Incorporating the use of children's literature when teaching mathematics to young children is a developmentally appropriate practice: "Literature … provides a means for children to encounter mathematical concepts and vocabulary in the context of something familiar, a story" (Fogelberg et al. 2008). Moreover, introducing culturally…

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three…

The aim of this study was to examine the concept development of decimal numbers in 244 Chinese elementary students in grades 4-6. Three grades of students differed in their intuitive sense of decimals and conceptual understanding of decimals, with more strategic approaches used by older students. Misconceptions regarding the density nature of…

This report focuses on key elements of teaching occurring during intensive, one-to-one instruction with 3rd- and 4th-graders. The study involves six cases in all, each consisting of video records of up to eight lessons, each of 30-45 minutes' duration, resulting in the analysis of about 33 hours of video data. A resulting framework of four stages…

The present study describes the usage of strategies of symbolic representation during teaching introduction of decimal system in primary school in Mexico. Our research is based on Activity Theory conception of teaching-learning process and of gradual introduction of scientific concepts in school age. The method includes symbolic external…

This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concrete learning…

This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that…

Barbanel, Brams, and Stromquist (in 2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable division of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two "almost"…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

While the value of "schematic representations" in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of "schematic…

Preservice elementary teachers often struggle with prime decomposition and other mathematical topics that correlate with number theory. This paper provides a framework for integrating prime factor tiles into their curriculum with a particular emphasis on prime decomposition. Using this framework, preservice teachers explored and evaluated numbers…

Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have…

This study, an education program was developed to improve addition-subtraction skills of 6-year old children using educational toys and smart boards. The program was implemented with children, and its effects on their operational skills were analysed. The study group of the research is composed of 90 children who attended preschool classes in…

This paper shares research from a pilot study in which young children were introduced to multiplication and division problems in their first year of school. The focus was on building children's conceptual understanding of the idea of "repeated groups" as a fundamental aspect of multiplication and its relation to division. The particular…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…