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Alexandria A. Viegut; Percival G. Matthews – Grantee Submission, 2023
Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…
Descriptors: Fractions, Mathematics Skills, Number Concepts, Skill Development
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Alexandria A. Viegut; Percival G. Matthews – Developmental Psychology, 2023
Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…
Descriptors: Fractions, Mathematics Skills, Number Concepts, Skill Development
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Al Farra, Nabil Kamal; Al Owais, Najla Sultan; Belbase, Shashidhar – Mathematics Teaching Research Journal, 2022
The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…
Descriptors: Foreign Countries, Mathematics Instruction, Problem Solving, Word Problems (Mathematics)
Siegler, Robert S.; Im, Soo-hyun; Schiller, Lauren K.; Tian, Jing; Braithwaite, David W. – Grantee Submission, 2020
Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…
Descriptors: Logical Thinking, Arithmetic, Numbers, Fractions
Davies, Charles – A.S. Barnes & H.L. Burr, 1859
This textbook seeks to (1) present to the young mind, unacquainted with the methods of exact reasoning, the elementary principles of arithmetic in their simplest form and combination; and (2) explain and illustrate the various applications of arithmetic in the transactions of business, and thus make known its great practical utility.
Descriptors: Arithmetic, Textbooks, Logical Thinking, Mathematical Applications
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Empson, Susan B. – Teaching Children Mathematics, 2001
Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)
Descriptors: Arithmetic, Division, Elementary Education, Fractions
Van de Walle, John A. – 1998
The goal of this book is to help students make sense of mathematics and become confident in their ability to do so. Section 1: "Foundations of Teaching Mathematics," includes chapters entitled: (1) "Teaching Mathematics: Reflections and Directions"; (2) "Exploring What It Means to Do Mathematics"; (3) "Developing Understanding in Mathematics"; (4)…
Descriptors: Algebra, Arithmetic, Calculators, Class Organization