Feedback in Software and a Desktop Manufacturing Context for Learning Estimation Strategies in Middle School

Abstract

The ability and to make good estimates is essential, as is the ability to assess the reasonableness of estimates. These abilities are becoming increasingly important as digital technologies transform the ways in which people work. To estimate is to provide an approximation to a problem that is mathematical in nature, and the ability to estimate is closely related to several key mathematical skills and aptitudes. These combined aptitudes allow individuals to judge reasonableness, or the proximity of estimates to the actual exact answer. Types of estimation such as computational and measurement estimation hinge on this sense of the reasonableness of an answer, but the concept of reasonableness itself is not given sufficient attention in primary and secondary grades in the U.S.Digital technology provides the means to explore and refine student estimation strategies. Four studies were conducted with upper-elementary and middle school student participants. These featured the Estimation Calculator that provides immediate feedback on the percent error of estimates.The first three exploratory studies provided a backdrop for the fourth study, which was conducted at a public middle school. This study also featured emergent desktop manufacturing technology. Such technology allows digital designs to be printed in three dimensions. The geometric nature of 3D design was used in conjunction with estimation instruction for a unit on computational and volume estimation. The guiding question in the research was whether instruction and practice with estimation-feedback software and 3D design software would influence students' estimates and strategies.Estimation skills vary widely by class assignment. Students in a standard seventh grade mathematics class made estimates that were significantly less reasonable (partial ω 2 = .02) than those of two advanced classes. The complexity of their strategies, as measured by digits that were included or ignored during rounding, was notably higher than their peers, suggesting that they were unfamiliar with simplification in estimation (Lefevre, Greenham & Waheed, 1993). An interaction effect (partial ω 2 = .03) was present between the complexity of their estimates and those of their peers in advanced mathematics classes, suggesting an aptitude-treatment-interaction. Estimates using volume were hindered by computational estimation errors for all groups.