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Courtney Nagle; Deborah Moore-Russo – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
This paper provides a case study account of a preservice secondary mathematics teacher's thinking while engaging in slope tasks using dynagraphs. The data included audio recordings and screen captures of a small group of preservice teachers engaging with these tasks, with our analysis focusing on the case of Robin. Despite familiarity using slope…
Descriptors: Mathematics Education, Algebra, Thinking Skills, Mathematics Skills
Beth Cory; Amy Ray – Electronic Journal for Research in Science & Mathematics Education, 2023
In this pedagogical action research study, we, as post-secondary mathematics teacher educators, built on an existing effort to improve pre-service teachers' mathematical vocabulary understandings by intentionally addressing their struggles related to polygonal area formulas. Utilizing cognitive load theory and Bruner's levels of developmental…
Descriptors: Preservice Teachers, Preservice Teacher Education, Mathematics Instruction, Plane Geometry
Vladimir Miškovic – Australian Mathematics Education Journal, 2023
The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…
Descriptors: Algebra, Geometric Concepts, Plane Geometry, Mathematical Formulas
Megan N. Cannon – ProQuest LLC, 2021
Young adolescents build notions of figures through experiences. When young adolescents begin middle school mathematics, they already have prior assumptions and conceptualizations about shapes (Herbst, Fujita, Halverscheid, & Weiss, 2017). Over years of experiences, interactions, and exposures with a particular concept, these students develop…
Descriptors: Middle School Students, Early Adolescents, Mathematical Concepts, Concept Formation
Farris, Frank A. – PRIMUS, 2017
The "domain-coloring algorithm" allows us to visualize complex-valued functions on the plane in a single image--an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the…
Descriptors: Color, Mathematical Concepts, Mathematical Logic, Plane Geometry
West, John – Australian Primary Mathematics Classroom, 2018
The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…
Descriptors: Mathematics Instruction, Mathematical Logic, Problem Solving, Fractions
Caglayan, Günhan – Mathematics Teacher, 2016
A Steiner chain is defined as the sequence of n circles that are all tangent to two given non-intersecting circles. A closed chain, in particular, is one in which every circle in the sequence is tangent to the previous and next circles of the chain. In a closed Steiner chain the first and the "n"th circles of the chain are also tangent…
Descriptors: Geometric Concepts, Geometry, Plane Geometry, Mathematical Concepts
Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni – International Journal of Mathematical Education in Science and Technology, 2016
In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…
Descriptors: Mathematics, Mathematics Instruction, Geometry, Numbers