ERIC Number: ED064405
Record Type: RIE
Publication Date: N/A
Reference Count: 0
Validating Learning Hierarchies for Sequencing Mathematical Tasks.
Phillips, E. Ray; Kane, Robert B.
A major problem encountered by both teachers and authors of instructional materials is the sequencing of instructional activities. A review of the literature is given and it is pointed out that there is substantial evidence to support the general theory of the hierarchical structure of knowledge. A learning hierarchy for the computational skills for addition of rational numbers with like denominators was constructed. Based on the hypothesized ordering of the subordinate levels, a test was constructed to assess mastery at each level in the hierarchy; it was administered to 163 elementary school children in grades 4 through 6. The pass-fail relationships were analyzed using the following indirect validation procedures adaptable for use with test data: item difficulty, the AAAS approach, the Guttman technique, pattern analysis, and correlation analysis. Materials consisted of an 11-lesson programed booklet on the addition of rational numbers with like denominators. Fourth grade Ss were selected to participate in the study on the basis of their performance on two pretests. The hierarchical orderings of the 11 subtasks generated by each of the indirect validation procedures are given in tabular form. A pattern analysis technique was used to determine the index of agreement of each ordering with the expected patterns. This index was above .86 for all orderings except the textbook and random sequences. Neither planned nor post hoc comparisons showed any significant differences between the logical sequence group and the other sequence groups on achievement, transfer, or retention. Careful analyses of instructional objectives to reveal the prerequisite subtasks is an adequate procedure for developing a valid hiererchy. (CK)
Publication Type: N/A
Education Level: N/A
Sponsor: Office of Education (DHEW), Washington, DC.
Authoring Institution: N/A