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Asghari, Amir – For the Learning of Mathematics, 2012

The purpose of this paper is to reclaim the place of specific examples. It is argued that a plausible step in experiencing the general is to start with a certain general process that can be applied to an already known and specific-for-the-learner object; the specific object is supposed to be there to be treated as a non-specific, particular…

Descriptors: Algebra, Mathematics Instruction, Mathematical Applications

Dawkins, Paul Christian – For the Learning of Mathematics, 2012

Weber and Alcock's (2004, 2009) syntactic/semantic framework provides a useful means of delineating two basic categories of proof-oriented activity. They define their dichotomy using Goldin's (1998) theory of representation systems. In this paper, I intend to clarify the framework by providing criteria for classifying student reasoning into…

Descriptors: Semantics, Syntax, Models, Mathematical Logic

Koichu, Boris – For the Learning of Mathematics, 2012

Identifying mathematical and didactical conditions under which mathematics learners can encounter an intellectual need for defining and proving is recognized as a challenging research enterprise. This paper presents a particular configuration of conditions under which a group of pre-service mathematics teachers successfully constructed a…

Descriptors: Mathematics Education, Mathematics Teachers, Identification, Mathematical Logic

Abrahamson, Dor – For the Learning of Mathematics, 2012

Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of…

Descriptors: Learning Theories, Discovery Learning, Mathematical Concepts, Teaching Methods

Rowland, Tim – For the Learning of Mathematics, 2012

This paper describes and analyses two mathematics lessons, one with very young pupils, about subtraction, the other for lower secondary school pupils, about gradients [slopes] and graphs. The focus of the analysis is on teacher knowledge, and on the fundamental mathematical and mathematics-pedagogical prerequisites that underpin teaching these…

Descriptors: Teacher Characteristics, Subtraction, Pedagogical Content Knowledge, Students

Pais, Alexandre; Fernandes, Elsa; Matos, Joao Filipe; Alves, Ana Sofia – For the Learning of Mathematics, 2012

In the last two decades some researchers have been using elements of Critical Theory to rethink the aims and the possibilities of school mathematics. The field known as critical mathematics education has become an important research area, and has been informing teachers who felt the need to change their practices. In this article, we explore the…

Descriptors: Critical Theory, Mathematics Education, Mathematics Teachers, Teaching Methods

Beisiegel, Mary; Simmt, Elaine – For the Learning of Mathematics, 2012

In this article, we explore the influence of mathematics graduate students' experiences with the teaching assistantships and texts that they encounter in their programs on their development and identity as teachers. We look to von Foerster's notion of trivial and non-trivial machines to interpret the graduate students' experiences and explain how…

Descriptors: Graduate Students, Teaching Assistants, Preservice Teacher Education, Identification

Wright, Pete – For the Learning of Mathematics, 2012

The Math Wars have been raging since the 1990's in the United States, where the world of mathematics education has become polarised into two camps: the reformers and the traditionalists. In this article I explore the background to the Math Wars, with specific reference to conflicting ideologies of mathematics education. I draw parallels with…

Descriptors: Foreign Countries, Mathematics Curriculum, Mathematics Education, Educational Change

Long, Julie – For the Learning of Mathematics, 2011

In this article, I explore tensions of care in the context of school mathematics by examining two accounts of a classroom moment involving labelling an angle. In particular, I draw attention to how caring for students and caring for mathematical ideas interplay in complex ways by inquiring into the two accounts through ideas of care and…

Descriptors: Caring, Symbols (Mathematics), Mathematics Instruction, Mathematics Education

Khan, Steven – For the Learning of Mathematics, 2011

I argue that until ethnomathematical frameworks are explicitly used to investigate the specific mathematical practices in networks of powerful elites the term will continue to index that which is Other to "traditional" mathematics and run a risk of desubstantialization. I suggest that the field ally itself with disciplines and perspectives in…

Descriptors: Mathematics Education, Ethnology, Mathematics, Investigations

Skovsmose, Ole – For the Learning of Mathematics, 2011

Modern conceptions of critique express preoccupations with obtaining certainty and truth, with establishing foundations, and with linking knowledge and rationality. Modern conceptions of critique have been challenged, and critique has taken new formats. In particular critique has developed without demands of providing foundations for knowledge and…

Descriptors: Imagination, Mathematics Education, Mathematical Concepts, Correlation

Tillema, Erik; Hackenberg, Amy – For the Learning of Mathematics, 2011

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in…

Descriptors: Educational Research, Experiments, Mathematics, Learning

Maheux, Jean-Francois; Roth, Wolff-Michael – For the Learning of Mathematics, 2011

Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

Descriptors: Mathematics Instruction, Geometry, Learning, Critical Thinking

Foster, Colin – For the Learning of Mathematics, 2011

In this paper I take a positive view of ambiguity in the learning of mathematics. Following Grosholz (2007), I argue that it is not only the arts which exploit ambiguity for creative ends but science and mathematics too. By enabling the juxtaposition of multiple conflicting frames of reference, ambiguity allows novel connections to be made. I…

Descriptors: Mathematics Education, Figurative Language, Scientific Concepts, Mathematics Instruction

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2011

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

Descriptors: Secondary School Mathematics, Mathematics Education, Knowledge Base for Teaching, Colleges