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Melhuish, Kathleen; Ellis, Brittney; Hicks, Michael D. – Educational Studies in Mathematics, 2020
Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Computation
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Miles, Sandra J. – Mathematics Teacher: Learning and Teaching PK-12, 2022
To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…
Descriptors: Science Instruction, Mathematics Instruction, Grade 7, Grade 6
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Rupnow, Rachel; Randazzo, Brooke – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…
Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Concept Formation
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Özcan, Bülent Nuri; Ates, Özlem – International Journal of Progressive Education, 2021
This study aims to reveal the perceptions that classroom teacher candidates have regarding the concept of computer-assisted mathematics instruction (CAMI), with the help of metaphors. Furthermore, the another aim of the study of this study consists of an analysis of whether these metaphors differed based on the teacher candidates' learning…
Descriptors: Correlation, Figurative Language, Preservice Teachers, Student Attitudes
Michael Duane Hicks – ProQuest LLC, 2021
Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…
Descriptors: Algebra, Mathematics Instruction, Learning Activities, Abstract Reasoning
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Rathnayake, Rovini; Jayakody, Gaya – International Journal of Research in Education and Science, 2023
In Sri Lankan advanced level mathematics curriculum, teachers are required only to provide the intuitive idea of the concept of limit. The purpose of this study is to explore the strategies used by mathematics teachers to achieve this. Twelve in-service secondary mathematics teachers working in government and private schools participated in the…
Descriptors: Intuition, Mathematics Instruction, Concept Formation, Mathematical Concepts
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Chin, Sze Looi; Choy, Ban Heng; Leong, Yew Hoong – Mathematics Education Research Journal, 2022
This article presents a case study on a secondary mathematics teacher, Mary (pseudonym), and her design of a set of instructional tasks in the context of proportional reasoning. In keeping with the way Singapore teachers generally conceive of instructional planning, we investigated the connections between four comparison tasks she designed through…
Descriptors: Instructional Design, Teaching Methods, Mathematics Instruction, Case Studies
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Rumbelow, Michael – For the Learning of Mathematics, 2021
"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…
Descriptors: Arithmetic, Mathematics Instruction, Mathematical Concepts, Figurative Language
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McCulloch, Allison; Lovett, Jennifer; Edgington, Cyndi – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
The purpose of this study is to examine the use of a Vending Machine applet as a cognitive root for the development of preservice teachers understanding of function. The applet was designed to purposefully problematize common misconceptions associated with the algebraic nature of typical function machines. Findings indicated affordances and…
Descriptors: Preservice Teacher Education, Preservice Teachers, Figurative Language, Mathematical Concepts
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Cipora, Krzysztof; Patro, Katarzyna; Nuerk, Hans-Christoph – Mind, Brain, and Education, 2015
The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this…
Descriptors: Arithmetic, Spatial Ability, Mathematical Concepts, Mathematics Skills
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Dawkins, Paul Christian – Journal of Mathematical Behavior, 2012
This study presents how the introduction of a metaphor for sequence convergence constituted an experientially real context in which an undergraduate real analysis student developed a property-based definition of sequence convergence. I use elements from Zandieh and Rasmussen's (2010) Defining as a Mathematical Activity framework to trace the…
Descriptors: Student Needs, Figurative Language, Mathematics Instruction, Mathematical Concepts
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Haltiwanger, Leigh; Simpson, Amber M. – Mathematics Teaching in the Middle School, 2013
As math teachers, the authors often encountered students who could ace a test but not explain their reasoning. This phenomenon was disturbing to them, and they fought for years to help students both understand mathematical concepts and develop meaning for them. Since their primary goal was to develop mathematically literate students, their…
Descriptors: Mathematics Instruction, Content Area Writing, Mathematical Concepts, Mathematical Logic
Oesterle, Susan, Ed.; Allan, Darien, Ed. – Canadian Mathematics Education Study Group, 2015
This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…
Descriptors: Mathematics Education, Time Management, Mathematics Instruction, Industry