Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…

Domino games are used to illustrate problem-solving techniques in a college principles-of-mathematics course. Students develop tables and use Pascal's triangle to find the total number of pips and the sum of numbers on the pieces. (DC)

Presents guidelines for designing and using extensions, which are exercises that follow or extend the basic presentation of an idea, in the mathematics area of the Montessori program to give children more experience and depth as they explore key mathematical concepts. Describes extensions that address counting, sorting, and working with decimals.…

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

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)

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 details problems and instructional approaches intended to promote preservice teachers' understanding of the reasoning underlying whole number multiplication. (Contains 9 figures.)