Predictive Values of Testing Vs. Teacher Recommendations in Assessment of Mathematical Competence of Middle School Students.

Abstract

This study assesses the relative effectiveness of two methods of selecting mathematically gifted sixth grade students in the Ann Arbor school system for a seventh grade accelerated math class: (1) an objective method based on test scores (2) a subjective method based on sixth grade teacher observations. Two sixth grade populations during the school years 1979-80 and 1980-81 are studied. Two measures are taken at the end of the sixth grade: (1) scores from a teacher-developed mathematics assessment test (MAT) which consists of a "computation test" (a 25 problem multiple-choice test of operations of rational numbers, geometric concepts and metric measurement) and a 12 problem open-ended word problem test (2) recommendations by each student's sixth grade teacher regarding placement in a seventh grade accelerated math course. At the end of the seventh grade, the observation is made of the presence or absence of a student's name on the eighth grade Algebra I course enrollment list. The diagnostic performance of the two methods of selection are evaluated with calculations of sensitivity, specificity, predictive value of a positive result, predictive value of a negative result, and efficiency. The results of this study indicate that the "computation test" scores are a better method of selection than the teacher recommendations for two reasons: (1) they have the advantage of providing predictive values for a range of scores (2) they reduce the chance of excluding meritorious students. Conclusions. (1) The "computation test" is more effective in detecting students who should be in accelerated math than the teachers are. (2) Teachers are more effective in detecting students who should not be in accelerated math than the test scores are. (3) Students who do well on a "computation test" in grade 6, also do well in a grade 7 accelerated math course, and enroll in Algebra I in grade 8, even if they are not recommended by their grade 6 teachers. (4) Student-parent requests for placement in Algebra I adds some yet-to-be-determined increment to the predictive formula. (5) The Galen-Gabino predictive value model is an appropriate and valid method for use in education studies.