Apr 1, 1979 - TREVOR G. BOND. Department of .... Bynum, T., Thomas, J., & Weitz, L. J. Truth-functional logic in formal operational thinking: In- helder and ...
COMMENTS AND CRITICISM
The Psychological Link across Formal Operations TREVOR G. BOND Department of Education Studies, Townsville College of Advanced Education Queensland, Australia, 481 4
Introduction
Lawson (1 979) addresses two questions of considerableimportance to science educators and Piagetian psychologists. They are: is there evidence to support the contention that a unified, structured whole of operations underlies the formal operational schemata of combining variables, controlling variables, and proportions and, if so, is this structured whole based on the system of 16 binary operations and the identity-negation-reciprocity-correlativity (INRC) group as claimed by Inhelder and Piaget (1 958)? Although Niemark (1975) finds the evidence for the existence of such a factor as being equivocal, Lawson’s evidence is somewhat compelling. This paper reports on a research project that is directly related to Lawson’s paper (1979). The aim of this project is to perform similar analyses on data extracted from another study carried out recently in Australia (Bond, I980a) and to compare the results with those of Lawson. Lawson’s rather rigid specifications for suitable subjects for an investigation are certainly worthy of further consideration by researchers. In particular, research at the formal stage needs to include adequate numbers of subjects at the upper limits of the stage, as well as subjects who have not developed formal operational ability and those in whom these abilities may still be developing. Evidence from large-scale investigations would tend to show markedly reduced measures of relatedness if the sample were to inadequately represent any of these three groups. One may wonder at Lawson’s further claim for the necessity of a restricted age sampIe when formal operational ability may be seen to develop over a number of years around adolescence. Perhaps age variations, if not taken into consideration with the criteria mentioned above, may have the potential to confound the Science Education 64( I ): 1 13- I 17 (I 980) 0 1980 John Wiley & Sons, Inc.
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results. While the present investigation did not intentionally adopt Lawson’s procedure, it was conducted considerably before and quite independently of the latter. For the sake of brevity, the description of the method will stress the few differences in procedure, rather than the numerous parallels. Method
Subjects The subjects were 30 students selected from grades 8-12 at a large provincial high school in Townsville, Queensland. The sample was independently selected by colleagues in order to represent the full range of scores achieved on the Bond’s Logical Operations Test (BLOT) (1980b). BLOT is a 30-item multiple-choice test based on the schemata of the formal operational stage described by Inhelder and Piaget (1 958). Furthermore, it is based on common language expressions of Piaget’s 16 binary operations and the I N R C four-group of operations mentioned by Lawson. The students’ age group ( 1 2+ to I8 years) and the widespread academic ability of the subjects should further ensure a wide range of formal operational ability within the sample.
Procedure Each of the 30 subjects attended an interview session during which the three tasks were administered. The investigator conducted all of the mCthode clinique interviews and made written notes of subject behaviors. These notes were later used to supplement audio recordings of the interviews so that accurate assessment of formal operational ability could be made.
Tasks The investigation fortuitously included the chemicals problem and the balance beam problem later selected by Lawson. The third task used was the pendulum problem, which lnhelder and Piaget (1958) relate to the bending rods problem (used by Lawson) thus: We have just seen how the subject goes about separating out factors in order to determine their respective effects in a multifactor experimental setup (bending rods). The present chapter takes up the reaction of the child and the adolescent in an analogous situation with the difference that only one of the possible factors actually plays a causal role; since the others have no effect they must be excluded after they have been isolated. (p. 67)
The criteria for performance for each stage of logical development for each task were independently developed by the investigator and an experienced colleague from an examination of Inhelder and Piaget’s description (1958). Originally the stages devised by Piaget (i.e., IIA, IIB, IIIA, IIIB) were adopted for the scoring of tasks; this was subsequently converted, for the purpose of these analyses, to a 1-7 scale as described by Lawson ( 1979, p. 69). The audiotapes and written notes were independently assessed by the two raters who had developed the criteria and this produced 100%agreement on the assignment of stages for all performances.
PSYCHOLOGICAL LINK ACROSS FORMAL OPERATIONS
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TABLE I Mean Scores and Standard Deviation of Task Responses
5T
S.D.
Chemical Combinations
3.77
1.76
Pendulum
4.27
1.68
Balance Beam
3.67
1.40
(a) Chemical combinations: As described by Lawson (1 979) and Inhelder and Piaget ( 1958) requires the use of combinatorial reasoning. (b) Pendulum: As described by Inhelder and Piaget (1 958), three weight? (of ratio I :2:3) and a variable length of string are manipulated by subjects to determine which variable (angle of amplitude, force on release, mass, length of string) affects the period of the pendulum. The task requires the isolation of variables and the exclusion of the irrelevant ones. (c) Balance beam: As described by Lawson (1979) and Inhelder and Piaget (1993, the subject is asked to balance the following weights on a meter-long beam: a one unit weight and a two unit weight; a two weight and a four weight; a two weight and a six weight; a four weight and a six weight; and a five weight and a six weight. The subjects had to calculate the length of both lever arms and explain the relationships devised. The task requires the understanding of proportionality. Results
Levels of Response As far as possible, the analysis of results followed Lawson’s description in order to enhance the comparability between the two sets of data. All tasks scored on the full range from 1-7. The mean scores and standard deviations are presented in Table I. The scores for each task were grouped into concrete (1-3), transitional (4), and formal (5-7) and are included in Table 11.
TABLE II Responses on Task According to Cognitive Stage Concrete N ~
(%)
Transitional N
(%)
Formal N
(%)
~
Chemical Combinations
18 (60%)
1 (3.3%)
11 (36.7%)
Pendulum
16 (53.3%)
0
14 (46.7%)
Balance Beam
19 (63.3%)
3 (10%)
8 (26.7%)
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Relationships among Level of Responses The relationships among scores for the three tasks are indicated in the following correlation coefficients (all p
