Date of Final Oral Examination (Defense)

8-2010

Type of Culminating Activity

Dissertation

Degree Title

Doctor of Education in Curriculum and Instruction

Department

Curriculum, Instruction, and Foundational Studies

Major Advisor

Jonathan L. Brendefur, Ph.D.

Abstract

The purpose of this study was to evaluate the effectiveness of a computer-based assessment to reveal mathematical understanding. Relevant literature suggested that developments in cognitive science and computer-based assessments could allow the outcomes of cognitively guided instruction to be made explicit. An assessment instrument designed to make mathematical thinking explicit was developed and administered, consisting of 15 animations showing the solutions of one and two digit multiplication problems. A consistent set of five questions followed each animation. The assessment was administered to four classes of fourth grade students in two elementary schools participating in cognitively guided instruction professional development programs.

Findings showed that students, individually and as a group, preferred a limited and consistent set of strategies to solve problems and that some students may have developed increased understanding of a problem over the course of the five questions. Results also showed that the group was weakest on the concept of place value, but was able to apply strategies appropriate to particular problems. Correlations between the data from different questions suggest students vary in their understanding of components of the proposed construct of multiplication, which might otherwise be viewed as a unitary concept. Individual student strengths and weaknesses could not be determined because of the data’s low reliability quotients.

For open-ended questions, smaller amounts of information in responses seemed to equate to lower levels of understanding. The assessment revealed possible instructional strategies at the group level, but refinement of the assessment will be necessary before individual student abilities can be reliably assessed.

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