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Erik Jacobson – Investigations in Mathematics Learning, 2024
This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…
Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Instruction, Methods Courses
Liu, Qiushan; Braithwaite, David – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2023
Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…
Descriptors: Fractions, Arithmetic, Mathematical Concepts, Affordances
Kirkland, Patrick K.; Guang, Claire; Cheng, Ying; Trinter, Christine; Kumar, Saachi; Nakfoor, Sofia; Sullivan, Tiana; McNeil, Nicole M. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…
Descriptors: Middle School Students, Number Concepts, Fractions, Arithmetic
Howe, Roger – ZDM: The International Journal on Mathematics Education, 2019
This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…
Descriptors: Number Concepts, Numbers, Error of Measurement, Computation
Boby Ho-Hong Ching; Xiang Yu Li; Tiffany Ting Chen – British Journal of Educational Psychology, 2024
Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. Aims: To examine the extent to which…
Descriptors: Number Concepts, Fractions, Arithmetic, Young Children
McDowell, Eric L. – Mathematics Teacher, 2016
By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…
Descriptors: Fractions, Number Systems, Number Concepts, Numbers
Putra, Zetra Hainul – International Electronic Journal of Mathematics Education, 2019
The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…
Descriptors: Foreign Countries, Preservice Teachers, Mathematics Education, Numbers
Chin, Kin Eng; Jiew, Fui Fong – EURASIA Journal of Mathematics, Science and Technology Education, 2019
This article focuses on how two mathematics teachers (Amy and Beth -- pseudonyms) cope with the changes of meanings in multiplication due to the changes of contexts. It highlights the qualitative similarities and differences between these two teachers in the sense-making process of multiplication. A potentially useful framework of supportive and…
Descriptors: Mathematics Teachers, Multiplication, Context Effect, Mathematics Instruction
Quane, Kate; Brown, Leni – Australian Primary Mathematics Classroom, 2022
Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…
Descriptors: Mathematics Instruction, Toys, Manipulative Materials, Foreign Countries
David W. Braithwaite; Robert S. Siegler – Grantee Submission, 2021
Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…
Descriptors: Fractions, Addition, Middle School Mathematics, Middle School Students
David W. Braithwaite; Robert S. Siegler – Journal of Educational Psychology, 2021
Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…
Descriptors: Fractions, Addition, Middle School Mathematics, Middle School Students
Ubah, Ifunanya J. A.; Bansilal, Sarah – South African Journal of Childhood Education, 2018
Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…
Descriptors: Preservice Teachers, Mathematics Instruction, Fractions, Mathematics Teachers
Rodrigues, Jessica; Dyson, Nancy I.; Hansen, Nicole; Jordan, Nancy C. – TEACHING Exceptional Children, 2016
Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…
Descriptors: Fractions, Mathematics Instruction, Mathematical Concepts, Teaching Methods
Aksoy, Nuri Can; Yazlik, Derya Ozlem – Journal of Education and Training Studies, 2017
In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method,…
Descriptors: Fractions, Error Patterns, Grade 6, Grade 5
Schumacher, Robin F.; Malone, Amelia S. – Elementary School Journal, 2017
The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…
Descriptors: Error Patterns, Mathematics Instruction, Computation, Mathematics Achievement