A COMPARISON OF THE EFFECTIVENESS OF INNOVATIVE INSTRUCTIONAL METHODS UTILIZED IN LOWER DIVISION MATHEMATICS AS MEASURED BY STUDENT ACHIEVEMENT: A META-ANALYSIS OF THE FINDINGS.

Abstract

Mathematics presents a stumbling block to many students, particularly those majoring in scientific fields, business administration, or elementary education. Improvement of student achievement in mathematics at the lower division college level is needed. Seven instructional methods were investigated in terms of student achievement: programmed instruction (P.I.), individualized instruction (I.I.), computer based instruction (CBI), laboratory and discovery methods (Lab), television (TV), audio-tutorial (A-T), and tutoring. The research questions were: (1) What is the relative effectiveness of the innovative instructional methods as measured by student achievement and compared to the traditional lecture method? (2) What is the relative effectiveness of the innovative instructional methods on students of differing ability and course levels. (3) What is the effectiveness of combinations of the innovative instructional methods? A meta-analytical approach was used. Studies comparing an innovative method to the lecture or to another innovative method were located, and the summary data in each were used to calculate an "effect size"--a standardized measure of the effectiveness of the innovative method--to which statistical procedures were applied. The meta-analysis found that (1) Relative to the lecture method, six of the innovative methods produced a positive effect on student achievement. The ranking of the methods in order of decreasing effectiveness was: tutoring, CAI, A-T, I.I., P.I., Lab, TV. (2) The most effective methods by level of course were: (a) Precalculus level: CAI, A-T, and tutoring; (b) Calculus level: tutoring, I.I., P.I., and A-T; (c) Foundations of Mathematics (elementary education majors): P.I.; Descriptive Geometry: TV. The most effective methods by ability level of the student were: (a) High ability: CAI and Lab; (b) Middle ability: CAI, I.I., and P.I.; (c) Low ability: P.I. and A-T. (3) The lack of empirical studies prevent a determination of the relative effectiveness of combinations of the innovative methods. Recommendations include the following: (1) Variation of instructional methods; (2) Incorporation of specific, effective elements of innovative methods into the lower division college mathematics instructor's repertoire; and (3) Empirical investigation of the effectiveness of combinations of methods and of various instructional methods on students of different ability levels.