The use of manipulatives is an essential key to teaching mathematics to young children. Throughout history, different types of manipulatives have been used to aid in comprehension of mathematical concepts including quipu, abaci and pattern blocks. Today, concrete and virtual manipulatives are the tools that early childhood teachers are using in…

The main purpose of this study was to investigate the level of student's achievement in mathematics in Yemen. This study use a sample of 200 male students and 200 female students, chosen from eight government schools on the basis of diversified sampling techniques. A mathematics test which composed of seventy five items that covered geometrical…

The primary purpose of the study was to determine if computer-based training programs promoted fluent and flexible use of reasoning strategies to solve addition problems using different tasks. Specifically, does participation in strategy training result in the fluent application of the target strategy on a traditional mental arithmetic task? Does…

Subtraction combinations are particularly challenging for children to learn (Kraner, 1980; Smith, 1921; see Cowan, 2003, for a review). This study examines whether the group of children receiving the "experimental subtraction-as-addition" training outperform the "control" group, which received training on a different reasoning…

The importance of understanding the various uses of the literal symbol in algebra, and in particular the idea of generalised number, is well documented in the literature. Many research findings have also reported student difficulties with this vital and central concept. This research study examines the use of a combination of historical and…

The persistent fear of physics by learners motivated the author to take action to increase all students' interest in the subject via a new curriculum for introductory college physics that applies Greene's model of Aesthetic Education to the study of contemporary physics, utilizing symmetry as the mathematical foundation of physics as well as the…

Digital game-based learning is a research field within the context of technology-enhanced learning that has attracted significant research interest. Commercial off-the-shelf digital games have the potential to provide concrete learning experiences and allow for drawing links between abstract concepts and real-world situations. The aim of this…

Recent reforms in mathematics education have increased the need for teachers to attend professional development programs. In order to motivate teachers to attend such programs and to maximize their effect on teachers' development, we believe it is important to adapt the contents of such programs to teachers' perceived needs. The current study was…

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

Many students graduate from K-12 mathematics programs without flexible, conceptual mathematics knowledge. This article reviews psychological and educational research to propose that refining K-12 classroom instruction such that students draw connections through relational comparisons may enhance their long-term ability to transfer and engage with…

This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of…

In standard treatments of probability, Pr(A[vertical bar]B) is defined as the ratio of Pr(A[intersection]B) to Pr(B), provided that Pr(B) greater than 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A[vertical bar]B) arise in the mind via implicit calculation of…

We consider how the arc length integral of the graph of a function in the plane is connected with the hyperbola and its rational parameterization.

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.