The study was conducted on students with mathematics difficulties in first grade general education classrooms in ten elementary schools in a suburban central Texas community.
The study sample included first grade students with mathematics difficulties from ten elementary schools. Students with disabilities were excluded from the study sample. The analytic sample was about 35 percent white, 25 percent Black, 5 percent Asian, and 35 percent Hispanic. About 48 percent of the study sample was male, and about 6 percent were English learners (ELL). About half of the study sample (51 percent) qualified for free or reduced-price lunch.
The intervention was a 19-week early numeracy Tier 2 small-group tutoring program that combines (1) systematic instruction, (2) scripted lessons to promote pacing, (3) concrete-semi-concrete-abstract procedure including visual representations to build students’ conceptual knowledge of mathematics, (4) multiple purposeful and meaningful practice opportunities, and (5) frequent and systematic progress monitoring including self-correcting (error correction by students).
Members of the research team delivered the tutoring sessions in various settings (a classroom, the library, the book room, or on a stage), depending on what was available in each school. Groups of 3-5 students received 25-minute tutoring sessions four days per week over 19 weeks (76 total tutoring sessions). The intervention had 11 units, each with 8 lessons. Each lesson includes a 3-minute warm-up of fluency activities on previously taught skills and two 10-minute daily lessons, plus practice and transition time after each lesson.
The intervention content included: (1) number and operation mathematical ideas, including problem solving; (2) activities on counting and number knowledge and relationships; (3) activities on partitioning and grouping of tens; and (3) activities on combining and separating sets and working with basic facts.
The intervention used “systematic intervention” pedagogy. Specifically, it involved a teaching routine of seven practices: (1) modeling (such as the teacher demonstrating how to solve problems by “thinking aloud”), guided practice, and independent practice (which teachers used for daily progress monitoring using a daily check-up sheet); (2) error correction procedures; (3) pacing; (4) opportunities for meaningful practice, such as students modeling problems or showing relationships using concrete representations (for example, base-ten models) and visual representations (for example, number lines); (5) examples; (6) review; and (7) unit check at the end of each unit containing representative items across unit lessons.
The intervention also used a behavior management system. At the beginning of the intervention and after winter break, the intervention taught students five behaviors to be “Math Ready”: (1) eyes on teacher, (2) listening, (3) ready to learn, (4) mouth quiet (no off-task talking), and (5) hands on table. Students were reminded of these at start of each lesson and during transitions, and interventionists reinforced the “Math Ready” behaviors by awarding students marbles that can then be exchanged for small rewards (such as stickers, pencils, pencil erasers).
Students in the comparison condition received “business as usual” mathematics instruction from their first grade teachers. These teachers used a variety of groupings and instructional materials for teaching mathematics to students with mathematics difficulties, but no well-defined treatment for these students. Most teachers used groups during mathematics instruction, typically for students to complete the whole-class assignment or to review for upcoming tests in smaller groups. One teacher used packets of work that were differentiated based on students’ academic levels and another paired higher-performing and lower-performing students together.
In general, the study authors drew five key conclusions about the comparison condition: (1) Business-as-usual mathematics instruction included no explicit, systematic math instruction for students with mathematics difficulties; (2) Business-as-usual mathematics instruction varied in instructional pacing, and students sometimes appeared disengaged in smaller groups when pacing was slower; (3) There was some student misbehavior while teachers worked with small groups during business-as-usual mathematics instruction; (4) Students did not receive multiple practice opportunities during business-as-usual mathematics instruction; (5) Business-as-usual mathematics instruction sometimes included checks for understanding, but not systematic progress monitoring and self-correcting (error correction by students).
Support for implementation
Interventionists received a three-hour initial training by the study principal investigator at the start of the academic year, focused on intervention lessons and instructional materials. Interventionists then practiced lessons, with each interventionist teaching a lesson and receiving feedback from experienced tutors who were using the same lessons with a group of students. The research team also conducted seven additional training sessions before each intervention unit throughout the school year.
The research team assessed fidelity of implementation by observing each interventionist during three tutoring sessions.