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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

Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2019

This study aims to explore a phenomenon of a one-off manifestation of mathematical creativity on the part of a student, against the background of her normative and not especially creative behavior--a flash of creativity. We seek to elaborate on this phenomenon in terms of the 4P (person, press, process and product) model of creativity. Namely,…

Descriptors: Creativity, Mathematics Instruction, Models, Personality Traits

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

Ingram, Jenni; Watson, Anne – For the Learning of Mathematics, 2018

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

Descriptors: Mathematics Instruction, Cooperative Learning, Interpersonal Communication, Foreign Countries

Heyd-Metzuyanim, Einhat – For the Learning of Mathematics, 2017

This theoretical paper suggests identity as a nexus of research on affect and discourse in mathematical learning. It broadens Sfard and Prusak's (2005) discursive definition of identity by building on an analytical framework that examines positioning of students at three levels: the objects described, the interactions achieved, and the alignment…

Descriptors: Mathematics Instruction, Identification (Psychology), Grade 7, Problem Solving

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

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

Morgan, Patricia; Abrahamson, Dor – For the Learning of Mathematics, 2016

We consider designs for conceptual learning where students first engage in pre-symbolic problem solving and then articulate their solutions formally. An enduring problem in these designs has been to support students in accessing their pre-conceptual situated process, so that they can reflect on it and couch it in mathematical form. Contemplative…

Descriptors: Mathematics Education, Problem Solving, Learning Processes, Reflection

Maciejewski, Wes; Barton, Bill – For the Learning of Mathematics, 2016

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

Descriptors: Mathematics Education, Mathematical Logic, Problem Solving, Imagination

Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2015

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A threeweek long solution process by a pair of ninth-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Descriptors: Attention, Grade 9, Attention Control, Educational Theories

Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth – For the Learning of Mathematics, 2015

In this article, we explore how the solving of linear equations is represented in English-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

Descriptors: Mathematics Instruction, Equations (Mathematics), Problem Solving, Algebra

Ingram, Jenni – For the Learning of Mathematics, 2014

This article examines the shifts in attention and focus as one teacher introduces and explains an image that represents the processes involved in a numeric problem that his students have been working on. This paper takes a micro-analytic approach to examine how the focus of attention shifts through what the teacher and students do and say in the…

Descriptors: Attention, Mathematics Instruction, Problem Solving, Interaction

Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta; Koike, Norio – For the Learning of Mathematics, 2014

It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…

Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Guessing (Tests)

Venkat, Hamsa – For the Learning of Mathematics, 2013

The notion of temporal range is introduced and discussed in this paper. Two dimensions of temporal range are identified: mathematical temporality relating to mathematical ideas, their precursors and horizons; and a mathematical learning temporality where what students say/do provides the ground on which future learning can be built. These…

Descriptors: Teaching Methods, Foreign Countries, Numeracy, Mathematics Instruction

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