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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

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

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

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

Boggs, George; Whitacre, Ian; Schellinger, Jennifer; Champagn, Zachary; Schoen, Robert – For the Learning of Mathematics, 2018

The literature concerning students' understanding of the equal sign has focused narrowly within the context of formal mathematics. Researchers have put forth a hierarchy of conceptions of the equal sign with only the top level regarded as correct. Meanwhile, we find that the equal sign is used widely and in a variety of ways in advertising and…

Descriptors: Symbols (Mathematics), Mathematical Concepts, Concept Formation, Teaching Methods

Alshwaikh, Jehad – For the Learning of Mathematics, 2018

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

Descriptors: Mathematics Education, Visual Aids, Semiotics, Grammar

Staats, Susan – For the Learning of Mathematics, 2018

A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause,…

Descriptors: Algebra, Mathematics Activities, Persuasive Discourse, Poetry

Radakovic, Nenad; Jagger, Susan; Jao, Limin – For the Learning of Mathematics, 2018

In this article, we explore the reading and writing of mathematical poetry from our experiences as mathematics teacher educators. First, we outline how our own engagement with mathematical poetry encouraged us to incorporate it into our teaching of pre-service teachers. We describe how our initial disappointment with the mathematical content of…

Descriptors: Mathematics Instruction, Poetry, Content Area Reading, Content Area Writing

Putra, Mulia – For the Learning of Mathematics, 2018

An important issue in mathematics education in many countries has long been how to make use of students' daily life mathematics (informal mathematics) in teaching mathematics at school (formal mathematics). This communication proposes an alternative framework of mathematics education that bridges informal and formal mathematics using…

Descriptors: Ethnology, Mathematics, Mathematics Instruction, Informal Education

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