# EFFECTS OF TEACHING SIXTEEN BINARY COMBINATIONS WITH OR WITHOUT THE INRC GROUP ON PROBLEM SOLVING

#### Abstract

This study was undertaken to determine whether the INRC group was an effective heuristic method, that is, a strategy to help the subject to develop subgoals in order to solve 16 binary combinations problems. If the INRC group is a facilitating, generalizable heuristic method, it should help subjects with the 16 binary combinations regardless of the subject area. The purpose of the present study was to determine which method, the INRC group as a possible heuristic, or wider practice through the direct teaching of generalizability, was more facilitative of generalizability in applying the 16 binary combinations to solve naturalistic problems (from sociology, economics, and social studies) and scientific problems (from biology, chemistry, and physics).^ The following null hypotheses were tested for both the naturalistic and scientific tests: (1) there are no significant differences among the three treatment mean scores across the three tests (mid-treatment test, posttest, and retention test); (2) there are no significant differences between the mean scores of the tests, across treatments; and (3) there are no significant interactions between treatment and time of administration.^ The sample of 84 students was selected from a 12th-grade elementary functions course in a selective mathematics high school in New York City in order to insure that subjects could perform the group logic.^ The treatments attempted to help subjects develop alternative solutions to problems involving two variables from two subject areas. The development of the solution structure involved combining the variables using the 16 binary combinations as a problem-solving technique. In two of the treatments, subjects were taught the 16 binary combinations with the INRC group and naturalistic and scientific problems, differing only in the order of presentation of naturalistic or scientific problems. In the third treatment, subjects received direct training in generalizing the 16 binary combinations to scientific and naturalistic problems, using an algorithm of increasing the number of binary combinations taken at a time.^ The instruments were naturalistic and scientific problem-solving tests adapted by the investigator. Questions described a situation which the subject was required to resolve by increasing and decreasing two variables. Students were asked to write each possible combination of the two variables in a separate sentence for each combination.^ In the analysis of the data for both the naturalistic and scientific tests, no significant differences were found between the three treatment mean scores across the mid-treatment, posttest, and retention tests. However, all subjects scored significantly higher on the posttests than on the mid-treatment tests, across the three treatments. Subjects did not differ in mean scores between posttest and retention test. No significant interactions were found between treatment and time of administration of test. In other words, there were no significant differences in the mean score achievement by the subjects in each of the three treatment groups (INRC and 16 binary combinations) at each of the three test trials (mid-treatment test, posttest, and retention test).^ The results of the study were inconclusive in support of the INRC group as an heuristic set of rules for solving naturalistic and scientific problems. However, the mid-treatment test comparisons indicate that the subjects trained with the INRC in one area were as equally effective with problems in two areas as the subjects trained with 16 binary combinations in the two areas. The INRC-trained subjects apparently overcame the problem of horizontal decalage at that point in the experiment.^ One implication of the study was that training with the INRC group only in one area might transfer consistently to other areas. ^

#### Subject Area

Curriculum development

#### Recommended Citation

ROTHENBERG, RICHARD LEWIS, "EFFECTS OF TEACHING SIXTEEN BINARY COMBINATIONS WITH OR WITHOUT THE INRC GROUP ON PROBLEM SOLVING" (1980). *ETD Collection for Fordham University*. AAI8021002.

http://fordham.bepress.com/dissertations/AAI8021002