Guilford (1956) presented a developing theory for the concept of human intelligence called “The Structure-of-Intellect” (SI). His theory, which evolved from much of his own and related research, differs from an earlier concept of human intelligence in that he considers human intellect to be an aggregate of many simple abilities, referred to as mental factors, as opposed to the earlier concept that human intelligence is dominated by a single general ability.

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- Author or Editor: Merlyn J. Behr x

### Merlyn J. Behr and Margariete Montague Wheeler

Kindergarten and first-grade children (N=30) used successive punches of a handheld calculator as a means for counting. Each child was presented 16 tasks in two individually videotaped interviews. Data concerning three questions were obtained: (a) Can children maintain a one-to-one correspondence between successive punches of a handheld calculator count and (i) an oral count, (ii) a manipulation of a set of objects, and (iii) a second calculator count?, (b) How do children account for an experimenter induced discrepancy in each of these correspondences?, and (c) With a calculator can children model counting strategies known to be used to process basic addition and subtraction facts? Data suggest an affirmative answer to each question. The authors conclude that it may be possible to facilitate a child's acquisition of addition and subtraction concepts by using the calculator to augment counting behaviors.

### Merlyn J. Behr and Helen Adi Khoury

Third and fifth graders were given a sequence of number pairs and asked ro discover the function rule relating them, test the hypothesis, and generalize it to other instances. The fifth graders were better than the third graders on all performance criteria. Task difficulty depended on the funcuon. Some functions were easier when presented in a graphic mode, others in a symbolic mode. Whether inferences made use of abscissa-ordinate pairs, in contrast to a sequence of ordinate values, appeared to depend on both function and mode of presentation. Unlike adults, the children seemed ready to relinquish a hypothesis in the face of disconfirming evidence.

### Kathleen A. Cramer, Thomas R. Post and Merlyn J. Behr

The aptitude-treatment interaction (ATI) study reported here explored the relationship between cognitive restructuring ability, as measured by the Group Embedded Figures Test (GEFT), and treatments varying in amounts of teacher guidance. It specifically investigated how these two variables affected performance on rational number tasks involving perceptual distracters.

### Merlyn J. Behr and Phillip M. Eastman

The purpose of this study was to replicate and generalize the findings of two earlier ATI studies. 205 Ss were pretested for cognitive ability and then were randomly assigned to 1 of 2 treatments (figural vs. verbal) on a unit in modulus seven arithmetic. Subjects were given 1 class period to study the programmed material and 1 week later retention and transfer tests were administered. The results did not support the earlier findings in this area and indicate that perhaps more investigation in the area of aptitude test construction might be justified. Although not limited to the ATI area, the results indicate that more replication studies are needed before we begin to weigh first results too heavily.

### Phillip M. Eastman and Merlyn J. Behr

The study reported is directly related to the work of Eastman (1975), which was a continuation of work begun by Carry (1968) and Webb (1971). Eastman obtained a significant interaction when the criterion measure of transfer was regressed on factors of general reasoning and spatial visualization. The Necessary Arithmetic Operations test and the Abstract Reasoning test of the Differential Aptitude Test Battery were used to measure these aptit udes, respectively. Two treatments, one graphical and the other analytical, were used to present methods for finding solution sets of quadratic inequalities. In the graphical treatment, concepts were presented in a symbolic-deductive mode. Eastman observed that factor analytic studies indicated that the measure for spatial visualization used by Carry and Webb (paper folding) had factor loadings on deduction. Conjecturing that the problem of deductive versus inductive presentation of the learning material might have been a confounding variable in the studies by Carry and by Webb, Eastman selected a different measure for spatial visualization, revised the instructional treatments to reflect a figural-inductive mode and a symbolic-deductive mode of presentation, and was successful in isolating an interaction.

### Donald H. Sellke, Merlyn J. Behr and Alan M. Voelker

This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. The experimental strategy consisted of building an intermediate problem representation to display the problem quantities in the form of a data table and using multiplicative reasoning. This strategy was compared with a traditional strategy of solving an analogous problem with simpler numbers. Five intact seventh-grade classes participated in the study. Significant effects in favor of the experimental group were found on an intermediate test and a posttest.

### Merlyn J. Behr, Ipke Wachsmuth, Thomas R. Post and Richard Lesh

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 11 interviews with each of 12 children during an 18-week teaching experiment. Six children were instructed individually and as a group at each of two sites. The instruction relied heavily on the use of manipulative aids. Children's explanations of their responses to interview tasks were used to identify strategies for comparing fraction pairs of three types: same numerators, same denominators, and different numerators and denominators. After extensive instruction, most children were successful but some continued to demonstrate inadequate understanding. Previous knowledge relating to whole numbers sometimes interfered with learning about rational numbers.

### Thomas R. Post, Ipke Wachsmuth, Richard Lesh and Merlyn J. Behr

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in an 18-week teaching experiment. Data from observations of, and interviews with, two children were employed to identify patterns over time in the strategies used in performing tasks. Three related characteristics of thinking are hypothesized to be related to the successful performance of tasks on order and equivalence: (a) thought flexibility in coordinating between-mode translations, (b) thought flexibility for within-mode transformations, and (c) reasoning that becomes increasingly independent of specific concrete embodiments.

### Merlyn J. Behr, Ipke Wachsmuth and Thomas R. Post

This report from the Rational Number Project concerns the development of a quantitative concept of rational number in fourth and fifth graders. In a timed task, children were required to select digits to form two rational numbers whose sum was as close to 1 as possible. Two versions of the task yielded three measures of the skill. The cognitive mechanisms used by high performers in individual interviews were characterized by a flexible and spontaneous application of concepts of rational number order and fraction equivalence and by the use of a reference point. Low performers tended either not to use such cognitive mechanisms or to apply concepts in a constrained or inaccurate manner.