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Doctor of Education (EdD)


John J Pantana

Primary Subject Area

Education, Curriculum and Instruction; Education, Mathematics


Algorithm, Fractions, Instruction, Middle School


The purpose of this quasi-experimental research study was to examine the effects of an alternative or transactional algorithm for subtracting mixed numbers within the middle school setting. Initial data were gathered from the student achievement of four mathematics teachers at three different school sites. The results indicated students who utilized the transactional algorithm demonstrated greater comprehension, retention, and computational accuracy than those who utilized traditional algorithms. The difference between the scores of the two groups was statistically significant. The follow-up investigation employed a quasi-experimental nonrandomized Test 1-Test2 control research with two teachers. An analysis of variance (ANOVA) was used to analyze the data obtained from 7th graders at one middle school setting. The null hypothesis was that there would be no difference in the achievement levels of students regardless of which algorithm was used to solve subtraction of mixed numbers. The null hypothesis was rejected as the difference between the two groups was statistically significant. Overall, the use of the transactional algorithm for subtracting fractions improved student performance in both the short term and long term. The implication of this study was that multiple strategies, especially ones that provided connections with real life experiences of the child, increased student achievement within the classroom.