Development of Numberline and Measurement Concepts

In a two-part study, children in Grades 1 through 3 were given a set of numberline estimation problems and a set of similar numberline estimation problems that were to be solved using specially designed rulers. The estimation tasks showed a complex pattern of change in accuracy and strategies over the three grade levels. This pattern indicated that children progressively altered their estimation strategies from strictly sequential ones to ones that incorporate elements of proportional reasoning. This shift was gradual and implemented school-learned numerical relationships in the solution of these novel tasks. There was no indication that, in the Piagetian sense, stage changes contributed to strategy development. However, the use of rulers with different spacings between the numbers indicated that children's acquisition of a principled concept of equal intervals required both the learned convention of equal intervals and the achievement of conservation of length.