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Demetra Pitta-Pantazi; Maria Chimoni; Constantinos Christou – International Journal of Science and Mathematics Education, 2025
This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…
Descriptors: Thinking Skills, Arithmetic, Mathematics Instruction, Algebra
Karen Zwanch; Brooke Mullins – Educational Studies in Mathematics, 2025
To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…
Descriptors: Mathematics Education, Mathematics Instruction, Teaching Methods, Algebra
Karen S. Karp; Sarah B. Bush; Barbara J. Dougherty – Mathematics Teacher: Learning and Teaching PK-12, 2025
Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…
Descriptors: Teaching Methods, Mathematics Instruction, Arithmetic, Mathematical Concepts
Daria Chudnovsky – Journal of Mathematics Education at Teachers College, 2024
This article explores the educational and philosophical contributions of Nikolai V. Bugaev, a prominent 19th-century Russian mathematician and founder of the Moscow philosophical-mathematical school. The study specifically focuses on Bugaev's textbook, "Arithmetic of Whole Numbers," analyzing Bugaev's pedagogical approaches within the…
Descriptors: Educational Philosophy, Mathematics Education, Textbooks, Content Analysis
Ding, Rui; Huang, Rongjin; Deng, Xixi – Educational Studies in Mathematics, 2023
The mathematics education literature indicates a consensus regarding the importance of developing algebraic thinking in elementary school mathematics. However, the approaches used to implement this concept vary around the world. This study examines how a popular standards-based elementary mathematics textbook series in China provides opportunities…
Descriptors: Textbooks, Mathematics Instruction, Teaching Methods, Task Analysis
Bishop, Jessica Pierson; Lamb, Lisa L.; Whitacre, Ian; Philipp, Randolph A.; Schappelle, Bonnie P. – Mathematics Teacher: Learning and Teaching PK-12, 2022
In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…
Descriptors: Thinking Skills, Problem Solving, Mathematics Instruction, Logical Thinking
Muñoz-Catalán, M. Cinta; Ramírez-García, Mónica; Joglar-Prieto, Nuria; Carrillo-Yáñez, José – Journal for the Study of Education and Development, 2022
In this article we aim to deepen our understanding of the content and nature of the early childhood teacher's knowledge, focusing on those aspects which might promote students' algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model "Mathematics Teachers'…
Descriptors: Preschool Teachers, Mathematics Teachers, Pedagogical Content Knowledge, Algebra
Marian Small – National Council of Teachers of Mathematics, 2025
This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…
Descriptors: Mathematical Concepts, Teaching Methods, Mathematics Instruction, Kindergarten
Roan, Elizabeth; Czocher, Jennifer – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…
Descriptors: Mathematics Instruction, Task Analysis, Mathematical Models, STEM Education
Chimoni, Maria; Pitta-Pantazi, Demetra; Christou, Constantinos – Journal for the Study of Education and Development, 2021
In this paper, we discuss the theoretical foundation and implementation of two alternative instructional courses that aimed to support the development of elementary school students' early algebraic thinking. Both courses approached three basic algebra content strands: generalized arithmetic, functional thinking and modelling languages. The courses…
Descriptors: Learning Activities, Algebra, Thinking Skills, Elementary School Students
Daiga, Michael; Driskell, Shannon – Mathematics Teacher: Learning and Teaching PK-12, 2021
This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…
Descriptors: Arithmetic, Visualization, Mathematics Instruction, Teaching Methods
Hornburg, Caroline Byrd; Brletic-Shipley, Heather; Matthews, Julia M.; McNeil, Nicole M. – Mathematics Teacher: Learning and Teaching PK-12, 2021
Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…
Descriptors: Elementary School Students, Mathematics Instruction, Algebra, Teaching Methods
What Works Clearinghouse, 2021
This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…
Descriptors: Mathematics Instruction, Instructional Effectiveness, Fractions, Elementary School Students
Kaya, Tugba Baran; Demir, Gönül Türkan – International Journal of Curriculum and Instruction, 2022
This research aims to give an idea of the approach of mathematics teaching in primary schools in the early years of Republic of Turkey and compare it with the current approach of teaching within the context of Mathematics Teaching Knowledge (MTK). Therefore, the sample of the study was the article entitled "Arithmetic (Mathematics) Courses in…
Descriptors: Foreign Countries, Educational History, Mathematics Education, Elementary School Mathematics
Bishop, Jessica P.; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Research in Mathematics Education, 2018
We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…
Descriptors: Thinking Skills, Numbers, Numeracy, Comparative Analysis