Hierarchical approach versus traditional approach to instruction in eighth grade mathematics

Hawco, Augustine (1976) Hierarchical approach versus traditional approach to instruction in eighth grade mathematics. Masters thesis, Memorial University of Newfoundland.

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Abstract

Purpose of the Study -- The main purpose of this study was to compare the achievement and retention of Grade VIII students taught a unit on solving equations using Gagne's Hierarchical Approach with a group using the Traditional Textbook Sequence. -- Procedures -- The investigation was carried out in three Grade VIII classes in one school in Avondale, Newfoundland. The sample consisted of 76 students. These students were randomly assigned to two groups of the same size. One group was randomly assigned the Textbook Approach and the other group the Hierarchical Approach. -- The Textbook Group learned how to solve first degree, one variable equations by studying a programmed booklet developed by following the exact sequence of the textbook that was used at this grade level. The Hierarchical Group studied a programed booklet prepared by following the ideas of Robert Gagne. This approach consisted of performing a task analysis on the terminal objective, setting up a learning hierarchy for these skills, and sequencing these tasks in the programed booklet according to the learning hierarchy. A prerequisite test would be given the Hierarchical Group and students would begin the instruction at the point where the prerequisite skills were missing. -- The students received two - forty minute periods of instruction per day. It took ten days for the students to complete the programed booklets. During the study, students remained in their own classrooms and worked entirely on their own with a minimal of teacher guidance. Students were not aware that they had been divided into groups and were taking part in a study. From the exterior, both instruction booklets appeared to be the same. -- Students were given a posttest one day after the completion of the instruction and a retention test was given two weeks later. These tests were alternate forms of each other. The statistical technique of the analysis of covariance was used to determine if the difference in achievement and retention between the two groups were significant. The level of significance was set at .05. -- Conclusions - 1. The Hierarchical Approach to instruction produced significantly better achievement results than the Textbook Approach. - 2. The Hierarchical Approach to instruction produced significantly better retention results than the Textbook Approach. -- 3. The Hierarchical Approach to instruction would be one method of reducing underachievement in our mathematics classrooms.

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