THE EFFECTIVENESS OF TWO METHODS OF TEACHING ELEMENTARY MATRIX ALGEBRA

IN RECENT YEARS several studies have been made of the effectiveness of linear programs com pared with other methods of learning, but the results are inconclusive. For example, Austwick (1) com pared learning and retention with programmed ver sus conventional instruction in English, and found that immediate post-test scores were better for the conventional instruction group, while retention sev eral weeks later was relatively better for the exper imental group. Brown (4) compared the same two variables for mathematics. The experimental group proved to be significantly superior to the control group in a test of general ability, and about the same level of superiority was maintained in eight out of nine achievement tests given during the school term. The author concludes that "... no student was penal ized in his level of mathematics achievement be cause of having used programmed materials. " Feld husen, et al (9) also compared the same two varia bles for teaching arithmetic. One group was taught by a program and the other by a teacher for the first seven weeks; the procedures were reversed for the second seven weeks. No significant differences were found between the groups either on achieve ment tests given after the seventh week or on others given after the 14th week. Smith (22) compared the teaching of elementary statistics by the conventional classroom method with the method of programmed instruction. He found no significant difference in performance between the experimental and the con trol group, although the program required less time. Barcus (2) and Bushanell (6) also did not find any significant difference between teaching by pro grammed text and conventional teaching. Beane (3) compared the linear and branching techniques of programmed instruction in plane ge ometry, and found no significant amount of learning during the experiment for all the treatments. Bur ton and Goldbeck (5) presented three programs to ninth-grade students. They consisted of a) construc ted responses, b) multiple-choice questions with dif ficult responses, and c) multiple^choice questions with easy responses. The results did not support the idea that constructed response is superior to multiple choice. Glaser and Reynolds (11) com pared linear with multitrack programs of mathemat ical decision-making. Results of testing indicated little difference in efficiency between the two pro grams. Roe (19) conducted an experiment to com pare simple branching methods with linear program ming. Introduction to certain probability concepts was taught to 189 freshman engineering students. Significant learning took place from the program, but there were no significant differences between any of the branching methods and the linear program when measured by the amount of learning. Zucker man (24) made a study of the effectiveness of differ ent response modes and of ordered versus random sequence of items. No significant differences were found in gain scores between groups which had stud ied constructed response, multiple-choice, and true false programs. Likewise, no significant differ ences were found between groups studying an or dered and a random program. McNeil and Keislar (15) performed an experiment to testthe hypothesis that because covert responses would occur more readily to questions than to statements a program made of questions would elicit more learning than one made of statements. No significant difference was found in the learning resultingfrom the two pro grams. Campbell's (7), Silverman's (21), and Hough's (12) studies are other examples of experi mentation of the same nature. Ginther (10) has suggested a conceptual model for analyzing instruction. Four studies have been made so far using the different cells of the model. Rippey (18) used four cells of the Ginther model in his doc toral dissertation. They were errorless teacher, errorless materials, dialectical teacher, and dia lectical materials. Analysis of the data showed that the achievement in English grammar, punctuation, and usage was not significantly affected by variation along the errorless-dialectical dimension of the in structional model, but was significantly affected by the involvement of the teacher. Sayegh (20) com pared the relative effectiveness and efficiency of lin ear programmed materials and conventional text books and found no significant difference between