An Experimental Study of Programed Instruction in Division o/Fraaions

CALVIN GREATSINGER

PURPOSE The purpose of this study was to compare the achievement of a group of sixth grade pupils who were taught division of frac- tions by using programed materials written by the author with the achievement of a control group of sixth grade pupils who were taught division of fractions by using the procedures pre- sented in the teacher's manual of a conventional arithmetic text- book.

Most of the research in programed instruction in elementary mathematics has compared the traditional textbook approach with programed instruction (6). Wesson (9) found no signifi- cant differences between the scores of fourth grade pupils using programed instruction and those using conventional arithmetic textbooks. Although Pikaart (8) found no differences between the two approaches involving problem solving, he did find that pupils who were weak in verbal reasoning performed better on arithmetic reasoning when programed materials were used in- stead of traditional instructional materials.

On the topic of fractions, Miller (7) found no significant dif- ferences between the two approaches; however, his research re- vealed a significant interaction between ability level and amount of gain for the programed instruction groups. Fincher (2) reported that programed materials involving addition and subtraction of fractions were more effective than the ongoing classroom approach. While Arvin (x) found no significant dif- ferences, his research disclosed that the group using programed materials spent approximately one-half of the amount of time used by the conventional textbook groups.

Calvin Greatsinger is a first grade teacher and intern supervising teacher at the Madison School, Greeley, Colorado.

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PROCEDURE

Keislar (5) reported that the subjects using programed ma- terials in a machine showed greater significant gains than a control group. Since Kalin (4) found no differences between the scores of intellectually gifted pupils using programed instruc- tion and those taught by conventional methods, he concluded that using a programed textbook would produce results similar to those obtained by using special teachers and special teaching conditions.

The following null hypothesis was tested: There is no sig- nificant difference between the performance of pupils who are instructed by means of specifically prepared programed mate- rials involving division of fractions and the performance of pupils who are instructed by following the procedures presented in the manual of a conventional textbook. The 365-flame linear program on division of fractions was de- veloped by the investigator. The developmental testing of the program was accomplished as an individual student worked through the frames and then as a class of zo sixth grade pupils completed the program. Further revisions were made after a critical examination of the program by the investigator's doc- toral committee.

The sample used in the experimental study consisted of zz sixth grade classes located in six elementary schools in Greeley, Colorado. In each of the six schools, one sixth grade class used the programed materials on division of fractions and another re- ceived instruction on the same topic by a conventional textbook procedure. These two treatments were randomly assigned to two sixth grade groups in each school. One hundred and fifty-six pupils were induded in the experimental group and one hun- dred and seventy pupils were in the control group.

A 4o-item criterion test was administered by the classroom teachers at the completion of the unit. These tests were scored by the investigator. The skills tested in the criterion test in- duded the following: (z} whole numbers divided by fractions and mixed numbers; (z) fractions divided by fractions, whole numbers, and mixed numbers; O) mixed numbers divided by fractions, mixed numbers, and whole numbers; and (4) reciprocals.

To determine the reliability of the criterion test, the split- half technique was used. This involved calculating a Pearson product-moment coefficient of correlation between the scores

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recorded for each half of the test. The reliability coefficient was found to be .89 .

The data from the criterion test and the covariant (Iowa Tests of Basic Skills) were analyzed using analysis of covariance. The sources of variation were isolated into the adjusted mean squares for the between groups and the adjusted mean squares within groups.

The hypothesis of no difference between treatment popula- tion means on the criterion test was tested by comparing the adjusted mean square between groups and the adjusted mean square within groups. On the basis of the computed F-ratio, the null hypothesis was retained at the .o 5 level of significance. No significant difference was revealed between the achievement of sixth grade pupils who were taught division of fractions by means of programed materials and the achievement of pupils who used a conventional textbook approach.

This study revealed that the experimental group spent 49.~ percent of the amount of time used by the control group. On an average, the control group took 954 minutes to complete the unit. The longest period of time taken by a pupil in the experi- mental group was 9~7 minutes. Thus, considering the saving of time, the use of programed materials proved to be a more efficient method of teaching division of fractions than the con- ventional textbook approach. Since the teachers in the experi- mental dasses were freed from preparing daily lesson plans and assigning and grading practice materials, they should have had more time available to devote to the problems of individual students. However, as pointed out in the work of Goebel (3), time gained through use of programed materials may not be utilized by teachers to provide individualized instruction.

REFERENCES z. Arvin, Charles. An Experimental Study of Programed Instruction in Multiplication of Fractions. Unpublished doctoral dissertation. Greeley: Colorado State College, ~965.

2. Fincher, Glen. The Construction and Experimental Application of a Programed Course on the Addition and Subtraction of Fractions for Grade Five. Unpublished doctoral dissertation. Athens: Ohio University, I963.

3. Goebel, L. G. An Analysis of Teacher-Pupil Interaction When Programmed Instruction Materials Are Used. Master's thesis. Uni- versity Park: University of Maryland, 5966.

4. Kalin, John. Development and Evaluation of a Programed Text- book in an Advanced Mathematical Topic for Intellectually Su-

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perior Fifth and Sixth Grade Pupils. Unpublished doctoral disser- tation. Tallahassee: Florida State University, ~96z.

5- Keislar, Evan. "The Development of Understanding in Arithmetic by a Teaching Machine." Journal of Educational Psychology 50: 247-53; December ~t959.

6. Lackner, Lois M. "Current Research on Programed Texts and Self- Instructional Learning in Mathematics and Related Areas." AV Communication Review 25: z8~-98; Summer ~t967.

7. Miller, Jack. An Experimental Comparison of Two Approaches to Teaching Multiplication of Fractions. Unpublished doctoral dissertation. Nashville, Tenn.: George Peabody College for Teach- ers, �9 96z.

8. Pikaart, Leonard. A Factor Analytic Study of Success in Programed Textbook Instruction in Elementary School Arith- metic. Unpublished doctoral dissertation. Charlottesville: Univer- sity of Virginia, 2963.

9. Wesson, James Burton. An Experimental Evaluation of Selected Techniques for Employing Programs in Elementary School Arithmetic. Unpublished doctoral dissertation. Charlottesville: University of Virginia, 2963.