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…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

According to social dilemma theory, students may be characterized as being indifferent to reciprocal behavior and disengaged from interacting with the board gaming process. Given a common goal, students' prosociality can affect the collective efficacy and goal achievement motivation that reflects their flow experience in a cooperative-competitive…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

The relationships between three critical elements, and the associated mathematical language, to assist students to make the critical transition from additive to multiplicative thinking are examined in this article by Chris Hurst.

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student…

Developing high levels of mathematical skills in students is a concern for teachers worldwide, since most of the fastest growing occupations require significant mathematics or science preparation. Teachers need to be prepared to teach mathematics successfully. If teachers are not fluent in simple mathematical calculations, they may not feel…

To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

This study examined interventions for addition and subtraction that were implemented through single-case design (SCD) research studies. We attempted to extend prior SCD meta-analyses by examining differences in effect sizes across several moderating variables and by including a novel index of effect, improvement rate difference (IRD). We also…

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…

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…