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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Lajoie, Caroline; Mura, Roberta – For the Learning of Mathematics, 2000
Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)
Descriptors: Algebra, Cognitive Processes, College Mathematics, Higher Education
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Bussi, Maria G. Bartolini; Mariotti, Maria Alessandra – For the Learning of Mathematics, 1999
Presents an exploratory study with expert university students to determine how students could reseal the rupture and restore a sense of unity between the figural and conceptual components of conic sections. Suggests certain tools of semiotic mediation which could be introduced to enable students to achieve the conceptual oversight that is possibly…
Descriptors: Abstract Reasoning, College Mathematics, Geometric Concepts, Higher Education
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Stevenson, Ian – For the Learning of Mathematics, 1999
Reflects on some aspects of learning mathematics that emerged along the way in creating a turtle-based exploratory tool for non-Euclidean geometry. Contains 14 references. (ASK)
Descriptors: College Mathematics, Computer Uses in Education, Geometric Concepts, Higher Education
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