Appropriate mathematical competencies for children of ages two, three, four, and five are presented. It is suggested that mathematics programs for young children be action oriented. (MP)

The author describes a dialogue with his three-year-old daughter about numbers. He discusses aspects of mathematics education and how his views about how students acquire mathematical knowledge have changed. (MP)

The role of mathematics education in the elementary school classroom over the next few years is reviewed. The need for extensive reform is emphasized, especially the inclusion of noncomputational number concepts. (MP)

Several types of problems designed to provide opportunities for mathematically able students to do original and analytic thinking at grades 3 and 4 while reinforcing numeration and computation skills are presented. (MP)

A method of teaching students how to recognize when zeros are necessary and when they may be omitted is presented. (MP)

Children and adolescents tested to determine the development of the operator construct of rational numbers employed different problem-solving strategies depending on test presentation. Three major phases in the rational number construct appear to be a primitive fractional construct, a unit operator phase, and a general operator phase. (SB)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

Activities are described in which number patterns in two-digit multiplication exercises are investigated. (DT)

This study assessed effects of response climate by examining effects of an additional testing experience on the conservation of number performance of 4- and 5-year-old lower socioeconomic status children (N=98). Results indicated significantly higher conservation of number performance scores for both males and females. (Author)

Examined role of linguistic demarcation of numerals on cognitive representations of numbers with Caucasian children, 5-7 years old. Theorized that the linguistic paradigm does not always support the idea that language affects number concepts and that children's performance is shaped by other constraints. Results suggest that the task reflects…

This article describes the modifications that 12 early childhood educators in Japan made to the Sorry! board game to encourage kindergartners' logico-mathematical thinking. Logico-mathematical knowledge is described as including classification, seriation, numerical relationships, spatial relationships, and temporal relationships. Examples of seven…

This article describes how two young children with moderate/severe mental retardation were taught functional counting skills by helping with a snack delivery activity. Instruction involved a task analysis, use of pictures to represent objects and numbers, self-monitoring to increase student independence, and ongoing evaluation. The importance of…

Two experiments tested claim that transparency of Korean fraction names promotes fraction concepts. Findings indicated that U.S. and Korean first- and second-graders erred similarly on a fraction-identification task, by treating fractions as whole numbers. Korean children performed at chance when whole-number representation was included but…

Performance of 5 students (ages 8 and 10) with moderate intellectual disability was compared as they received the DISTAR Arithmetic instructional intervention and a Discrimination Learning Theory (DLT) intervention not requiring a fast-paced verbal student response. Academic engagement and skill mastery were greater during the DLT intervention.…

Reviewed is an integrated approach to teaching place-value concepts. A semi-integrated approach is proposed which may provide a more effective implementation of the technique. (CW)