This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…

This study compares three methods of introducing two-digit numeration. It is concluded that teachers should build on the preschool exposure children have in counting past ten, rather than have children begin by counting out groups of tens and ones and only later in the process use the normal number names. (MN)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…

Examines strategies used by preschool children to subdivide items and focuses on how counting and sharing relate to one another. Indicates that children exhibited alternative strategies--suggesting use of a recipient as a mental cycle-marker and an adjacent recipient strategy--with pauses between allocations suggesting a re-presentation of lots…

A nine-year-old's conception of fractions was compared with his knowledge of units. He had effective schemes for solving some partition problems but did not consistently use units of different sizes in interpreting fractions. His solutions to equivalence problems showed no coherent method of verification. (MNS)

Investigates possibilities for and manifestations of collaborative work with pairs of kindergarten students as they worked on tasks designed to promote early number development. Students generated four strategies, and three themes emerged from the analysis of the cooperative solutions. Contains 34 references. (Author/ASK)

A hierarchical-clustering technique was used to examine relationships among computation-related skills by pupils in grades one to four in two Irish schools. A clear hierarchical ordering of skills was obtained at each grade. (MNS)

Data on sex differences in rote-counting ability for 4722 first-grade children are presented. How different data-gathering methods and different statistical treatments of the data can yield differing results are indicated. (MNS)

Investigated whether second grade children were aware that dealing without counting was sufficient to ensure equality of shares in a discrete sharing situation. Seventeen children were interviewed after watching a videotape of preschooler's actions on sharing activities. (YP)

Attainment relative to six cognitive operations and four number and computational skills was assessed for 90 elementary students using clinical procedures. Variance associated with conservation of number, seriation, and logical classification competency accounted for a significant proportion of the variance in achievement scores. (Author/MK)

The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

The results of this study indicate no significant differences on two achievement tests and one aptitude test between calculator and non groups. Nevertheless, the investigator notes several advantages of using the calculator. (MK)

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Provides information on the number sense of Taiwanese students in grades six and eight. Indicates that student performance on questions requiring written computation was significantly better than on similar questions relying on number sense. Supports the need to look beyond correct answers when computational test results are reported. Contains 29…

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)