Learning Hierarchies: Numerical Considerations

Eisenberg, Theodore; Walbesser, Henry H.

doi:10.2307/748482

Cited by 3 publications

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“…Additional data analyses providing internal evidence of differential transfer effects resulting from attainment versus nonattainment of prerequisite skills were also explored as tests of effectiveness (Gagné et al, 1962, Table 3, p. 9). Several quantitative measures for evaluating learning hierarchies are described by Eisenberg and Walbesser (1971).…”

Section: Validating Learning Hierarchiesmentioning

confidence: 99%

1: Learning and Instructional Sequence

Gagné¹

1973

Review of Research in Education

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Anyone who undertakes to bring about learning of a particular sort finds himself arranging a set of stimulus conditions that act upon the learner. In the simplest of cases, these stimuli may need to be made to occur only during a single brief period of time in order for the desired learning to take place. Far more frequently, however, the expected learning requires a stimulus situation that extends over a period ranging from seconds to minutes, even when one is dealing with a single learning objective. Since such durations are involved, the question of sequence naturally arises with respect to the arrangement of conditions for learning. What conditions need to occur first, what next, and what last in order for effective learning to be assured?The problem of arranging sequences of learning conditions, or, in other words, sequences of instruction, continues to be a topic of considerable importance for those who design and carry out instruction. In empirical research, the topic of this review has been capably addressed by several previous writers, sometimes in part and sometimes comprehensively. Interest in research related to instructional sequence continues to be reasonably high, and a substantial number of reports of empirical investigations has appeared from 1967 to the present. STATEMENT OF THE PROBLEMBefore reviewing research studies and their results, it is necessary to make a somewhat detailed analysis of the problem of instructional sequence. This LEE S. SHULMAN, Michigan State University, was the editorial consultant for this chapter.

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Section: Validating Learning Hierarchiesmentioning

confidence: 99%

1: Learning and Instructional Sequence

Gagné¹

1973

Review of Research in Education

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“…Critical analyses of the efficacy of these techniques are also reported (Resnick &Mang, 1969;Eisenberg & Walbesser, 1971;White, 1973;White, 1974a, 1974b: Phillips, 1971, 1974. Many of these techniques are concerned with the analysis of data collected on hypothesized hierarchies.…”

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An Intraconcept Analysis of Rational Number Addition: A Validation Study

Uprichard¹,

Phillips²

1977

Journal for Research in Mathematics Education

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A hierarchy for learning to solve different types of addition wit fractions problems was hypothesized on the basis of both content a lysis and psychological considerations. Problem types were defined acco ding to the relationship of the two denominators to each other (e.g., e al, prime, etc.) Students in grades 4 through 8 were each given 45 ad tional problems to perform. Papers which were totally correct or totally, incorrect were deleted leaving a sample of 200. These papers were analyzed using both the Walbesser Technique and Pattern Analysis. No ordering of the tasks was found to yield acceptable levels for all of the Walbesser ratios (consistency, adequacy, completeness). However, with few exceptions, task comparisons yielded acceptable values on two of the three ratios. The empirically determined sequence was analyzed and seven implications for teaching addition with fractions were determined. (SD) * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original.

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Conservation of Volume: Testing as a Means of Instruction

Bright¹

1972

The Journal of Psychology

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Learning Hierarchies: Numerical Considerations

Cited by 3 publications

References 0 publications

1: Learning and Instructional Sequence

1: Learning and Instructional Sequence

An Intraconcept Analysis of Rational Number Addition: A Validation Study

Conservation of Volume: Testing as a Means of Instruction

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