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Pinto, Alon; Karsenty, Ronnie – For the Learning of Mathematics, 2020

While proof is often presented to mathematics undergraduates as a well-defined mathematical object, the proofs students encounter in different pedagogical contexts may bear salient differences. In this paper we draw on the work of Dawkins and Weber (2017) to explore variations in norms and values underlying a proof across different pedagogical…

Descriptors: Validity, Mathematical Logic, Undergraduate Study, College Mathematics

Mesa, Vilma; Mali, Angeliki – For the Learning of Mathematics, 2020

We reflect on the evolution of an instrument designed to gather data about student actions with dynamic textbooks in university mathematics in a large-scale project. We also discuss the evolution of our understanding of the mediating role of this instrument in gathering data remotely that allow us to access student use and reconstruct their…

Descriptors: Textbooks, Electronic Publishing, College Students, College Mathematics

Gabel, Mika; Dreyfus, Tommy – For the Learning of Mathematics, 2020

In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman's New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by…

Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic

Lee, Hwa Young; Hardison, Hamilton L.; Paoletti, Teo – For the Learning of Mathematics, 2020

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Descriptors: Mathematics Instruction, Teaching Methods, Visual Aids, Graphs

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

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

Kontorovich, Igor' – For the Learning of Mathematics, 2018

How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…

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

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

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

McChesney, Jane; Wilson, Susanna – For the Learning of Mathematics, 2016

Two mathematics teacher educators describe their responses during a year disrupted by a serious earthquake and the ongoing effects on students and staff. We discuss our pedagogical responses to unforeseen changes in courses and in students' lives, including the re-calibrating of social relationships. We describe our work in a postgraduate course…

Descriptors: Mathematics Education, Natural Disasters, Graduate Study, Educational Change

Ribeiro, Miguel; Mellone, Maria; Jakobsen, Arne – For the Learning of Mathematics, 2016

We present excerpts from a research project initially focused on the inquiry and the development of prospective teachers' mathematical knowledge. The research started from the design of a particular task for prospective teachers built onto the request to interpret pupils' answers suitably selected. The focus of inquiry has gradually changed to…

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

Zazkis, Dov – For the Learning of Mathematics, 2015

Personification is the attribution of human qualities to non-human entities. The method of eliciting personification, which requires participants to attribute human qualities to non-human entities, takes advantage of a naturally occurring means through which (some) people discuss the emotional relationship they have with those entities. Eliciting…

Descriptors: Mathematics Education, Attribution Theory, Identification (Psychology), Preservice Teachers

Dawkins, Paul Christian – For the Learning of Mathematics, 2014

This paper demonstrates how questions of "provability" can help students engaged in reinvention of mathematical theory to understand the axiomatic game. While proof demonstrates how conclusions follow from assumptions, "provability" characterizes the dual relation that assumptions are "justified" when they afford…

Descriptors: Mathematical Logic, Teaching Methods, College Mathematics, Mathematical Concepts

Lockwood, Elise – For the Learning of Mathematics, 2014

In this article, I present the notion of a set-oriented perspective for solving counting problems that emerged during task-based interviews with postsecondary students. Framing the findings within Harel's "ways of thinking", I argue that students may benefit from this perspective, in which they view attending to sets of outcomes as…

Descriptors: Mathematics Instruction, Number Concepts, Postsecondary Education

Neumayer-Depiper, Jill – For the Learning of Mathematics, 2013

Becoming a teacher is not developing an identity, but is developing identity as a continuous process of constructing and deconstructing understandings within the complexities of social practice, beliefs, experiences, and social norms. I take up this stance on identity as articulated in Judith Butler's (1999) work with gender identity and…

Descriptors: Mathematics Teachers, Professional Identity, Teacher Education, Preservice Teachers

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