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Tiffany Berman; Casey Hord – Insights into Learning Disabilities, 2024
Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships…
Descriptors: Mathematics Instruction, Visual Aids, Problem Solving, Arithmetic
Phillips, Matthew; Robb, Kayla; Shipman, Barbara A. – PRIMUS, 2023
In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and…
Descriptors: Capstone Experiences, Algebra, Mathematics Education, Mathematics Instruction
Holton, Derek – Australian Mathematics Education Journal, 2023
This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…
Descriptors: Mathematics Activities, Mathematics Education, Arithmetic, Learner Engagement
Peyser, Elizabeth E.; Bobo, Jessica – Mathematics Teacher: Learning and Teaching PK-12, 2022
Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…
Descriptors: Number Concepts, Elementary School Mathematics, Arithmetic, Computation
Lou, Hongwei – International Journal of Mathematical Education in Science and Technology, 2023
In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…
Descriptors: Mathematics Instruction, Addition, Multiplication, Arithmetic
Marah Sutherland; David Furjanic; Joanna Hermida; Ben Clarke – Intervention in School and Clinic, 2024
This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…
Descriptors: Number Concepts, Arithmetic, Mathematics Instruction, Teaching Methods
Norton, Anderson; Flanagan, Kyle – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two…
Descriptors: Mathematics Instruction, Arithmetic, Elementary School Students, Addition
Padrón, Miguel A.; Plaza, Ángel – International Journal of Mathematical Education in Science and Technology, 2021
Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to…
Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic
Brian Darrow Jr. – Journal of Mathematics Education at Teachers College, 2023
Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedagogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetitive drill…
Descriptors: Mathematics Education, Educational History, Teaching Methods, Arithmetic
Taylor Lesner; Marah Sutherland; Cayla Lussier; Ben Clarke – Intervention in School and Clinic, 2024
Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…
Descriptors: Number Concepts, Fractions, Arithmetic, Mathematics Skills
Csíkos, Csaba – Journal of Intelligence, 2022
The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more…
Descriptors: Metacognition, Mathematics Skills, Arithmetic, Cognitive Development
Corovic, Ellen – Australian Primary Mathematics Classroom, 2022
This article aims to outline the important role of the summary phase within a mathematics instructional model and provide six strategies to support teachers to move beyond "share time." By drawing upon good teaching strategies during the summary phase, teachers can enhance the learning experience for themselves and for their students.…
Descriptors: Mathematics Instruction, Teaching Methods, Visualization, Learning Experience
Karen C. Fuson; Shannon Kiebler; Robyn Decker – Mathematics Teacher: Learning and Teaching PK-12, 2024
The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…
Descriptors: Mathematics Instruction, Multilingualism, Teaching Methods, Teacher Student Relationship
Marianna Bosch; Angel Gutierrez; Salvador Llinares – ZDM: Mathematics Education, 2024
This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…
Descriptors: Foreign Countries, Mathematics Education, Preservice Teacher Education, Mathematics Skills
White, Dorothy Y. – Mathematics Teacher: Learning and Teaching PK-12, 2022
Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…
Descriptors: Mathematics Skills, Cooperative Learning, Problem Solving, Puzzles
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