An Evaluation of Number Rockets: A Tier 2 Intervention for Grade 1 Students At Risk for Difficulties in Mathematics
Intervention description
Instructional interventions in early math should emphasize developing an understanding of numbers, or number sense—the foundation for subsequent math skills (Gersten and Chard 1999).3 In addition to focusing on critical math content, such interventions should incorporate key design principles. Three recent meta-analyses4 incorporated 111 studies on low-achieving students (Baker, Gersten, and Lee 2002) and students with learning disabilities (Kroesbergen and Luit 2003; Gersten et al. 2009). Their results point to three critical design principles of effective math interventions: explicit and systematic instruction, visuals and models, and think alouds.5
Addressing all three design principles, small group tutoring incorporates systematic and explicit instruction that provides students with clear steps to follow and visuals and models to work with (Fuchs et al. 2005). The teacher describes and models the steps to solve the problem using examples before the students solve similar problems independently. Teachers also provide individual feedback to students on their work.
In a meta-analysis of research on the effects of grouping practices on reading outcomes for students with reading disabilities, small group instruction was found to result in the largest positive impacts on student achievement (Elbaum et al. 2000). Similarly, in a related meta-analysis for students without disabilities, students who received small group instruction learned significantly more than those not taught in small groups (Lou et al. 1996). Positive impacts for small group instruction in math and science achievement have also been documented (Springer, Stanne, and Elizabeth 1999), though most of the studies reviewed were quasi experimental and unable to provide the highest level of evidence.
In the Fuchs et al. 2005 study—one of the four studies focusing on tier 2 interventions for math that did use random assignment—students were assigned to either at risk or not at risk groups based on their screening test scores. Approximately 21 percent of students screened were identified as at risk. In each class students at risk were randomly assigned to receive either small group tutoring (intervention) or no tutoring (control). The intervention group received approximately 16 weeks of small group tutoring. At the end of this period, students' math skills were assessed using several measures—the Woodcock-Johnson III test of calculation (Woodcock, McGrew, and Mather 2000), a test of concepts and applications (Fuchs, Hamlett, and Fuchs 1990), and a test of story problems (Jordan and Hanich 2000). Tutored students received higher scores than control students. The following effect sizes6 demonstrate the magnitude of the impact of the small group tutoring intervention on students' test scores: 0.57 standard deviations on the Woodcock-Johnson III calculation test, 0.67 standard deviations for concepts and applications, and 0.70 standard deviations for story problems. A recent estimate of typical change on standardized test performance from the end of kindergarten to the end of grade 1 in math is an effect size of 1.14 (Hill et al. 2007). The results from Fuchs et al. (2005) are thus roughly equivalent to 10 months of at-risk student progress accomplished in 5 months of instruction.
3 Number sense is defined as having important central features such as: "a child's fluidity and flexibility with numbers, the sense of what numbers mean, and an ability to perform mental mathematics and to look at the world and make comparisons" (Gersten and Chard 1999, p. 20).
4 A meta-analysis is "a form of survey research in which research reports, rather than people, are surveyed" (Lipsey and Wilson 2001, p. 1). Meta-analyses encompass several procedures to formally aggregate findings across studies.
5 Think aloud is an instructional strategy in which the teacher describes his or her thought processes during the problem-solving process.
6 An effect size is a measure of change or of a relationship between two variables, usually expressed in standard deviation units on the normal curve (Cohen 1988). It can be used to express the impact of an intervention. For example, if an intervention had an effect size of 0.50 (and operated equally on all individuals in a normal distribution), then an individual originally at the 10th percentile would move to the 23rd percentile. The relationship between standard deviations and percentile rank is not linear. Given a fixed effect size, the amount an individual would shift in percentile units depends on initial location on the normal curve.