The effect of Factor Blocks(TM), a manipulative, on student understanding of greatest common factor (GCF), least common multiple (LCM), and prime factorization (PF)

Student understanding of mathematics is an issue paramount in political and educational circles. This concern about student understanding has led educators to use various strategies to promote both the alignment of standards to their curriculum, and the accountability of instruction and learning. Fraction concepts, fraction operations, and the related skills using greatest common factor (GCF), least common multiple (LCM), and prime factorization (PF), as well as ideas about number theory in general, continue to baffle middle school students. As a result, finding the right method of instruction on these topics based upon a mix of historical perspective and present-day emphasis is necessary to improve student understanding. One attempt to address the challenge of teaching number theory-related fraction concepts led to this experimental study on Factor Blocks™, a new manipulative used as an instructional intervention for a variety of topics. In this study, Factor Blocks™ were used to teach and assess student learning and understanding of GCF, LCM and PF.; Teachers in the experimental group taught their own sixth-grade classes by using a pre-designed two-week teaching unit on GCF, LCM, and PF based on the Factor Blocks™ manipulative. These teachers were taught how to use the manipulative with their students prior to the start of the study. Teachers in the control group taught those same concepts without using Factor Blocks™ or any other manipulative. All students took a pre-test, which was used to establish baseline data. At the conclusion of the teaching unit, teachers administered a post-test, which was used as an indicator of immediate achievement. Seven months later students took a delayed post-test, which was used to evaluate retention of concepts.; An analysis of the data clearly showed that the experimental group had a statistically greater increase in test scores on the post-test compared to the students in the control group. This suggests that the regular use of Factor Blocks™ during the two-week unit of study led to increased understanding of GCF, LCM, and PF for the experimental group on the post-test. This experimental study thus supports the use of the manipulative Factor Blocks™ in the mathematics classroom to teach fraction skills and related number theory concepts.; Implications for learning, teaching, and testing are discussed in the final chapter of the dissertation. It is recommended that a replication study be conducted to include the ongoing use of Factor Blocks™ throughout the year so students in both groups are involved in short periods of review throughout the year. It is also recommended that students be matched to their learning styles and preference of learning time for mathematics. Clearly more research is needed to provide convincing evidence that using manipulatives on an ongoing basis can solidify concept development and long-term retention of mathematical understanding.