This case study aims to describe the learning characteristics of a child and evaluate his preferences for using physical manipulatives (PM) and virtual manipulatives (VM) to solve fraction problems. The participant in this study was a fourth-grade child. The child was given similar problems to solve using PM and VM. Data sources were observations…

Time is an area of measurement that is difficult for children. This interview study addresses the question: What are children's solution approaches to position the hands of an analog clock? To explore this, we investigated problem solving when using a clock manipulative with mechanically linked hands. We compare overall success rates among…

In this study, we investigated how Grade 3 and 4 students' organizational structure for volume units develops through repeated experiences with a virtual manipulative for building prisms. Our data consist of taped clinical interviews within a micro-genetic experiment. We report on student strategy development using a virtual manipulative for…

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal's analysis of the fraction concept, we regard "comparing," rather than "fracturing," as the primary activity from which students are…

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and…

Soroban abacus training is called as mental arithmetic training in our country. It is known for mental arithmetic to increase the ability of four mode operations. Besides this, how is the situation for the students which are having Soroban abacus training in the terms of problem solving abilities, creativity, development of concepts, attraction…

This research presents a preliminary overview of the teaching practices of fourth grade teachers throughout the state of New Jersey. These teachers were all involved in professional development experiences designed to help them revise their approach to the teaching and learning of mathematics. In this aspect of the study, we observed at least…

Finding the number of cubes in rectangular solids provides a cognitive framework for understanding the measurement of volume. This study reveals whether the activities provided in the context of equal investing and equal sharing that emphasize both numerical and spatial aspects of cube configurations cause any improvement in student strategies…

This paper presents the results of a comparison of data from the Lutheran Church-Missouri Synod (LCMS) 4th (n=179) and 8th (n=143) grade student and teacher samples to the data from the 1990 National Assessment of Educational Progress (NAEP) 4th and 8th grade student and teacher samples. This is part of a larger study of mathematics education in…

The specific focus of this research was to determine how the outcomes on two alternative forms of assessment (multiple-choice and hands-on/manipulative) for science process skills were related when students were grouped on the basis of sex, race/ethnicity, and poverty level. Subjects were 1,381 fourth graders in a culturally diverse city school…