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…

Improving the strength of alignment between educational components is essential for quality assurance and to achieve learning goals. The purpose of the study was to investigate the strength of alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns. The study contributes to…

First-semester general chemistry is a known "gatekeeper" course due to its high failure rate. These higher education courses are taken by students who for the most part are regularly admitted freshmen, yet many struggle to succeed. In this investigation researchers from six higher-education institutions of varied sizes with student…

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to…

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…

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…

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…

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…