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Christy Pettis; Aran Glancy – Mathematics Teacher: Learning and Teaching PK-12, 2024
As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…
Descriptors: Mathematics Instruction, Numbers, Addition, Subtraction
Samuel B. Allan; Peter K. Dunn; Robert G. McDougall – International Journal of Mathematical Education in Science and Technology, 2024
In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Addition
Leah M. Frazee; Adam R. Scharfenberger – Mathematics Teacher: Learning and Teaching PK-12, 2023
The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…
Descriptors: Mathematics Instruction, Addition, Subtraction, Mathematical Concepts
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
Jennifer M. Tobias; Neet Priya Bajwa – Mathematics Teacher: Learning and Teaching PK-12, 2024
After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…
Descriptors: Benchmarking, Fractions, Addition, Mathematics Instruction
Melissa A. Gallagher; Jennifer E. Scholla – Mathematics Teacher: Learning and Teaching PK-12, 2025
Adaptive teachers use student data to guide instruction. Learn about using an anecdotal record form to support adaptive teaching. In this article, the authors describe how teachers can use learning trajectories to make adaptive decisions to meet the needs of their students. They provide an example using the U .S. Math Recovery Council's learning…
Descriptors: Mathematics Instruction, Learning Trajectories, Developmentally Appropriate Practices, Student Needs
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
Tessa L. Arsenault; Sarah R. Powell – TEACHING Exceptional Children, 2024
Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…
Descriptors: Word Problems (Mathematics), Mathematics Instruction, Schemata (Cognition), Addition
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
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
Malola, Mayamiko; Symons, Duncan; Stephens, Max – Australian Primary Mathematics Classroom, 2020
In this article, the authors argue that teachers need to possess appropriate understanding and diverse pedagogies to successfully move learners from additive to multiplicative thinking. Herein, they offer five pedagogical strategies that teachers can use to help students make this transition. Some of the challenges of learning multiplicative…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Thinking Skills
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
Hamdan, May – International Journal of Mathematical Education in Science and Technology, 2019
The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Logic
Cetin, Hatice – Universal Journal of Educational Research, 2019
Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…
Descriptors: Numbers, Mathematics Instruction, Elementary School Mathematics, Mathematical Concepts
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