This article focuses on how the representational properties of manipulatives affect the strategies children employ in problem solving. Two studies examined the effect of physical materials on 4-7-year-old children's problem solving strategies in a numerical (i.e., additive composition) task. The first study showed how children not only identified…

Gap thinking has been categorised as one of several whole number strategies that interfere with early fraction understanding. This study showed that this claim is not supported by interview data of Grade 6 students' gap thinking explanations during a fraction pair comparison task. A correlation with equivalence performance was uncovered, leading…

The spatial component of numerical and ordinal information has been explored in previous research. However, how such mapping emerges and how it is affected by the learning experience are issues still under debate. In the current study, we examined the orientation of the mental number line for different numerical notations in Chinese readers. Our…

Numerical fractions are commonly used to express ratios and proportions (i.e., real numbers), but little is known about how they are mentally represented and processed by skilled adults. Four experiments employed comparison tasks to investigate the distance effect and the effect of the spatial numerical association of response codes (SNARC) for…

A classification of the simple combinatorial configurations which correspond to various cases of distribution and ordering of objects into boxes is given (in French). Concrete descriptions, structured relations, translations, and formalizations are discussed. (MNS)

A mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)

Two samples of kindergarten children's representation and understanding of written number symbols were examined in two time points in one academic year. About 85% of Chinese five year olds (mean = 5 years 10 months) were able to use conventional number symbols to represent the quantity of 30 or larger. At the end of the kindergarten year, 94% of…

Described are instructional techniques and inexpensive manipulative materials that can be used to teach basic multiplication to blind and partially sighted children. (LH)

AN ATTEMPT WAS MADE TO ASSESS THE EFFECTS ON ADULT LEARNING OF DIFFERENTIALLY STRUCTURED INTRODUCTORY COGNITIVE LEARNING TASKS AND MATERIALS, AND THE INTERACTION OF INTELLIGENCE WITH THE EXPERIMENTALLY MANIPULATED MATERIAL AND TASK CATEGORIES. ABOUT 96 ADULTS WHO WERE UNFAMILIAR WITH THE CONCEPT OF NUMBER BASES WERE CLASSIFIED ACCORDING TO A 4X3X4…