Dimensions and Levels of Students' Understanding of Area Measurement
Based on a synthesis of prior research, this study proposes a three dimensional framework to describe the cognitive achievements important for understanding area measurement in upper elementary school years (grade 4-6). Levels within each of the three dimensions were specified. Items were developed to elicit performances indicative of those levels. To refine the items prior to field testing, cognitive interviews were conducted with 28 students (grade 4-5) recruited from two schools in the southeastern US. Sixty items were selected and revised based on results of the cognitive interviews. These 60 items were then piloted with a sample of 267 students (grade 4-6) recruited from the same schools from which participants of the cognitive interviews were recruited. The psychometric properties of the items were analyzed using both classical methods and item response theories (IRT) models. The IRT analyses indicate that the three-dimensional model fits better than the one- and two-dimensional models. Furthermore, the order of the items in general follows the order of the levels they targeted. Quality of the assessment was examined regarding both its reliability and validity. While there might be some concerns of gender DIF in a few of the items, in general the psychometric properties of the assessment were satisfactory. In summary, the results of this study supports the three dimensional framework for describing cognitive achievements in understanding area measurement.