Intellectual Development Beyond Elementary School IV: Ratio, The Influence of Cognitive Style

Abstract

In order to resolve ambiguities remaining after our earlier investigations,112 we have continued our investigation of students' ability to apply the ratio concept in a simple task of measurement and prediction. We can now report significant progress toward clarifying the relationships among students' responses to the task. It appears that many of the subjects who do not use proportional reasoning have access to several alternate procedures; they make use of one suggested by some particular aspect of the task presentation. This personal preference, we believe, reflects the individual's cognitive style3 rather than a developmental level in the Piagetian sense.4 These conclusions were derived from the use of a new form of the ratio task administered to 616 students in grades 4 through 9. We shall call the new procedure Form B, to distinguish it from the original version to be called Form A. Method of PresentationFor all groups studied, Form B was administered by one of the authors. The subjects were given answer pages as described previously (Fig.

Intellectual Development Beyond Elementary School VIII: Proportional, Probabilistic, and Correlational Reasoning

“…In this respect, the present data are consistent with earlier results using the Paper Clips Task (Karplus, Karplus, and Wollman 1974; Karplus and Peterson, 1970;Karplus et al, 1975), which was found by Kurtz (1976) to be closely equivalent to the Cylinder Task.…”

“…Our findings for Item 1 (proportions) in Table 2 indicate that most of the sixth graders used additive procedures (Category A), while the majority of the upper-middle-class high school students used proportional reasoning (Category R). In this respect, the present data are consistent with earlier results using the Paper Clips Task (Karplus, Karplus, and Wollman 1974;Karplus and Peterson, 1970;Karplus et al, 1975), which was found by Kurtz (1976) to be closely equivalent to the Cylinder Task.…”

Student Performance in Water Pouring and Balance Beam Tasks: effect of manipulation of perceptual field factor

“…Study I 4-6 6-X Study II 3-5 4-X of the task enables a significant number of Ss to overcome two of the most common kinds of error factors (Pascual-Leone, 1976): (a) overlearned schemes or structures: solving the problem by ADDITION (Karplus, Karplus & Wollman, 1974) and maintaining a difference of two levels, a reasoning structure developed successfully in other situations, but irrelevantly elicited in the present situation and (b) Organismic disposition to produce performance: Field-activated figurative schemes impose the dominant feature of maintaining a difference of two levels. It is interesting to note that in the Water Pouring Task I: (a) 68% (217 out of 318) of the Ss responded incorrectly water level 8 in Study I and after the manipulation of the perceptual field factor 46% (52 out of 113) of the Ss responded incorrectly water level 6, in Study II and (b) 21% (66 out of 318) of the Ss responded correctly water level 9 in Study I and after the manipulation of the perceptual field factor 45% (51 out of 113) of the Ss responded correctly water level 6%, in Study II.…”

Math*Logo: A Project to Develop Proportional Reasoning in College Freshmen

“…Subjects then completed a 30-hour course in basic mathematical skills in either the control group or the experimental group (Math*Logo). Subjects were also administered two different forms of the Karplus (1974) paper clip task prior to and after completing the 10-week course to verify their change in proportional reasoning skills. The subjects completed the pencil-and-paper form of the paper clip task, as shown in Figure 1, to the best of their ability in ten minutes.…”