The low level of mathematics performance of U.S. students in relation to national standards and in international comparisons has concerned educators and policy makers for many years. The authors' primary goals were to design a feasible and usable intervention and gather data on the promise of the intervention to foster students' conceptual…

This paper reports on an exploration of students' learning derived from the implementation of learning materials developed in a previous collaborative project. The purpose of the study was to examine the development of third-year students' understanding of the Reimann Sum. These concepts were taught to undergraduate teacher trainees wishing to…

A design research study was conducted over two years with 20 second grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked to count in multiple bases. After doing so, they were asked how they knew when to go to a new place value and why it was necessary. All 20…

Previous research has consistently shown that the left parietal cortex is critical for numerical processing, but the role of the right parietal lobe has been much less clear. This study used the intraoperative cortical electrical stimulation approach to investigate neural dissociation in the right parietal cortex for subtraction and…

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, "Cognition, 110", 198-207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the…

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this…

When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…

A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on…

This qualitative study was conducted to identify the potential of using iPad as a supplement to teach math to students with learning disabilities. Ten teacher candidates from a university in the south provided one-on-one math tutoring services to ten students in a self-contained classroom at a local high poverty elementary school. The students…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

The authors compared the performance of students who received integration of number sense activities in instruction with students who received instruction using regular mathematics textbooks. Two classes of third-grade students (N = 60) were randomly assigned to experimental and control groups. Students in each group were given a pretest, post I…

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students' construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in…

Previous research has revealed that problem solving and attainment in chemistry are constrained by mental capacity and working memory. However, the terms mental capacity and working memory come from different theories of cognitive resources, and are assessed using different tasks. The current study examined the relationships between mental…

Asian children, including Chinese children, perform better than their English-speaking peers in cross-national mathematics studies. This superior Asian performance is attributed to several factors including cultural beliefs, educational systems and practices, and the Chinese number naming system. Given the limited empirical evidence on pre-school…

Math is everywhere! Mathematics is "a way of describing the world--a way of thinking, knowing, and problem-solving" (Virginia's Early Childhood Development Alignment Project 2008, 83). Infants and toddlers are natural mathematicians. Even without adult support, infants and toddlers use math concepts to make sense of their world. An important role…