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Ahl, Linda; Aguilar, Mario Sánchez; Jankvist, Uffe Thomas – For the Learning of Mathematics, 2017

While distance education (DE) is often considered as a means to provide mathematical education to students in remote locations or to promote the professional development of mathematics teachers, this article reports a case showing that DE may also be useful in providing mathematical instruction to individuals who are marginalized or disadvantaged…

Descriptors: Distance Education, Mathematics Education, Educational Technology, Technology Uses in Education

Chorney, Sean – For the Learning of Mathematics, 2017

This paper approaches the concept of the circle through the framework of mathematics-as-becoming. This paper focuses specifically on how a concept can be thought of as a process, and on the implications that this might have for mathematics learning. Contrary to long-standing assumptions about mathematical concepts as ideal, inert, Platonic forms,…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Geometric Concepts

Wasserman, Nicholas; Weber, Keith – For the Learning of Mathematics, 2017

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Teaching Methods

Abtahi, Yasmine – For the Learning of Mathematics, 2017

In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

Descriptors: Problem Solving, Fractions, Addition, Children

Kontorovich, Igor'; Zazkis, Rina – For the Learning of Mathematics, 2017

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

Descriptors: Mathematics Education, Mathematical Concepts, Mathematical Applications, Definitions

Tunstall, Luke; Ferkany, Matthew – For the Learning of Mathematics, 2017

We examine the extent to which mathematics is necessary for students to flourish, a principle that consists of realizing objective goods in a lifestyle endorsed from the inside. Our conclusion is that, through the end of compulsory schooling, all students should take coursework that fosters quantitative literacy, or the ability and disposition to…

Descriptors: Mathematics Education, Role of Education, Required Courses, Numeracy

Coles, Alf; Sinclair, Nathalie – For the Learning of Mathematics, 2017

In this article, we question what is an appropriate balance of ordinal and cardinal work in the early learning of number. We see an over-emphasis, in current research and practice, on the cardinal that leads, for example, to only using small numbers. We report on empirical work we have carried out in the UK and Canada that suggests the potential…

Descriptors: Number Concepts, Computer Oriented Programs, Charts, Foreign Countries

Reinholz, Daniel L.; Gillingham, Denny – For the Learning of Mathematics, 2017

Prior learning provides the basis for new learning. Mathematics educators employ formative assessment to "elicit" and "use" student thinking as the foundation of their instruction. Yet, information can be elicited and used in a variety of ways, so not all formative assessment is equally "formative." This means that…

Descriptors: College Students, Student Evaluation, Mathematics Tests, Formative Evaluation

Zazkis, Rina – For the Learning of Mathematics, 2017

In many Canadian schools the acronym BEDMAS is used as a mnemonic to assist students in remembering the order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. In the USA the mnemonic is PEMDAS, where 'P' denotes parentheses, along with the phrase "Please Excuse My Dear Aunt Sally". In the UK the…

Descriptors: Mnemonics, Mathematics Instruction, Learning Strategies, Teaching Methods

Armstrong, Alayne – For the Learning of Mathematics, 2017

This article presents a case study of a small group of Grade 8 students performing bricolage during a classroom mathematics task. The data analysis involves the use of 'tapestries', a style of transcript that enables the consideration of both the group and individuals within the group as learning agents. I characterize bricolage as an emergent,…

Descriptors: Mathematics Instruction, Grade 8, Middle School Students, Secondary School Mathematics

Caron, France; Fellus, Osnat; Glanfield, Florence; Phakeng, Mamokgethi Setati; Maheux, Jean-Francois – For the Learning of Mathematics, 2017

Prior to the 2016 Canadian Mathematics Education Study Group/Groupe Canadien D'étude En Didactique Des Mathématiques (CMESG/GCEDM) meeting at Queen's University in Kingston a Pre-Conference session was organised to discuss the theme of "Challenges and opportunities related to linguistic and cultural diversity in research and publishing /…

Descriptors: Cultural Differences, Language Usage, Mathematics Education, Educational Research

Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P. – For the Learning of Mathematics, 2016

Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…

Descriptors: Mathematics Instruction, Numbers, Number Concepts, Mathematical Logic

Creager, Mark A.; Jacobson, Erik; Aydeniz, Fetiye – For the Learning of Mathematics, 2016

Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose…

Descriptors: Preservice Teachers, Mathematics Teachers, Pedagogical Content Knowledge, Teacher Attitudes

Tillema, Erik; Gatza, Andrew – For the Learning of Mathematics, 2016

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

Descriptors: Mathematics Instruction, Multiplication, Mathematics Skills, Thinking Skills

Roth, Wolff-Michael – For the Learning of Mathematics, 2016

It has become a truism to state that mathematical knowledge or "meaning" and the norms and practices of (school) mathematical communities are negotiated and socially constructed before individuals construct (internalize) them for themselves. In this study I suggest that the social in existing conceptualizations is based on a trivial…

Descriptors: Elementary School Mathematics, Grade 2, Mathematics Curriculum, Social Environment