The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Research findings on decimals and money are briefly summarized, followed by suggestions for classroom use. (MNS)

Four third-grade and three fourth-grade students received individualized instruction on addition and subtraction of fractions for three weeks. Students overgeneralized the meanings of symbolic representations for whole numbers to fractions and vice versa. (MKR)

Investigated the continuous fraction concepts of (n=59) students in grades four, five, and six. Students were confident and accurate when performing sharing tasks, but were much less successful on continuous quantity tasks involving formal fraction language and symbol manipulation fraction tasks. (14 references) (Author/MKR)

Describes an attempt to encourage fifth- and sixth-graders to invent their own ways of solving problems involving division with fractions. Emphasizes the importance of social interaction in Piaget's constructivism and explains why debate and verification are important for children's construction of logico-mathematical knowledge. (22 references)…

Discusses the use of children's literature to help children develop personal understandings of fraction concepts. Includes 23 citations to children's literature that incorporates ideas related to fractions. (MKR)

Discusses the role of concrete materials in teaching for understanding, including research on the use of concrete materials, seeing mathematical ideas embodied in them, and identifying what teachers want students to understand. (Contains 16 references.) (MKR)

Two experiments explored the relationship between conceptual and procedural knowledge. Results revealed that fourth and sixth graders made computational errors even though they possessed conceptual knowledge. Fifth graders mastered conceptual knowledge before procedural knowledge. Results support the dynamic interaction theory. (BC)

The issue of division by zero is discussed. Activities that cover the topics of measurement division, partition division, relationship to fractions, confusion with dividing into zero, dividing zero by zero, and relation to more formal numbers are presented. (KR)

Addresses the questions of how documented opportunities to learn can be aligned with NCTM Standards, and how elementary teachers' efforts to provide such opportunities can be supported. Conducts a study of the effects of curriculum (problem solving versus skills) and professional development (subject-matter focused versus collegial support) on…

A study of 125 elementary students with and without learning disabilities compared effects of concrete to semiconcrete to abstract (CSA) instruction in fraction concept and skills to instruction that was based on textbook curriculum. Students taught fraction concepts and skills in a CSA sequence performed significantly better. (Author/CR)

Disagrees with research showing that socioeconomic status has little impact on parental involvement in children's education. From the author's own experience, working-class parents are as concerned as affluent ones about children's progress, but have less energy/time for participation. In other research, a new assessment instrument may help…

Describes how to incorporate the concept of significant figures into science activities to promote understanding. Provides helpful classroom examples using measurements of volume and length. (SAH)

A study examined the effectiveness of an intervention program designed to promote numeracy skills in children with deafness by addressing additive composition, additive reasoning, multiplicative reasoning, and ratio and fractions. The 23 participants in the intervention performed significantly better than 65 controls on a mathematics achievement…

Describes how third grade students worked together to investigate relationships between fractions and percents using a spreadsheet tool. Highlights a dynamic classroom environment in which students and teachers work together as a community to learn and do mathematics. (ASK)