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Cheeseman, Jill; Downton, Ann; Ferguson, Sarah; Roche, Anne – Mathematics Education Research Journal, 2023
Children's multiplicative thinking as the recognition of equal group structures and the enumeration of the composite units was the subject of this research. In this paper, we provide an overview of the Multiplication and Division Investigations project. The results were obtained from a small sample of Australian children (n = 21) in their first…
Descriptors: Foreign Countries, Multiplication, Thinking Skills, Arithmetic
Jérôme Proulx – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…
Descriptors: Mathematics Skills, Thinking Skills, Abstract Reasoning, Arithmetic
Urban-Rural Differences in Early Arithmetic Performance Are Accounted for by Phonological Processing
Wei Wei; Junyi Dai; Chuansheng Chen; Yingge Huang; Xinlin Zhou – Journal of Cognition and Development, 2024
Urban and rural children have different levels of performance in arithmetic processing. This study investigated whether such a residence difference can be explained by phonological processing. A total of 1,501 Chinese primary school students from urban and rural areas were recruited to complete nine cognitive tasks: two in arithmetic performance…
Descriptors: Rural Urban Differences, Arithmetic, Phonology, Language Processing
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
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
Taylan, Rukiye Didem – Journal of Mathematics Teacher Education, 2017
This study investigated a highly accomplished third-grade teacher's noticing of students' mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom…
Descriptors: Mathematical Logic, Grade 3, Multiplication, Arithmetic
Schulz, Andreas – Mathematical Thinking and Learning: An International Journal, 2018
Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…
Descriptors: Computation, Mathematics Instruction, Multiplication, Arithmetic
Izsák, Andrew; Beckmann, Sybilla; Bradshaw, Laine – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016
The present study extends recent advances coordinating research on cognition and psychometric modeling around fractions. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct components necessary for reasoning in terms of quantities when solving fraction…
Descriptors: Thinking Skills, Growth Models, Outcome Measures, Preservice Teachers
Chesney, Dana L.; McNeil, Nicole M. – Journal of Problem Solving, 2014
Many children in the U.S. initially come to understand the equal sign operationally, as a symbol meaning "add up the numbers" rather than relationally, as an indication that the two sides of an equation share a common value. According to a change-resistance account (McNeil & Alibali, 2005b), children's operational ways of thinking…
Descriptors: Thinking Skills, Arithmetic, Undergraduate Students, Interference (Learning)
Lee, Jae Ki; Licwinko, Susan; Taylor-Buckner, Nicole – Journal of Mathematics Education at Teachers College, 2013
PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…
Descriptors: Case Studies, Mathematics, Mathematics Instruction, Mathematical Logic
Johanning, Debra I.; Shockey, Kimberly S. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…
Descriptors: Fractions, Mathematics Instruction, Mathematics, Thinking Skills
Roberts, Tim – Australian Primary Mathematics Classroom, 2007
It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on…
Descriptors: Mathematical Concepts, Primary Education, Mathematics Education, Arithmetic
Arizona Department of Education, 2009
Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…
Descriptors: Numeracy, Number Concepts, Grade 3, Mathematics Education
Arizona Department of Education, 2009
Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…
Descriptors: Numeracy, Number Concepts, Grade 5, Mathematics Education
Vale, Colleen; Davies, Anne – Australian Primary Mathematics Classroom, 2007
Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…
Descriptors: Grade 5, Multiplication, Mathematics Instruction, Arithmetic
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