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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

Oktaç, Asuman; Trigueros, María; Romo, Avenilde – For the Learning of Mathematics, 2019

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Descriptors: Mathematics Instruction, Learning Theories, Knowledge Level, Constructivism (Learning)

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

Brown, Stacy – For the Learning of Mathematics, 2019

Recognizing identity not only as an important educational outcome but also as being inter-related to students' knowledge and practice, this paper explores an affordance of proof scripts; exploring students' identities. Specifically, drawing on data from teaching experiments and the construct of perceptual ambiguity, this paper presents an analysis…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, College Mathematics

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

Ryan, Ulrika – For the Learning of Mathematics, 2019

In this article, I examine how a focus on preciseness in the mathematics classroom could affect group activity. The preciseness relates to the ways mathematical concepts, in this case angles are described in discourse between students. In this context, I consider how 'micro-invalidations', can limit students' opportunities to learn in a social and…

Descriptors: Mathematics Instruction, Epistemology, Mathematical Concepts, Foreign Countries

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

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

Coles, Alf – For the Learning of Mathematics, 2018

This article brings an enactivist perspective to the question of what can be said about mathematics teacher learning from observations of talk (including transcript, interview and questionnaire data). From an enactivist stance, doing and knowing are equivalent and learning is a change in knowing/doing. Through an analysis of transcript data, four…

Descriptors: Mathematics Teachers, Mathematics Instruction, Teacher Behavior, Knowledge Level

Larsen, Sean – For the Learning of Mathematics, 2018

The purpose of this article is to explore the use of didactical phenomenology as an instructional design heuristic. In doing so, I will articulate ways in which didactical phenomenology can be used in conjunction with the guided reinvention and emergent models heuristics to support instructional design. This discussion will be supported by…

Descriptors: Phenomenology, Instructional Design, Heuristics, Algebra

Bussi, Maria G. Bartolini – For the Learning of Mathematics, 2018

In this paper, I wish to reply to the questions posed by Gascón & Nicolás (2017) about the (possibly) prescriptive nature of the research results in didactics of mathematics: To what extent, how, under which conditions can (or must), didactics set value judgments and normative prescriptions in order to provide criteria about how to organize…

Descriptors: Mathematics, Mathematics Instruction, Research

Maffia, Andrea; Mariotti, Maria Alessandra – For the Learning of Mathematics, 2018

Multiplication can be presented to students through different models, each one with its pros and cons. In this contribution we focus on the repeated sum and the array model to investigate the relations between the two models and those between them and multiplication properties. Formal counterparts are presented. Taking both a mathematical and…

Descriptors: Models, Numbers, Multiplication, Correlation