Although an increasing number of studies have suggested that students with low mathematics achievement (LMA) tend to perform worse in arithmetic strategy use than children with typical development, the potential reasons remain unclear. Accordingly, the current study investigated the potential impact of task switching on strategy use for children…

Skills and understanding of operations with negative numbers, which are typically taught in middle school, are crucial aspects of numerical competence necessary for all subsequent mathematics. To more swiftly and coherently develop the field's understanding of how to foster this critical competence, we need shared measures that allow us to compare…

This research aims to give an idea of the approach of mathematics teaching in primary schools in the early years of Republic of Turkey and compare it with the current approach of teaching within the context of Mathematics Teaching Knowledge (MTK). Therefore, the sample of the study was the article entitled "Arithmetic (Mathematics) Courses in…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

In this paper, the hypothesis that Developmental Dyscalculia (DD) is a characteristic of Down syndrome (DS) is proposed. Implications for the hypothesis are addressed: If it were to be confirmed that DS implies DD, what would be the consequences for the mathematics education of learners with DS? The use of prosthetic devices to overcome the…

Pronouns encouraging a second-person perspective (e.g., "you/your") affect peoples' mental representations constructed while reading and improve learning. The present study applied these insights to a domain in that such pronoun effects have yet been unexplored: mathematical word problem solving. Specifically, we encouraged a…

The aim of this research is to determine the misconceptions among 6th, 7th and 8th grade students about the order of operations in line with arithmetic expressions and posing and solving problems related to arithmetic expressions. The research has a mixed-method research design with concurrent-triangulation design. The study group for the research…

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Background: Teaching using manipulatives is emphasised, especially in the early grades, to help learners conceptualise operations on whole numbers. Therefore, teachers' competencies in using manipulatives is the key in helping learners master these basic operation skills. Aim: Drawing from the literature on using manipulatives to improve learners'…

Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…

Twenty-five first-year preservice teachers attending a university in the Midwest of the United States of America participated in a whole-class-setting study aimed at investigating their knowledge of how they made sense of fraction concepts and operations, and how the development of this knowledge was facilitated during a mathematics education…

How does linguistic structure affect children's developing cardinal number knowledge? The bootstrapping theory proposes that children might use syntactic information provided by known words such as quantifiers to bootstrap the meanings of unfamiliar words such as number words. Prior studies of numeral and quantifier development have indicated that…

While response time and accuracy indicate overall performance, their value in uncovering cognitive processes, underlying learning, is limited. A promising online measure, designed to track decision-making, is computer mouse tracking, where mouse attraction towards different locations may reflect the consideration of alternative response options.…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…