Investigates the arithmetical and algebraic problem-solving strategies and skills of preservice primary and secondary school teachers in Flanders, Belgium. Compares aspects of preservice teachers' own problem-solving behavior with the way in which they evaluated students' arithmetical and algebraic solutions to problems. Discusses teachers' use of…

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…

Discusses an attempt to promote the development of prospective elementary teachers' own subject-matter knowledge of the division of fractions as well as their awareness of nature and likely sources of related common misconceptions held by children. Indicates that before the described mathematics methods course, most participants knew how to divide…

Examines the relationship between problem-solving performance and the quality of the organization of students' knowledge. Reports on findings on the extent to which content and connectedness indicators differentiated between groups of high-achieving and low-achieving Year 10 students undertaking geometry tasks. (Contains 29 references.)…

Analyzes open-ended interviews and written responses from 62 students in grades 3, 6, and 9 to a questionnaire to understand the characteristics of students' constructions of the concept of sample. Identifies six categories of construction in relation to the sophistication of developing concepts of sampling by illustrating helpful and unhelpful…

Researchers are being exhorted to gather and analyze data for evaluating the efficacy of various instructional approaches and curricula in mathematics education. Addresses one of the fundamental notions in mathematics education research, the concept of evidence. (Contains 12 references.) (ASK)

One major issue in the field of mathematics education is what type or types of research should play the critical role. Describes major research categories and applications, and elaborates on the future of mathematics education research toward consensus and rapprochement in this area. (Contains 26 references.) (ASK)

Presents research in which mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and…

Presents a study in which children in four grade 2 classrooms learned about transformational geometry and symmetry by designing quilts, while their four teachers participated in professional development focused on understanding children's thinking in arithmetic, and two of the teachers participated in additional workshops on students' thinking…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

Explores insights that may be provided by a situated perspective on learning. Considers the ways in which a focus on the classroom community and the behaviors and practices implicit within such communities may increase understanding of students' mathematical knowledge production and use. (Contains 22 references.) (Author/ASK)

Focuses on the strategies young children (N=115) use to solve rectangular covering tasks before they have been taught area measurement. Children's solution strategies were classified into five developmental levels. Emphasizes the importance of understanding the relationship between the size of a unit and the dimensions of the rectangle in learning…

Suggests that radical constructivists draw on a weak image of the role of social life. Argues that a thick notion of "social" leads to a complexity of sociocultural theories concerning the teaching and learning of mathematics, a perspective that is firmly located in the debates surrounding cultural theory over the last two decades.…

Mathematics education in schools can be viewed either as primarily a sociocultural phenomenon or as a nurturing of the individual's mathematical development. Argues that instead of taking the dichotomous view, contrasting the Vygotskian and the Piagetian perspectives, the two may be seen as separate "truths" providing different lenses…

Compares problems that followed content presentation of the addition and subtraction of integers in several American and Chinese mathematics textbooks to illuminate cross-national similarities/differences in expectations related to students' mathematics experiences between the United States and China. Differences found in the problems' performance…