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Camille Lund – Mathematics Teacher: Learning and Teaching PK-12, 2024
Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…
Descriptors: Mathematics Instruction, Difficulty Level, Mathematics Skills, Teaching Methods
Estela A. Vallejo-Vargas – Educational Studies in Mathematics, 2025
Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…
Descriptors: Mathematical Logic, Problem Solving, Role, Mathematical Concepts
Radford, Luis – ZDM: Mathematics Education, 2022
The overwhelming presence of a procedural meaning of equality and equations reported in previous research has led to a call for suitable pedagogical interventions to nurture a relational meaning of these concepts. This paper is a response to that call. Drawing on the theory of objectification, the first part deals with the configuration of a Grade…
Descriptors: Algebra, Mathematics Instruction, Grade 3, Elementary School Students
Rafi' Safadi; Nadera Hawa – Mathematics Teacher: Learning and Teaching PK-12, 2025
Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…
Descriptors: Mathematics Education, Mathematics Instruction, Problem Solving, Troubleshooting
Sharma, Sameer – Mathematics Teaching Research Journal, 2023
The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…
Descriptors: Mathematical Concepts, Mathematical Logic, Theories, Graphs
Lie Group Method for Constructing Integrating Factors of First-Order Ordinary Differential Equations
Feng, Yuqiang; Yu, Jicheng – International Journal of Mathematical Education in Science and Technology, 2023
This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…
Descriptors: Equations (Mathematics), Mathematical Concepts, Problem Solving, Algebra
Ismael Cabero; Carl Winsløw – International Journal of Mathematical Education in Science and Technology, 2025
The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…
Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Secondary School Mathematics
She, Xiaobo; Harrington, Timothy – Mathematics Teacher: Learning and Teaching PK-12, 2022
Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…
Descriptors: Word Problems (Mathematics), Problem Solving, Mathematics Instruction, Visual Aids
Mark McCartney – International Journal of Mathematical Education in Science and Technology, 2024
Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.
Descriptors: Mathematical Concepts, Computation, Equations (Mathematics), Geometric Concepts
Gravier, Sylvain; Ouvrier-Buffet, Cécile – ZDM: Mathematics Education, 2022
Discrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, 'gluing',…
Descriptors: Mathematical Logic, Problem Solving, Mathematical Concepts, Epistemology
Wonsavage, F. Paul – Mathematics Teacher: Learning and Teaching PK-12, 2022
Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…
Descriptors: Mathematics Instruction, Secondary School Mathematics, Problem Solving, High School Students
Robert J. Fisher – Chemical Engineering Education, 2025
Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…
Descriptors: Chemical Engineering, Mathematics, Problem Solving, Skill Development
Sacco, Donna M.; Spies, Tracy; Pfannenstiel, Kathleen – Learning Disabilities Research & Practice, 2022
Eliciting student thinking during mathematics instruction allows teachers to choose tasks with high cognitive demand while also engaging students to use productive struggle to solve mathematical problems, thus increasing their conceptual understanding. Often, students who require intensive intervention in mathematics, in particular, students who…
Descriptors: Intervention, Scaffolding (Teaching Technique), English Language Learners, Academic Language
Stewart, Seán M. – International Journal of Mathematical Education in Science and Technology, 2022
For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions x [right arrow] -- x, [pi] -- x, and [pi] + x, allow one to decide which of the…
Descriptors: Mathematics Instruction, Trigonometry, Mathematical Concepts, Equations (Mathematics)
Fox, Courtney; DeJarnette, Anna – Mathematics Teacher: Learning and Teaching PK-12, 2022
If students are asked, "What is the world water crisis?" how would they respond? In the authors precalculus classes, this question is often met with blank stares and students avoiding eye contact. Many students are unaware of the world water crisis--what it is, why it is, or who it affects. Even fewer realize the utility of trigonometry…
Descriptors: Trigonometry, Mathematics Instruction, Water, Crisis Management