Analyzes three textbook series to find what meaningful learning experiences with fractions the books offer relative to modes of representation, pictorial models, qualitative reasoning, and students' informal knowledge of partitioning. Discusses implications for teacher use, including supplementation, teacher-support materials, alternative…

This article proposes use of a restructured hundreds chart that involves a right-to-left sequence of numbers (similar to the direction of computations) and inclusion of zero. Specific instructional activities using the restructured chart are suggested for teaching such skills as counting, number identification, numerical relationships, place…

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

Assesses the competence of children (N=215) between the ages of 5 and 9 at addition by asking them to estimate the answers to addition sums. Reports that children at higher levels tend to produce more reasonable estimates than children at lower levels. Discusses the existence and nature of a zone of partial knowledge and understanding. Contains 31…

Presents an activity that integrates music, dance, and mathematics. (ASK)

Discusses the use of quick-image activities in which the teacher flashes one particular image consisting of dots on the overhead projector screen for three seconds, hides it from view, then asks students to tell how many dots were shown and to describe what they saw. (ASK)

Presents a study to develop better understanding of the processes involved in the construction of oral and written symbolic systems and to grasp their role in the elaboration of the modeling function of numbers. Proposes ideas for teaching in light of this study and contributes better understanding of the relationship between numeration and…

Describes three calculations used to make students aware of the size of Avogadro's number: (1) the new size of a 6-inch diameter ball with volume increased by a factor of Avogadro's number; (2) the number of moles of sand grains in the Sahara Desert; and (3) the dimensions and length of a mole of hydrogen atoms shaped into a cube, a square, and a…

Explores students' abilities in mental computation, finds out the strategies they use most naturally, and develops a theoretical framework by giving 60 children a questionnaire and interviewing them on a series of arithmetic operations to be solved by mental computation. Generates a classification of children's strategies. Contains 31 references.…

Describes an activity in which students investigate the symmetry of factor sets of composite numbers using the TI-83 graphing calculator. This activity allows students to observe patterns, make predictions, and verify their accuracy. (ASK)

Examines the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems, including an experimental and control group each consisting of 34 elementary students, in Japan. The experimental group showed a significantly better performance on the retention test…

Evaluated an instructional procedure that focused on reflective problem-solving and used young children's fascination with stars as a starting point to develop their concept of numbers. Found that test group performance on mathematics problem- solving tasks indicated developing understanding of the concept of numbers 1 through 5, compared to that…

Describes how the creation of a musical composition suggested a theorem concerning the Fibonacci sequence. (ASK)

Tested in three experiments hypothesis that coordinating saying number-words and pointing to each object to count requires use of the central executive and that cost of coordination decreases with age. Found that for 5- and 9-year-olds and adults, manipulating difficulty of each component affected counting performance but did not make coordination…

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…