Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting. Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their…

Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners' developmental trajectories. Given…

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…

Given the vital importance of using a scientific approach for curriculum development, the authors employed a design experiment methodology (Brown, 1992; Shavelson et al., 2003) to develop and evaluate, FUSION, a first grade mathematics intervention intended for students with or at-risk for mathematics disabilities. FUSION, funded through IES…

A study investigating the linguistic structure of Oneida and Lakota number systems found that base-10 numeracy is communicated more explicitly in these languages than in English. Further research is needed to determine whether teaching Oneida and Lakota students in their Native languages would help them to develop better number sense. A sample…

This study describes a teacher preparation program in mathematics and science and explores what impact the reformed curricula and teaching methods instituted in the program have on prospective teachers' understanding of rational numbers and integers. The study pursues obtaining in-depth insights regarding prospective teachers' concept development.…

This study investigates the development of 5th grade children's understanding of quotient and the classroom norms and practices that constrain or enable that understanding. It reports not only how the children's understandings develop, but also why and under what conditions they develop. The results of this study indicate that children progressed…

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…

In the last two decades, mathematics teachers have shown a great deal of interest in how students learn mathematics through journal writing. I have also used journals in mathematics classes for the last five years. Based on the analysis of more than 1800 journal entries written by approximately 200 students in the last five years, I conclude that…

Children's nonschool learning provides a foundation for school instruction and problem-solving. Examples of nonschool learning are taken from various cultures. This study examines what young children know about written numerals in their everyday environment, how they come to understand the meaning of written numerals, and how they use this…

Contrasts student achievement using commercial curricula (CC) for initial fraction learning with that of using the Rational Number Project (RNP) fraction curriculum. Indicates that students using RNP materials had statistically higher mean scores on concepts, order, transfer, and estimation. Interview data showed differences in the quality of…

This paper reports the formative evaluation of six curriculum units related to initial number sentence writing. These units were used for a coordinated study carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The units were tried during the 1977-78 and 1978-79 school years at a…

This report considers how the mathematical knowledge children develop on their own outside of formal school instruction can be used to increase the distribution and level of mathematical knowledge attained by students in grades K-3. Included are preliminary results of an investigation of the counting and calculating abilities brought to…

Described in the final report is a project designed to develop, field-test, and disseminate a dual, compatible system of curriculum and criterion-referenced evaluation based on a sample of 40 trainable mentally retarded students (5-15 years old) in self help, basic language, number, and prevocational skills. Program summary information includes a…

This report summarizes a project to develop computational estimation materials for students in grades 6, 7, and 8. In chapter 1, the need for estimation skills is discussed and the goals of the project are stated: to develop a carefully sequenced set of lessons, activities, and maintenance work on estimation with whole numbers, fractions,…