we investigated the interaction between teachers and students in two classes, a Third Grade and a Fifth Grade of São Paulo State public school. During the interaction, we identified a variety of dialogic…

Descriptors: Mathematics Instruction, Teaching Methods, Dialogs (Language), Interpersonal Communication

Staples, Megan; Lesseig, Kristin – For the Learning of Mathematics, 2020

Mathematical argumentation, justification, and proof are practices at the heart of mathematics. Yet mathematics teachers generally operate without clear definitions of these practices making it difficult to communicate expectations, decide what to accept or expect from students at different grade levels, and distinguish these activities from…

Descriptors: Mathematics Instruction, Teacher Attitudes, Learning Activities, Mathematics Teachers

Maffia, Andrea; Sabena, Cristina – For the Learning of Mathematics, 2020

Literature has already shown that gestures play a relevant role in classroom interactions between students and teacher. We integrate the perspective of Theory of Semiotic Mediation with the notion of Semiotic Bundle to illustrate how gestures can be used as "pivot signs" in semiotic chains. This means that gestures can be performed by…

Descriptors: Mathematics Teachers, Teaching Methods, Nonverbal Communication, Mathematical Concepts

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

Mahlaba, Sfiso Cebolenkosi – For the Learning of Mathematics, 2020

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

Descriptors: Geometry, Logical Thinking, Mathematical Logic, Validity

Jungic, Veselin; Yan, Xiaoheng – For the Learning of Mathematics, 2020

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

Descriptors: Number Concepts, Mathematics Instruction, Cognitive Processes, Numbers

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

Rosa, Milton; Orey, Daniel Clark – For the Learning of Mathematics, 2019

The application of ethnomathematics and mathematical modelling allow us to see a different reality and give us insight into mathematics accomplished holistically. In this context, a pedagogical action that connects ethnomathematics and the cultural aspects of mathematical modelling with its academic features is referred to as ethnomodelling. This…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Models, Cultural Pluralism

Gascón, Josep; Nicolás, Pedro – For the Learning of Mathematics, 2019

In the first part of the dialogue between theories, which gave rise to a paper in this journal, we discussed the role played by normativity in didactics. In this work, with the aim of taking a step forward in this dialogue, we state explicitly some of the postulates of the anthropological theory of the didactic. They shape the object of study, the…

Descriptors: Educational Theories, Educational Anthropology, Educational Research, Mathematics Instruction

McCloskey, Andrea; Tanner, Samuel – For the Learning of Mathematics, 2019

This paper seeks to integrate a scholarship of "ritual" with a scholarship of "improvisation" and relate the intersection thereof with mathematics teaching and learning and with mathematics education research. Drawing on their experiences as classroom teachers, as practicing improvisers, and as current education researchers,…

Descriptors: Mathematics Instruction, Creative Teaching, Mathematics Teachers, Teaching Methods

Dawkins, Paul Christian – For the Learning of Mathematics, 2019

This paper sets forth a construct that describes how many undergraduate students understand mathematical terms to refer to mathematical objects, namely that they only refer to those objects that satisfy the term. I call this students' pronominal sense of reference (PSR) because it means they treat terms as pronouns that point to objects, like…

Descriptors: Mathematics Instruction, Calculus, College Mathematics, Undergraduate Students

Venkat, Hamsa; Askew, Mike; Watson, Anne; Mason, John – For the Learning of Mathematics, 2019

In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…

Descriptors: Mathematics Instruction, Mathematical Concepts, Algebra, Mathematical Formulas

Andrà, Chiara; Rouleau, Annette; Liljedahl, Peter; di Martino, Pietro – For the Learning of Mathematics, 2019

Tensions are an integral part of mathematics teachers' practice and have been recognised as playing a pivotal role in guiding teachers' choices, and in driving teacher change. Professional development particularly elicits dilemmas. Tensions appear to be a crucial aspect of mathematics teacher education and therefore a deeper understanding of…

Descriptors: Faculty Development, Mathematics Teachers, Mathematics Instruction, Elementary School Teachers

Godino, Juan D.; Baternero, Carmen; Font, Vicenç – For the Learning of Mathematics, 2019

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

Descriptors: Problem Solving, Mathematics Instruction, Mathematical Concepts, Knowledge Level

Gjære, Åsmund Lillevik; Blank, Natalia – For the Learning of Mathematics, 2019

L.V. Zankov (1901-1977), a student and colleague of Vygotsky, developed a system of developmental education for elementary education through 20 years of extensive research. Since 2009, a number of Norwegian schools have been using textbooks in mathematics based on Zankov's system. In this article, we present and discuss the experiences of some…

Descriptors: Foreign Countries, Mathematics Instruction, Elementary School Mathematics, Mathematics Teachers