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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
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
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
Peer reviewed
Burton, Martha B. – For the Learning of Mathematics, 1988
A major component of student difficulty with algebra is the inability to make sense of the algebra symbol system as a language. Accordingly, remedies should be sought by considering algebra in a linguistic sense. (PK)
Descriptors: Algebra, College Mathematics, Communication Skills, Linguistics
Peer reviewed
Samurcay, Renan – For the Learning of Mathematics, 1985
This study concerned conceptual difficulties of college students learning programming and ways the teacher can simplify the process. An analysis of general strategies used in solving problems involving loops is given, with four types of hierarchical strategy categorized. Students had difficulty transforming their algebraic descriptions into…
Descriptors: Algebra, College Mathematics, Computer Science Education, Educational Research
Peer reviewed
Watson, Jane M. – For the Learning of Mathematics, 1988
Presents a selection of solutions of the "Three Hungry Men" problem from grade three to college students with three different strategies used: backward, forward, and forward/backward strategies. Provides error patterns in each strategy. Discusses some implications for teaching of problem solving. (YP)
Descriptors: Algebra, College Mathematics, Elementary School Mathematics, Error Patterns
Peer reviewed
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