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Kathryn Lavin Brave; Izzy Berman; Debita Basu; Alexis Szkotak – TEACHING Exceptional Children, 2025
Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…
Descriptors: Teaching Methods, Manipulative Materials, Fractions, Mathematical Concepts
Yuling Zhuang – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
Proof validation plays a significant role in students' understanding and learning of mathematical proofs. Recent studies have shown that university students were lacking skills in proof validation and were challenged by the implementation of the appropriate acceptance criteria when validating proofs. Drawing on Habermas' construct and rational…
Descriptors: Mathematical Concepts, Mathematics Instruction, Validity, Mathematical Logic
María Trigueros; Angel Can Cabrera; Mario Sánchez Aguilar – ZDM: Mathematics Education, 2024
This study contributes to the literature on linear algebra instruction by designing and researching a teaching sequence based on APOS Theory to introduce engineering students to vector spaces. The sequence offers students multiple opportunities to understand the concept. Another contribution is the evidence that introducing prerequisite…
Descriptors: College Students, Engineering Education, Mathematics Instruction, Algebra
James Russo; Jane Hubbard – Australian Primary Mathematics Classroom, 2023
Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…
Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Concept Formation
Karina J. Wilkie – Mathematics Education Research Journal, 2024
Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…
Descriptors: Algebra, Mathematics Instruction, Mathematical Concepts, Grade 10
Ronald G. Foley Jr. – ProQuest LLC, 2024
This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to…
Descriptors: Mathematics Instruction, Mathematical Logic, High School Students, Problem Solving
Margaret Walton; Janet Walkoe – Mathematics Teacher: Learning and Teaching PK-12, 2025
Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…
Descriptors: Mathematics Instruction, Prior Learning, Knowledge Level, Algebra
Harel, Guershon – ZDM: Mathematics Education, 2021
The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Concepts
Laudano, Francesco – International Journal of Mathematical Education in Science and Technology, 2022
We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Geometry
Patrick L. Sullivan; Joann E. Barnett; Kurt Killion – Mathematics Teacher: Learning and Teaching PK-12, 2023
This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…
Descriptors: Fractions, Mathematical Logic, Mathematics Instruction, Teaching Methods
Hawthorne, Casey; Gruver, John – Mathematics Teacher: Learning and Teaching PK-12, 2023
The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…
Descriptors: Algebra, Symbols (Mathematics), Mathematical Logic, Mathematics Skills
Soosloff, Elisa; Huey, Maryann; Alexander, Daniel S. – PRIMUS, 2023
In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…
Descriptors: Mathematics Instruction, Visual Aids, Prior Learning, Teaching Methods
Ceneida Fernández; Mar Moreno; Gloria Sánchez-Matamoros – ZDM: Mathematics Education, 2024
Research has shown that there is a need to examine prospective teachers' development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16-18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing…
Descriptors: Secondary School Teachers, Adolescents, Secondary School Students, Thinking Skills
Dixon, Juli K. – Solution Tree, 2023
How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…
Descriptors: Multiplication, Grade 3, Grade 4, Grade 5
Zhao, FangFang; Schuchardt, Anita – International Journal of STEM Education, 2021
Scientific ideas are often expressed as mathematical equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these…
Descriptors: Equations (Mathematics), Mathematical Concepts, Problem Solving, Teaching Methods