This article explicates the development of top-view numeric coding of 3-D cube structures within a design research project focused on 3-D visualization skills for elementary grades children. It describes children's conceptual development of 3-D cube structures using concrete models, conventional 2-D pictures and abstract top-view numeric…

In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

The purpose of this study was to explore the impact of incorporating Magic Board in the instruction of concepts related to area. We adopted a non-equivalent quasi-experimental design and recruited participants from two classes of third-grade students in an elementary school in Taoyuan County, Taiwan. Magic Board was used as a teaching aid in the…

The purpose of this study was to examine pictorial representations, whether in static or dynamic modalities, and their impact on student learning in a classroom with low-achieving students. The investigation emerged from a classroom teacher's action research project. During a three-week fraction unit, nineteen third-grade low-achieving students…

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands-on) manipulatives as compared with virtual (computer-based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest-posttest design was employed with a sample of 91…

Two randomized control/treatment experiments tested the effectiveness of Chartworld software on enhancing mathematical knowledge of 3rd-graders. In Experiment 1, 196 children were randomly assigned to receive either Chartworld or textbook instruction on number operations. ANCOVAs indicated significant group differences in favor of Chartworld in…

The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for…

Nathan entered third grade having already constructed a Generalized Number Sequence (GNS) for whole numbers that enabled him to coordinate sequences of multiples to find a common multiple of two whole numbers. Nathan was able to apply the operations of his GNS to his understanding of part-whole relations and his emerging use of fractional…