Development Of An Instrument To Measure Proportional Reasoning Among Fast-Track Middle School Students

Abstract

The purpose of the study was to develop a reliable and valid instrument for measuring proportional reasoning among fast-track middle school girls in Wake County, North Carolina. The study sample consisted of 70 girls who attended the summer 2000 Girls on Track program at Meredith College located in Raleigh, North Carolina. The grade level for each of the participants ranged from 6th grade through 8th grade for the 2000-2001 school year. The instrument used in this study is the Proportional Reasoning Assessment Instrument. This instrument was developed by the researcher and is based upon problems discussed in relevant literature. The test items chosen include missing value, comparison, mixture, associated sets, part-part-whole, graphing and scale problems. The instrument is comprised of 10 open-ended items of varying difficulty levels. Data were analyzed using Statistical Package for the Social Sciences Version 10.0 (SPSS) and EXCEL. A four-point grading rubric was used to score each test item. Two measure of internal consistency were calculated to determine reliability: Chrombach's coefficient alpha and inter-rater reliability. A panel of experts examined the test instrument for the qualities of relevance, balance, and specificity to establish content validity. Criterion validity was established through determining the correlation between students' scores on the Proportional Reasoning Assessment Instrument and the students' scores on the North Carolina End-of-Grade exam. A detailed item analysis was performed including item difficulty, item discrimination, item means, item variances, and inter-item correlations.Results from the study reveal the Proportional Reasoning Assessment Instrument is a reliable and valid test instrument for measuring proportional reasoning among fast-track middle school girls. In addition, the instrument revealed common misconceptions among the students in the sample. The overall coefficient alpha is α = .7083 and inter-rater agreement was 96%. The average difficulty is P[subscript mean] =.4 and the average discrimination is D[subscript mean]=.405714 . Each test item contributed to the central purpose of the instrument due to the absence of negative discrimination indices.