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Direct linkKeith 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
Zambak, Vecihi S.; Magiera, Marta T. – International Journal of Mathematical Education in Science and Technology, 2020
We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in collective argumentation while solving crypto-arithmetic…
Descriptors: Preservice Teachers, Preservice Teacher Education, Elementary School Mathematics, Middle School Mathematics
Uygun, Tugba – International Journal of Mathematical Education in Science and Technology, 2020
The purpose of this study is to investigate pre-service middle-level mathematics teachers' noticing of student mathematical thinking and teacher identity in the context of virtual professional experimentation performed through the Story"Circles" model. This study examined how pre-service middle-level mathematics teachers' education…
Descriptors: Preservice Teachers, Mathematics Teachers, Middle School Teachers, Mathematics Instruction
Lommatsch, Christina W.; Moyer-Packenham, Patricia S. – International Journal of Mathematical Education in Science and Technology, 2020
Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, 'If H … , then C … ', where 'H' is a hypothesis and 'C' is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested a…
Descriptors: Mathematical Logic, Logical Thinking, Mathematics Skills, Thinking Skills
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
