We investigate thirty-three second and fifth-grade students' solution strategies on integer addition problems before and after analyzing contrasting cases with integer addition and participating in a lesson on integers. The students took a pretest, participated in two small group sessions and a short lesson, and took a posttest. Even though the…

The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

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…

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and…

The language that students use with whole numbers can be insufficient when learning integers. This is often the case when children interpret addition as "getting more" or "going higher." In this study, we explore whether instruction on mapping directed magnitudes to operations helps 88 second graders and 70 fourth graders solve…

This study examines students' procedural and conceptual achievement in fraction addition in England and Taiwan. A total of 1209 participants (561 British students and 648 Taiwanese students) at ages 12 and 13 were recruited from England and Taiwan to take part in the study. A quantitative design by means of a self-designed written test is adopted…

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…

This study, an education program was developed to improve addition-subtraction skills of 6-year old children using educational toys and smart boards. The program was implemented with children, and its effects on their operational skills were analysed. The study group of the research is composed of 90 children who attended preschool classes in…

There is a need for further investigation of evidence-based practices for students with autism spectrum disorders and developmental disabilities leading to students' success within the general education curriculum (Cihak & Foust, 2008; Rockwell, Griffin, & Jones, 2011; Schaefer-Whitby, Travers, & Harnik, 2009). The purpose of this…

This study examined the influence of kindergarten teachers' orientations toward student-centered teaching and their influence on their students' understanding of addition. The study examined 120 students across 10 classrooms. Based on an interview and two classroom observations, 10 teachers were classified as either student centered or mainly…

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…

The Common Core State Standards (2010) involve the demonstration of conceptual knowledge of numbers and operations. For students who struggle with mathematics and have not responded to instruction, it is important that interventions emphasize this understanding. In order to address conceptual understanding of numbers and operations in meeting the…