Facility with number and measure is necessary for independent, functional living in today's society. The concept of a unit within a measure system provides the basis for understanding mathematical topics such as place value, common fractions and indirect estimation. Mastery of these topics underlies computational facility and is necessary for future self-sufficiency and quantitative literacy. However, many young children experience their first academic failure when they encounter these topics in the school curriculum. Due to the hierarchical nature of mathematics, this early failure may limit the children's potential for subsequent mathematics learning, resulting in cumulative failures. One explanation of this initial failure is that children lack the requisite cognitive maturity to understand the concept of a unit. Another explanation is that current curricular emphasis on the number/unit concept as a characteristic of discontinuous quantity leads to erroneous generalizations regarding the unit concept. Because the Logo microcomputer programming language provides an opportunity for children to increment and decrement unit size and quantity, thus experiencing and controlling numerosity as an abstraction, it offers a valuable research setting for examining children's understanding of measurement and the unit concept. This study will assess young children's developing conceptualization of number/unit and the influence of logical reasoning abilities on that conceptualization. Kindergarten and first-grade children will be administered Piagetian length conservation and transitivity tasks prior to Logo instruction. Small group Logo instruction will occur in a microcomputer laboratory as part of the established curriculum in the children's school. An Estimation of Distance task, which will assess the children's interpretation of number, unit and measure properties, will be individually administered after 2, 5 and 9 hours of Logo instruction. In particular, this task will assess the children's interpretations of these unit/measure properties: a distance can be traversed by iterating a given unit; a distance can be traversed by constructing a new unit, which consists of a multiple of the initial unit, and iterating that new unit; the number of units required to traverse a distance varies inversely with the size of the unit; and distance is independent of the spatial/perceptual features of the display.
