Extending Responsiveness-to-Intervention to Math Problem-Solving at Third Grade
Fuchs, Lynn S., Fuchs, Douglas, Hamlett, Carol L., Hope, Susan K., et al., Teaching Exceptional Children
The Center on Accelerating Student Learning (CASL) is a collaborative partnership among faculty at Vanderbilt University (Lynn and Doug Fuchs), Columbia University (Joanna Williams), and the University of Maryland (Steve Graham and Karen Harris, Vanderbilt University). CASL's goal is to identify instructional practices that accelerate the learning of children with disabilities in kindergarten through Grade 3. This includes the development of effective, multicomponent instructional interventions in reading, writing, and math, which focus on basic skills and higher-order learning, and promote fluency, transfer, and maintenance. As part of the CASL research program, we validated an intervention to enhance mathematical problem-solving at third grade. We call this intervention "Hot Math." (See Fuchs, Fuchs, Prentice, Burch, & Paulsen, 2002.)
More recently, within the context of another grant sponsored by the U.S. Department of Education's Office of Special Education Programs, we have been studying how hot Math might be used within a multitiered response-tointervention (RTI) system. The first intervention tier occurs in general education. The second tier involves more intensive tutoring of children deemed at risk for poor problem-solving outcomes, even with the validated hot Math Tier 1 intervention. In other areas, primarily reading at first grade, RTI has undergone some study (e.g., Speece & case, 2001; Vellutino et al., 1996). In math, where less research has been conducted, the only major experimental RTI study was conducted at first grade, addressing more foundational skills (Fuchs et al., 2005b). Our goal was to extend RTI to third-grade math problem-solving.
Toward that end, across 2 years, we worked in 13 schools. At Tier 1, we randomly assigned 20 general education classrooms to conventional methods for teaching math problem-solving and the other 40 general education classrooms to Tier 1 hot Math whole-class instruction, that occurred 2 to 3 times per week for 16 weeks for 25 to 40 minutes per session. We assessed students in these 60 classrooms at the beginning of the school year to identify children for Tier 2 intervention, and randomly assigned two thirds of the 144 lowest-scoring students to Tier 2 hot Math tutoring and one third to no tutoring. Tier 2 hot Math tutoring occurred three times weekly for 13 weeks. We could estimate the effects of each tier of hot Math intervention separately and in combination because students had been randomly assigned to four conditions: (a) no hot Math in either Tier, (b) hot Math only at Tier 1, (c) hot Math only at Tier 2, and (d) hot Math at both tiers.
How We Structured Intervention at Tiers 1 and 2
Tier 1 hot Math Whole-Class Instruction
Hot Math integrates two practices to promote mathematical problem-solving:
* Explicit instruction about transfer.
* Self-regulation strategies.
The first 3-week unit is dedicated to basic problem-solving information: making sure answers make sense, lining up numbers from text correctly to perform math operations, and labeling work with words and mathematics symbols. Each of the next four 3-week units focuses on one of these problem types (see Table 1; also see Fuchs et al., 2002 for sample problems):
* "Buying Bags" problems.
* "Shopping List" problems.
* "Half" problems.
* "Pictograph" problems.
Teachers can apply the instructional principles to other problem types as well.
Each of the four units provides instruction on skill acquisition and transfer. In each unit, the first four sessions focus on skill acquisition (what the problem is asking and how to solve the problem), with cumulative review across units incorporated in Session 4. During the third week of each unit, teachers provide two transfer lessons in Sessions 5 and 6, incorporating cumulative review again in Session 6. In each unit, the first acquisition lesson (Session 1) and the first transfer lesson (Session S) last 40 minutes; the others last 25 to 30 minutes. …