Increasing multiplication and division fluency : embedding self-regulation strategies within systematic, strategic instruction
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Students need to develop computational proficiency with basic facts (i.e., addition, subtraction, multiplication and division) to be successful in more advanced mathematics such as instruction in fractions, decimals, ratios, and rates (Gersten et al., 2009; NCTM, 2010; NMAP, 2008). Specifically, the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (NCTM, 2006) stresses the importance of automaticity in basic facts and the application of these skills to solving word problems. For older elementary students, it is vital that they are proficient in multiplication and related division facts in preparation for working with fractions and other algebra readiness skills. Thus, the purpose of this study was to teach multiplication and division facts using systematic, strategic instruction with and without self-regulation strategies. A single-subject, time-series design was employed to measure items correct on daily probes with nine, fourth grade students. The daily probes were designed with 15 review facts and 25 new facts to measure the ability to solve easy, review facts with automaticity and hard facts specifically taught during instruction. All instruction occurred in small groups (4 – 5 students), after school, with a trained instructor. The students received strategic, systematic instruction in hard multiplication and division facts (9s, 4/6/8s and 7s) with and without additional self-regulation components (self-correction, graphing and goal setting). Multiplication and division were taught together as a fact family, rather than apart, to increase conceptual understanding of the relation between multiplication and division. The findings showed that the students made positive growth in both operations in terms of items correct and fluency; with an increase in accuracy and decrease in time to reach phase change criteria when the intervention was embedded with self-regulation components. Findings from social validity measures from participants support the use of self-regulation as a means to increase motivation.