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Hilja Lisa Huru; Annica Andersson; David Wagner – For the Learning of Mathematics, 2023
We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…
Descriptors: Abstract Reasoning, Mathematics Education, Alienation, Relevance (Education)
Panorkou, Nicole; Germia, Erell – For the Learning of Mathematics, 2023
In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…
Descriptors: Elementary School Students, Grade 6, Mathematics Skills, Thinking Skills
Khatin-Zadeh, Omid; Farsani, Danyal; Yazdani-Fazlabadi, Babak – Cogent Education, 2022
In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…
Descriptors: Mathematical Concepts, Mathematics, Symbols (Mathematics), Concept Formation
Shipman, Barbara A.; Stephenson, Elizabeth R. – PRIMUS, 2022
Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Students, Topology
Mark A. Creager – Australian Mathematics Education Journal, 2023
Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…
Descriptors: Secondary School Students, Mathematical Concepts, Mathematics Instruction, Logical Thinking
Luke T. Reinke; Michelle L. Stephan; Jerold R. Griggs – Mathematics Teacher: Learning and Teaching PK-12, 2024
Many teachers use problems set in real or imaginary contexts to make mathematics engaging, but these problems can also be used to anchor conceptual understanding. By constructing an understanding of mathematical ideas through solving problems in contexts that make sense to students, they have a better chance of actually understanding those…
Descriptors: Middle School Mathematics, Middle School Students, Middle School Teachers, Mathematical Concepts
Khatin-Zadeh, Omid; Farsani, Danyal; Yazdani-Fazlabadi, Babak – Cogent Education, 2022
Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Problem Solving
Hinton, Vanessa; Flores, Margaret – Rural Special Education Quarterly, 2022
Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not…
Descriptors: Mathematics Instruction, Addition, Mathematical Concepts, Teaching Methods
Lingefjärd, Thomas; Hatami, Russell – Policy Futures in Education, 2020
This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…
Descriptors: Abstract Reasoning, Aesthetics, Mathematics, Mathematical Concepts
Stephan, Michelle L.; Reinke, Luke T.; Cline, Julie K. – Mathematics Teacher: Learning and Teaching PK-12, 2020
Teachers readily welcome instructional materials that situate mathematics in the real world because they provide the relevance of mathematics to students who genuinely seek the answer to the question, "When are we ever going to use math in real life?" Although using the real world as a motivational hook is often effective for engagement,…
Descriptors: Mathematics Instruction, Instructional Materials, Relevance (Education), Middle School Teachers
Ichinose, Cherie Lynn; Martinez-Cruz, Armando M. – Mathematics Teacher, 2018
The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…
Descriptors: Mathematics Instruction, Teaching Methods, Problem Solving, Common Core State Standards
Neuper, Walther A. – Acta Didactica Napocensia, 2017
This is a position paper in the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP). Experience shows, that "teaching" abstract models, for instance the wave equation in mechanical engineering and in electrical…
Descriptors: Engineering Education, Technology Uses in Education, Educational Technology, Models
Simon, Martin A. – PNA, 2016
This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…
Descriptors: Instructional Design, Sequential Learning, Mathematics Instruction, Mathematical Concepts
Yakubova, Gulnoza; Hughes, Elizabeth M.; Baer, Briella L. – Preventing School Failure, 2020
With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…
Descriptors: Autism, Pervasive Developmental Disorders, Video Technology, Mathematics Instruction
Taylor, Tara; Knoll, Eva; Landry, Wendy – PRIMUS, 2016
Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…
Descriptors: Algebra, Mathematical Concepts, Generalization, Abstract Reasoning