For learning math, non-symbolic quantity skills, symbolic skills and the mapping between number symbols and non-symbolic quantities are all important precursors. Little is known, however, about the interrelated development of these skills. The current study focuses on numerical development by: (a) investigating the structure of non-symbolic,…

The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

The determinants of student decisions to take or not take mathematics were studied. The variables selected for the study were derived from the expectancy/valve model of behavior. Choice is found to be influenced most directly by the utility valve of mathematics for attaining future goals and the interest of on-going mathematics activities.…

This study is one of a series which attempts to arrive at generalizations about the learning of mathematics and the use of its terminology in the context of mathematical structure by young children. The first half of the document describes an experimental training program designed to integrate mathematical concepts of metric space, arc length, and…

This study investigated whether young, poor, inner-city children are deficient in the mathematical skills and concepts necessary for later success in school arithmetic. Children of pre-kindergarten and kindergarten age, black or white, and lower class or middle class, were given a wide variety of mathematical tasks, including Piagetian measures,…

Although geometry and spatial reasoning are important as a way to interpret and reflect on the physical environment and also form the foundation for learning mathematics and other subjects, many early childhood and primary school teachers spend little time instructing their students in these areas. This paper examines how young children learn…