Abstract. The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for students in the primary grades: number combinations and story problems. We then focus on seven principles of effective intervention. First, we describe a validated, intensive remedial intervention for number combinations and another for story problems. Then, we use these interventions to illustrate the first six principles for designing intensive tutoring protocols for students with mathematics disabilities. Next, using the same validated interventions, we report the percentage of students whose learning outcomes were inadequate despite the overall efficacy of the interventions and explain how ongoing progress monitoring represents a seventh, and perhaps the most essential, principle of intensive intervention. We conclude by identifying issues and directions for future research in the primary and later grades.
Approximately 5-9% of the school-age population may be identified with mathematics disability (e.g., Badian, 1983; Gross-Tsur, Manor, & Shalev, 1996). Although this estimate is similar to the prevalence of reading disability, less systematic study has been directed at mathematics disability (Rasanen & Ahonen, 1995), even though poor mathematics skills are associated with life-long difficulties in school and in the workplace. For example, mathematics competence accounts for variance in employment, income, and work productivity even after intelligence and reading have been explained (Rivera-Batiz, 1992).
Some research illustrates how prevention activities at preschool (e.g., Clements & Sarama, 2007), kindergarten (e.g., Griffin, Case, & Siegler, 1994), or first grade (e.g., Fuchs, Fuchs, Yazdian, & Powell, 2002) can substantially improve math performance. For example, at the beginning of first grade, Fuchs and colleagues (2005) identified 169 students in 41 classrooms as being at risk for math difficulties based on their low initial performance. These children were randomly assigned to a control group or to receive small-group tutoring three times per week for 16 weeks. Results showed that math development across first grade was significantly and substantially superior for the tutored group than for the control group on computation, concepts, applications, and story problems. In addition, the incidence of students with mathematics disability was substantially reduced at the end of first grade, and this reduction in mathematics disability remained in the spring of second grade, one year after tutoring ended (Compton, Fuchs, & Fuchs, 2006).
Nevertheless, despite the efficacy of tutoring, students were not universally responsive. A subset of the tutored students, approximately 3-6% of the school population (depending on the measure and cut-point for the severity of mathematics performance used), manifested severe mathematics deficits. As this example illustrates, the need for intensive remedial intervention persists even when prevention services are generally effective.
In this article, we focus on serious mathematics deficits at third grade. In third grade, serious mathematics deficits are clearly established, and identification of mathematics disabilities typically begins (Fletcher, Lyon, Fuchs, & Barnes, 2007). We provide background information on two aspects of mathematical cognition that present major challenges for students in the primary grades: number combinations and story problems. We describe validated, intensive interventions for number combinations and another for story problems and use these interventions to illustrate six principles for designing interventions for students with mathematics disabilities. …