An empirical investigation of Gagne's cumulative learning theory vs. Piaget's developmental theory regarding the conservation of liquid

Abstract

The purpose of this study was to determine if some of the major "rules" mentioned in Gagne's hierarchy for learning conservation (FIG. 1) are in fact acquired in the order suggested by the hierarchy. Three rules were distinguished and defined from the hierarchy and two hypotheses were developed regarding the order of those rules (see pp. 6-8). To measure the subject's mastery over the rules, a test was developed for each of the first two rules (Rule 1, area of rectangle; and Rule 2, volume of rectangular container). For Rule 3, the conservation of liquid, two parallel tests were chosen from Inhder, Sinclair, and Bovet, 1974. One of these tests was used as a pretest and the other as a posttest (for more details on the tests, see CHAPTER III and APPENDIX 1). The subjects were 100 K-4 students chosen at random from a rural school in Texas. Each subject took a pretest for Rule 3 and the tests for Rules 1 and 2. One half of the subjects took the tests for Rule 1 before the test for Rule 2 and the other half took the same tests in a reverse order. A posttest for Rule 3 was given only to those who failed the pretest. All subjects took part in the test for Hypothesis I, while only those who failed the pretest (n = 72) took part in the test for Hypothesis II. To test for Hypothesis I, a method of generating task analysis (Bart and Airasian, 1974) was applied to see if Rule 1 was prerequisite for Rule 2 and Rule 2 prerequisite for Rule 3. As to the Hypothesis II, the order of taking the tests for Rule 1 and Rule 2 was considered as a treatment dividing the subjects into the experimental and control groups. A Chi-Square test was used to find out if the order of presenting the two rules had any influence on the subject's performance on the posttest for conservation of liquid (Rule 3). Both null hypotheses defined for this study were accepted, and the idea that Rule 1 is prerequisite for Rule 2 and Rule 2 is prerequisite for Rule 3 (as suggested by Gagne's hierarchy) was not supported. However, a series of ancillary investigations revealed that a sequential order between each of the Rules 1 and 2 with Rule 3 can be assumed.