Date of Award
Doctor of Philosophy
College of Education and International Services
Larry D. Burton
R. Lee Davidson
Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an out-of-school-time geometry curriculum and looked at its impact on mastery of geometric concepts. This program was entitled Geometry in Real-life Application Curriculum Experiences (G.R.A.C.E.).
The instructional product development procedure of Baker and Schutz was employed in this study. First the need for an empirically developed geometry education product for Pathfinders was established. Then behavioral objectives were written, based on the standards developed by the National Council of Teachers of Mathematics and geometry education literature. Instructional activities were prepared to help meet each objective and organized in logical sequence. Bloom’s Revised Taxonomy served as a resource during initial instructional development. The Baker and Schutz process stipulated that the instructional product undergo repeated tryouts with members of the target population. The development process would be considered complete when a minimum of 80% of G.R.A.C.E. Project participants scored at least 80% on each of the stated objectives. Accordingly, the instructional product was subjected to repeated revision during its developmental stages. Appropriate adjustments were made to eliminate specific weaknesses. Both developer’s and participant’s manuals were created in their final forms.
The completed G.R.A.C.E. Project consists of a developer’s manual, pre- and post-tests for participants, and a participant’s manual. The developer’s manual covers both relevant content and detailed procedures for project presentation and test administration. The participants’ manual presents mathematics content to be mastered by participants. In addition, review questions and answers, diagrams, and charts are included to facilitate mastery of project contents. The pre-/post-test inventory consists of a 25-item cognitive instrument combined with a 20-item affective instrument. After three field trials and revisions of the curriculum, the product was delivered to 25 subjects. These subjects were able to achieve cognitive mastery at the level specified for the 25 objectives. Based on the assumptions of the Baker and Schutz model the percentage difference between affective post- and pre-test scores was expected to be positive, yielding a moderate effect size. However, the average effect size for all four groups was .868, indicating a high impact of program on subjects’ interest in and appreciation of geometry concepts.
This study provided insight into the role of curriculum developers as they engage in the process of empirical development. It also provided a resource for instructors in Pathfinder instructional programs in the Lake Union Conference of Seventh-day Adventists. Other Seventh-day Adventist audiences may also utilize a modified version of the instrument in their instructional programs for Pathfinders.
Geometry--Study and teaching; Pathfinders (Organization)
Williams, Donaldson, "Empirical Development of an Instructional Product and its Impact on Mastery of Geometry Concepts" (2009). Dissertations. 1724.
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