Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)

A study comparing 65 deaf and hearing Australian children, aged 7-13, found that deaf subjects were delayed in number and liquid conservation, but equally mature in justice reasoning. Deaf subjects were less likely to disagree with a reward allocation proposed by an adult and to make cognitive progress when encountering conflict. (Author/JDD)

Presents the use of manipulatives in the three stages of concept learning called concrete, bridging, and symbolic. Examines the three stages in developing the concept of rounding two-digit numbers. (MDH)

Tests of computational estimation ability (CEA), strategy (CES), and mental computation ability (MCA) of (n=124) fourth, (n=143) fifth, and (n=84) sixth graders found significant relationships between CEA and MCA and between CEA and CES but not between MCA and CES. (12 references) (Author/MKR)

Investigated children's preferred learning styles when exploring spatial concepts. Found that young children first develop the spatial concept of topology, which supports Piaget's theory, followed by the concepts of position. The two separate groups of children appeared to exhibit different learning styles when exploring space concepts. (AP)

The concept of fractional number was studied with 10- to 12-year-old and 13- to 16-year-old students who were deaf and hard of hearing (n=21) and comparison groups of hearing students (n=26). The deaf and hard-of-hearing students achieved similarly to younger hearing students in overall performance by fraction type and problem solving strategies.…

Urges that the search for origins of European exploration extend to Africa and East Asia and their international trade. Cites contributions of India and the Arabs, Chinese, and Malaysians. Emphasizes the importance of mathematics, navigation, and sailing technology. Argues that without these contributions the European voyages would not have been…

Describes the Quipu, a mathematical device invented by the Incas of Peru that used the base-10 number system to store information. Suggests ways of incorporating material on the quipu into the arithmetic class. (MDH)

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

Discusses how students at the end of the French primary school-cycle (10- to 11-year-old pupils) resolve multiplication and related division problems within an assessment perspective taking into account the 3 factors of the problem's representational structure, the numerical values used, and the context of the problem statement. (25 references)…

A 7-month longitudinal study of 20 2- and 3-year-old children shows that children at an early age already know that counting words each refer to a distinct numerosity, although they do not know to which numerosity. It takes children a long time to learn the latter. (SLD)

Discusses opportunities to use nursery rhymes to aid in the mathematical development of young children. Considers rhymes that involve patterns, ordering, and problem solving. (MKR)

Stresses recognition and application of the identity property of 1 across the mathematics curriculum to help students overcome difficulties. (MKR)