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Hicks, Michael D. – For the Learning of Mathematics, 2022
Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…
Descriptors: Logical Thinking, Mathematics Skills, Mathematics Education, Undergraduate Students
Cook, John Paul; Dawkins, Paul; Reed, Zackery – For the Learning of Mathematics, 2021
In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…
Descriptors: Equations (Mathematics), Mathematical Concepts, Measurement, Concept Formation
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
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
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