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Keith Gallagher; Nicole Engelke Infante – International Journal of Mathematical Education in Science and Technology, 2023
Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students' reasoning in topology is…
Descriptors: Undergraduate Students, College Mathematics, Topology, Mathematics Skills
Dorner, Christian – International Journal of Mathematical Education in Science and Technology, 2021
This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…
Descriptors: Problem Sets, Geometry, Mathematics Instruction, Problem Solving
Stewart, Sepideh; Epstein, Jonathan; Troup, Jonathan – International Journal of Mathematical Education in Science and Technology, 2019
In this study, we analysed a mathematician's teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall's ["How humans learn to think mathematically: Exploring the three worlds of mathematics." Cambridge University Press] three-world model of embodied, symbolic and formal as a…
Descriptors: Mathematics Instruction, Professional Personnel, Teaching Methods, Reflection
Mkhatshwa, Thembinkosi P. – International Journal of Mathematical Education in Science and Technology, 2019
A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12…
Descriptors: Mathematics Instruction, Calculus, Mathematical Logic, Thinking Skills