As national and international assessments continue to show students struggle with rational concepts, which are seen as a major stumbling block for future career in STEM fields, we used the certainty of response index (CRI) as a method of analysis to investigate a group of 40 United Arab Emirates (UAE) seventh grade students' understanding of basic…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms' mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy…

Expecting teachers to support their students in making mathematical connections is an unreasonable request when teachers themselves have not had opportunities to connect their own understandings. This study investigates how prospective elementary teachers can deepen their mathematical understanding using recommendations developed by mathematics…

Adaptive teachers use student data to guide instruction. Learn about using an anecdotal record form to support adaptive teaching. In this article, the authors describe how teachers can use learning trajectories to make adaptive decisions to meet the needs of their students. They provide an example using the U .S. Math Recovery Council's learning…

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in…

This qualitative case study investigates how, and to what extent, primary school teachers notice students' mathematical thinking in the context of whole number subtraction. A task involving a student's invented strategy was used to collect data. Three noticing questions connected to the task were asked to 45 teachers. Their written answers were…

The objective of this study was to evaluate and characterize the argumentation patterns used by seventh-grade students in the context of algebraic addition and subtraction problems. A qualitative case study was conducted using the Claim-Evidence-Reasoning (CER) model (McNeill & Krajcik, 2008) and argument quality framework. To describe the…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

The notion that mental arithmetic is associated with shifts of spatial attention along a spatially organised mental number representation has received empirical support from three lines of research. First, participants tend to overestimate results of addition and underestimate those of subtraction problems in both exact and approximate formats.…

The aim of this research is to determine the mental processing strategies used by 3rd grade primary school students in addition and subtraction using the empty number lines. The model of the research is a case study, one of the qualitative research methods. The participants consist of 143 students; 75 girls and 68 boys, attending the third grade…

Computation competence (CC) in simple addition and subtraction using non-counting (NC) strategies is an important learning objective in Grade 1 mathematics but many children, especially low achievers in mathematics, struggle to acquire these skills. To provide these students with the support they need, it is important to have valid and reliable…

Word problem solving is an approach that can increase knowledge, improve performance and develop learners' critical thinking skills that can assist them in solving mathematical and real-life problems. This study examined the effectiveness of using a word problem solving approach to improve Grade 3 learners' performance when learning addition and…

Integers present a global challenge for students due to their abstract nature and complex operations. To delve into the challenge students encountered, error analysis served as an alternative method to investigate errors diagnostically. This study aimed to explore error patterns related to integer addition and subtraction among seventh-grade…

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…