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)

A survey study asked Australian experienced teachers during workshops to rate what they believed to be the most difficult aspects of mathematics in grades seven and eight. Problem solving, number sense, and rational numbers were rated as most difficult. The research question provided a catalyst for action in professional development programs. (MDH)

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…

Interviews with five Shoshoni elders during a 1-year study showed that mathematics was integral to daily life and reflective of their culture. Classroom activities are described that integrate traditional Shoshoni mathematical knowledge into mathematics instruction. This knowledge may help Shoshoni students develop a deeper understanding of…

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…

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

Middle school students consolidate their understanding of integers and rational numbers, increasing their facility with fractions, decimals, and percents and encountering proportionality. This book shows how students can explore these important ideas in such diverse activities as exchanging currency and using area models to develop algorithms for…

This article addresses some of the issues relevant to the cognitive goals of information and communication technology (ICT) integration in the mathematics classroom. It focuses on the development of conceptual understanding through multiple representations. Specifically, it informs about a group of middle school mathematics teachers' learning and…

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…