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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

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

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

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

Beaugris, Louis M. – For the Learning of Mathematics, 2013

In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…

Descriptors: Mathematics Instruction, Algebra, College Mathematics, Observation

Andra, Chiara – For the Learning of Mathematics, 2013

Starting from an interest in the teachers' use of diagrams and gestures during a traditional front lesson at tertiary level, this research takes a narratologic perspective to see a mathematical lesson as a story, and hence the students' notes as re-tellings of a mathematical story. The first minutes of a traditional mathematics lecture…

Descriptors: Mathematics Instruction, Teaching Methods, College Mathematics, Lecture Method

Larson, Christine; Zandieh, Michelle – For the Learning of Mathematics, 2013

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

Descriptors: Algebra, College Mathematics, Mathematics Instruction, Introductory Courses

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

Weber, Keith – For the Learning of Mathematics, 2010

Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…

Descriptors: Mathematical Concepts, Mathematics Instruction, Mathematics Education, Mathematical Logic

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2009

Mathematical knowledge used in teaching has attracted the interest of many researchers, but was mainly explored considering teaching at the elementary school level. This paper attends to mathematical knowledge used in teaching at the University level. We present a story about a student suggesting reconsideration of Cantor's diagonal method and the…

Descriptors: Mathematics Education, Mathematics Teachers, Classroom Environment, Pedagogical Content Knowledge

Berger, Margot – For the Learning of Mathematics, 2004

In this article and part 2, the author focuses on how an individual appropriates notions from the socially-sanctioned body of knowledge called mathematics. Specifically, the author is concerned with how students, to a greater or lesser extent, internalise mathematical ideas that exist in the social world (on the chalkboard, in textbooks, in the…

Descriptors: Concept Formation, Mathematics, Mathematics Instruction, Mathematics Education

De Carvalho, Ana; Cabral, Tania – For the Learning of Mathematics, 2003

Ana De Carvalho and Tania Cabral write here that they think the learning process rests heavily on the ability of speech, so they recommend placing students more and more in the position of speaking. Not happy with prompt, correct answers, they confront their students with further related questions trying to establish if they have fairly consistent…

Descriptors: Mathematics Instruction, Teacher Student Relationship, Teaching Methods, Interpersonal Communication