Academic journal article Learning Disability Quarterly

Developing Automaticity in Multiplication Facts: Integrating Strategy Instruction with Timed Practice Drills

Academic journal article Learning Disability Quarterly

Developing Automaticity in Multiplication Facts: Integrating Strategy Instruction with Timed Practice Drills

Article excerpt

Abstract. Automaticity in math facts has been of considerable interest to special educators for decades. A review of the intervention literature suggests at least two common approaches to developing automaticity in facts. One is grounded in the use of strategies for teaching facts, the other emphasizes the use of timed practice drills. Recent research indicates that students might benefit from an integration of these two approaches. This experimental study contrasted an integrated approach (i.e., strategies and timed practice drills) with timed practice drills only for teaching multiplication facts. Participants were 58 fourth-grade students with a range of academic abilities. Fifteen of the students in the study had IEPs in math. Results indicated that both approaches were effective in helping students achieve automaticity in multiplication facts. However, students in the integrated approach generally performed better on posttest and maintenance test measures that assessed the application of facts to extended facts and approximation tasks. These results have implications for teaching a range of skills and concepts that are considered important to overall mathematical competence in the elementary grades.


Information-processing theory supports the view that automaticity in math facts is fundamental to success in many areas of higher mathematics. Without the ability to retrieve facts directly or automatically, students are likely to experience a high cognitive load as they perform a range of complex tasks. The added processing demands resulting from inefficient methods such as counting (vs. direct retrieval) often lead to declarative and procedural errors (Cumming & Elkins, 1999; Goldman & Pellegrino, 1987; Hasselbring, Goin, & Bransford, 1988). Potential difficulties extend well beyond operations on whole numbers. Finding common multiples when adding fractions with unlike denominators or factoring algebraic equations are but two examples from secondary-school mathematics where automaticity in math facts can facilitate successful performance.

Advocates of contemporary approaches to mathematics, ones that tend to place more emphasis on conceptual understanding and problem solving than on computational skills, see an important place for automaticity in math facts. Isaacs and Carroll (1999), for example, note that automaticity is essential to estimation and mental computations. These skills, particularly the ability to perform mental computations (e.g., make approximations based on rounded numbers such as 10s and l00s), are central to the ongoing development of number sense. In an effort to reach consensus on the current state of K-12 mathematic education, Ball and colleagues (2005) also affirm the importance of automaticity in math facts.

Unfortunately, decades of research show that academically low-achieving students as well as those with learning disabilities (LD) exhibit considerable difficulty in developing automaticity in their facts. Difficulties and delays are apparent from the beginning of elementary school. These students fail to retrieve facts directly when presented in isolation or when embedded in tasks such as multidigit computations. Research on primary-grade students indicates that students with LD are more likely to rely on counting strategies than direct retrieval when working single-digit fact problems (Geary & Brown, 1991; Hanich, Jordan, Kaplan, & Dick, 2001; Hoard, Geary, & Hamson, 1999). These students also tend to make more retrieval and counting errors on simple addition problems than their non-LD peers.

Results of Goldman and her colleagues' research on second- through sixth-grade students with LD show that these students tend to rely heavily on counting over direct retrieval methods (Goldman, Pellegrino, & Mertz, 1988). When compared with non-LD peers, students with LD often employ suboptimal strategies when retrieving facts. …

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