Twenty-four children (ages 6-9) with mild mental retardation received individualized instruction with either emphasis on Piagetian concepts or emphasis on verbal and number concepts. Although both groups made significant gains over a year, the children receiving the Piagetian emphasis usually gained more and progressed at almost the rate of…

Using case studies that are functionalist in orientation and computational in technique, the role of control knowledge in developing constructive thinking is illustrated. Further, the integration of related knowledge structures, emanating from diverse sensory modes and pertaining to both place value in addition and angle relationships in geometry,…

Citing examples from the author's third grade mathematics classroom, describes problems stemming from the use of concrete objects (e.g., fraction bars, base-10 blocks, and popsicle sticks). The vignettes show the fallacy of assuming that students will automatically draw the conclusions that their teachers want simply by interacting with particular…

Profiled interviews of (n=41) kindergarten and first-grade children's numerical development over a school year. Significant mismatches between children's numerical development and typical curricula are described, and changes to current practice are recommended. Appendix includes sample interview tasks. (Contains 21 references.) (MKR)

The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)

Examined the home and school numeracy experiences of young Somali children living in the United Kingdom. Results indicated that the home numeracy experience was in a more formal setting than the majority of school learning experiences. Explored cultural conflicts and recommended that teachers take into account children's home learning experiences.…

Identifies the types of reasoning involved in middle grade mathematics with regard to multiplicative structures and the difficulties students have with the concepts, why these difficulties might occur, and the interconnections within this content area. Offers four recommendations for the preparation and professional development of teachers.…

First-grade children at risk for a learning disability (LD) in mathematics, reading, or both were compared to a control group on experimental tasks assessing number comprehension and production skills, counting knowledge, arithmetic skills, working memory, and ease of retrieving information from long-term memory. Found different patterns of intact…

This article describes a valuable lesson that university mathematics faculty members learned from fifth grade and middle school teachers in a professional development workshop. The goal of the workshop was to show how models for whole number operations could be linked to models for rational numbers and to connect the traditional algorithms to the…

The number skills of groups of 7- to 9-year-old children with specific language impairment (SLI) attending mainstream or special schools were compared with an age and nonverbal reasoning matched group (age control [AC]) and with a younger group matched on oral language comprehension. The SLI groups performed below the AC group on every skill. They…

This article demonstrates how a child's invented algorithm about tens and ones generated "transitional thinking" on the way to the construction of a mathematical understanding of place value. The articles also discusses how two important "best practice" classroom strategies, mathematical discourse, and the role of wait time in that discourse take…

This document, which was developed to meet the needs of trainers and workers in Australia's automotive industry for learning activities designed to boost auto workers' numeracy skills, contains a total of 33 learning activities organized into 8 sections. The topics covered in the individual sections are as follows: calculators (key words and…

This study evaluated the generally recommended concrete-to-abstract hierarchy for presenting a new skill, with three students with learning disabilities in grades 1, 2, and 4. The three subjects enrolled in the Multidisciplinary Diagnostic and Training Program's classroom housed on the University of Florida campus in Gainesville. Following…

This study investigated children's ability to interpret a natural social situation, depicted in a narrative story, and to use their understanding of that situation to generate and apply a mental model of debts and assets in solving problems including negative quantities. Fifty-one American students from a parochial school in a predominantly middle…

A plenary address to an Australian conference on adult literacy focuses on cultural barriers to numeracy. Mathematics, and therefore numeracy, is considered as part of cultural knowledge. It is noted that over the last decade there has been a growing awareness of the cultural basis of mathematical knowledge and teachers can no longer assume that…