Interviews with (n=55) children and their teachers in years one, two, and three showed a closer association between knowledge of place value and levels of counting than between levels of counting and the ability to explain the counting sequence. (13 references) (MKR)

Describes the process through which four high-achieving second graders constructed their knowledge and misconceptions of rounding concepts gained from using computer-based practice sessions which provided full solutions to examples but without verbal explanations. (31 references) (MKR)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

Middle-school students were asked to determine the dimensions of a hotel atrium so that guests could enjoy the maximum area of scenic view, given that 650 feet of brass railing could be used around each floor. Several solution approaches are described. (MKR)

Describes a wide range of activities based on a grade-number theme of "two" in second grade, "three" in third grade, and "four" in fourth grade. (MKR/SW)

Interviewers asked (n=10) 6th- and (n=10) 10th-grade students to solve nonroutine number problems. Task analysis of perseverers, those students who continued after reaching "dead-ends," found that students who were ultimately successful were more inclined to be flexible in their strategies. (28 references) (MKR)

Focuses on a single case study of a mentally handicapped child to examine directly the relation between the development of number-after rules and a counting-on from the larger addend (COL) strategy. Examines the development of children's proficiency with n+ and 1+n combinations and the evolution of their counting-on strategies over time. (AA)

Two fourth-grade classes served in a study that employed computers for promoting autonomous learning processes through solving challenging problems adapted to students' aptitudes using the number line as an intuitive model. Findings showed that students have preinstructional intuitions and informal knowledge of negative numbers. (24 references)…

Discusses research on children's speed in identifying digits and letters in continuous lists and discrete trials. Latency for word identification and digit naming varied considerably. Naming speed contributed variance in reading skill independently of measures of phonological awareness. (Author/GH)

Describes the development, refinement, and validation of a framework for nurturing and assessing multidigit number sense in young children. Major constructs incorporated were counting, partitioning, grouping, and number relationships. The framework was validated through case studies of six first-grade children. (30 references) (MKR)

Investigated (n=124) preservice school teachers' reasoning and concepts of invariance of fractional numbers under numeration systems in different bases. The majority of students believed that fractions change their numerical value under different symbolic representations. (Author/MKR)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

Discusses topics that are especially appropriate for investigation by young learners and describes activities that stimulate children's curiosity. Suggestions about ways to focus children's attention on mathematical aspects of the activities are offered. (BB)

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)