The purpose of this study was to develop a valid and reliable, instrument for determining the mathematics subject matter knowledge of Thai preservice elementary teachers at eight (8) teachers' colleges in eight (8) provinces in northern Thailand. The focus of the content of interest was the operation of division of rational numbers in the context of an appropriate taxonomy of the cognitive domain categories suggested by Wilson (1971). The Delphi technique, item analysis, and "known group" techniques were utilized in the instrument development phases of the study. Hypotheses were tested to determine whether significant differences existed between colleges and between teachers with different backgrounds. The dependent variable was the mean test score for preservice teachers at eight Thai teachers' colleges. The study included the testing of significance for colleges, background, and whether there was significant interaction between colleges and teachers' backgrounds (liberal arts and science). The pilot instrument consisted of 52 items representing four cognitive levels (computation, comprehension, application, and analysis). Based on an analysis of pilot test data, 10 items were eliminated. The final draft instrument consisted of 42 items and was administered to 272 preservice elementary teachers. When field test data were analyzed and compared to "known group" data, 10 items were found to be outside of the acceptability range for difficulty. Item difficulty was used for selecting items for inclusion in the final instrument to measure the operation of division of rational numbers with Thai college preservice elementary teachers. This step in the research served to reduce the number of test items to 32, which constituted the content for the final instrument. The internal consistency reliability was .81 for the 42-item instrument. Content and construct validity were verified by various procedures. / Graduation date: 1994