Efficient Class-Wide Remediation: Using Technology to Identify Idiosyncratic Math Facts for Additional Automaticity Drills.

Researchers have found evidence that many students do not master basic mathematics skills and in 2009, for the first time in two decades, national U.S. math scores at a fourth-grade level did not improve (National Center for Educational Statistics, 2009). These findings support the need for the development and evaluation of science-derived basic math skills interventions (Maccini, Mulcahy, & Wilson, 2007). Haring and Eaton (1978) developed a multi-stage hierarchy of skill development. During the initial stage, acquisition, the focus is on enhancing response accuracy. Once a skill can be performed accurately the focus shifts to developing speed of accurate responding, also known as fluency or automaticity (Deno & Mirkin, 1977; Hasselbring, Goin, & Bransford, 1988. Several theories may explain why students who are fluent or automatic with basic addition, subtraction, multiplication, and division facts are more likely to experience success acquiring and mastering more advanced mathematics objectives (Deno & Mirkin, 1977; Haring & Eaton, 1978; Johnson & Layng, 1992; McCallum, Skinner, Turner, & Saecker, 2006; Shapiro, 2004; Skiba, Magneusson, Marston, & Erickson, 1986; Skinner, 1998). Individuals have limited cognitive capacity and automatic responding is thought to require fewer cognitive resources, including working memory and attention. Because many complex mathematics objectives require students to perform basic computations, those who expend too much of their cognitive capacity performing basic operations may have insufficient capacity to apply toward acquiring complex mathematic skills (Gagne, 1983; LaBerge & Samuels, 1974; Skinner & Schock, 1995; Woodward, 2006). Students who can complete basic math computations problems with rapidity are likely to expend less time and effort on math activities and have less math anxiety (Billington, Skinner, & Cruchon, 2004; Cates & Rhymer, 2003). Consequently, those with greater basic-fact fluency are more likely to choose to engage in math activities, which further enhance skills (Skinner, 1998; Skinner, 2002; Skinner, Pappas, & Davis, 2005). Idiosyncratic Target Behaviors and Behavioral Consultation Researchers have drawn an important distinction between fluency and automaticity (Skinner & Daly, in press). The term fluency reflects the ability to respond to a group of stimuli both quickly and accurately. Thus, a fluent typist can type 150 words correct per minute. However, when discussing mathematics researchers have used the term automaticity to describe a students' ability to respond to a specific fact (e.g., 6 x 7 =_) rapidly, accurately, and with minimal effort or cognitive resources (Hasselbring et al., 1987; 1988; Poncy, Skinner, & Jaspers, 2007; Poncy, Skinner, & O'Mara, 2006). Developing the ability to respond fluently to a class of basic math facts (e.g., single-digit multiplication facts) may be caused by becoming automatic with each specific fact in that class (Skinner & Daly, in press). Consequently, as students are developing fluency, it is likely that they will have developed automaticity with some math facts (e.g., 5 x 5 = 25), but not others (Poncy et al., 2006; Poncy et al., 2007). Behavioral consultation has been used to remedy idiosyncratic academic skill deficits (e.g., Saecker, Skinner, Brown, & Roberts, 2009). When working with academic skill deficits, one of the first steps in behavioral consultation is to identify target behaviors in need of remediation (Shapiro, 2004). Skinner and Daly's (in press) conceptualization of automaticity versus fluency makes it apparent that each student is likely to have different math facts which require targeted remediation (i.e., in need of automaticity building). Additionally, within each student, as automaticity develops with some facts, the curricula should be altered so that the student is not wasting valuable instructional/learning time on facts that he/she has already developed to the point of automaticity (Cates et al. …