Use of the microgenetic method to assess estimation of length strategies in third grade students

Following a microgenetic design, this study investigated third-grade students' construction of mathematical knowledge during novel problem solving, as reflected in their strategies for solving estimation of length problems over an extended period of 6 weeks.{09}Tasks varied in type and complexity and represented the full spectrum of estimation of linear length activities. Performance measures were collected and the student's measurement behavior during the problem-sessions was audio- and videotaped. Quantitative and qualitative analyses resulted in the identification of 8 strategies for estimation of length. Each of these strategies fit within three categories: 'strategies requiring visual processing', 'strategies requiring verbal processing' and 'combination strategies'.; The role of individual differences (gender and cognitive processing style) in strategy usage and development was also investigated. As was hypothesized prior to data collection, student estimators demonstrated preferred styles for solving estimation of linear length tasks, and preliminary results suggest that these preferred styles were related to gender. Overall, female and male estimators utilized the 3 'visual strategies' identified equivalently. However, gender differences were found in which 'visual strategies' they used, and the estimation tasks in which they employed these strategies. Male estimators split their usage evenly between the 3 'visual strategies' while female estimators underutilized '2-d mental rotation'. Female estimators however utilized 'verbal strategies' more often than their male counterparts. Usage by female estimators accounted for 76.2% of the utilizations of 'verbal strategies'.; In considering the educational implications, these findings suggest that in order to improve both classroom practice and student performance, the range of estimation-tasks presented to students needs to be broadened to include the full spectrum of estimation activities. Additionally, given the underlying visual nature of measurement demonstrated by the findings, estimation-activities that include and encourage the use of 'imagery' should be emphasized.