Research Examples: Math Study

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The purposes of this study were to examine efficacy of first-grade preventive instruction, to assess math disability (MD) prevalence and severity as a function of method with and without instruction, and to explore pretreatment cognitive abilities associated with development.

Design of study

The reading and math studies were initiated in subsequent years, so that the samples of students did not overlap with each other. Ten elementary schools among the Metropolitan Nashville Public Schools participated in this study. In the fall, students within 41 first-grade classes were screened using a battery of math tests, and the lowest quintile of students were identified as "low study entry." These students were randomly assigned to receive Tier 2 tutoring or to serve as a control group, which did not receive Tier 2 tutoring.

All low-study-entry students and a sample of average-achieving classroom peers were assessed with a comprehensive battery in the fall of first grade. In addition, the low-study-entry and average-study-entry students were assessed weekly using CBM math computation tests for nearly 30 weeks.

Math intervention

For Tier 2, a standardized tutoring protocol, which consists of the following elements, was used:

  • Small groups (two to three students)
  • 17 weeks, three sessions per week, 40 minutes per session
  • Conducted by trained and supervised personnel (not the classroom teacher)

The following research-based elements of instruction were incorporated:

  • Point system for motivation
  • Immediate corrective feedback
  • Mastery of content before moving on
  • More time on difficult activities
  • More opportunities to respond
  • Fewer transitions
  • Setting goals and self-monitoring
  • Special relationship with tutor

Students were tutored in small groups of two to three and received instruction outside of the general education classroom three times per week for 17 weeks. They covered 17 different topics in 48 sessions, and each session lasted 40 minutes. Each session was broken down into the following: 30 minutes of tutor-led instruction and 10 minutes of student use of math software (Math Flash) to enhance automatic retrieval of math facts.

The tutor-led instruction used the concrete-representational-abstract model, which relies on concrete objects to promote conceptual understanding (e.g., base-10 blocks for place value instruction). The following 17 math topics and concepts were taught:

  • identifying and writing numbers to 99
  • identifying more, less, and equal with objects
  • sequencing numbers
  • using <, >, and = symbols
  • skip counting by 10s, 5s, and 2s
  • understanding place value (introduction)
  • identifying operations
  • place value (0-50)
  • writing number sentences (story problems)
  • place value (0-99)
  • addition facts (sums to 18)
  • subtraction facts (minuends to 18)
  • review of addition and subtraction facts
  • place value review
  • 2-digit addition (no regrouping)
  • 2-digit subtraction (no regrouping)
  • missing addends

Each lesson was scripted for the tutors with detailed steps and exact wording of the instructions to be provided to the students. On the first day of each topic, the students completed a cumulative review worksheet covering previous topics.

The Math Flash software design reflects the assumption that active and repeated pairing of the problem stem with the correct answer in the short-term memory establishes the association in long-term memory. The facts are organized in families of increasing difficulty. Once response to a math fact is consistently correct, it is moved to a "mastered" set. Cumulative review on mastered facts is provided; if a student responds incorrectly, that fact is moved out of the mastered set. An example of the process a student follows as he works with Math Flash is as follows:

  1. Math fact flashes on and disappears from computer screen.
  2. Student is prompted to type the fact from short-term memory.
  3. If the student is correct, the computer applauds, says the fact, and awards a point (5 points = a "trinket" for the toy box at the bottom of the screen).
  4. If the student is incorrect, the computer removes the incorrect fact, replaces it with the correct fact, and says the fact.
  5. At the end of each session, the computer provides feedback about the number of facts typed correctly and the highest math fact mastered.

Each day, the student's mastery of the topic was assessed. If every student in the group achieved mastery prior to the last day of the topic, the group moved on to the next topic (a few topics required completion of all three days). For mastery assessment, students completed worksheets independently, with the percentage of correct answers determining mastery (for most topics - 90 percent accuracy). After the last day on a topic, the group progressed to the next topic regardless of mastery status.

Fidelity of implementation

Fidelity of implementation of the tutoring protocol was quantified in the same manner as with the reading study and documented as strong.

Results

At the end of Tier 2 (17 weeks), students' math performance as a function of condition (average-study-entry versus low-study-entry control versus low-study-entry tutor) was assessed. Results showed that tutoring substantially enhanced student performance, with improvement for low-study-entry tutored students exceeding that of low-study-entry control students. Also, on some measures, the tutored students' improvement exceeded that of average-study-entry classroom peers. In addition, math disability (MD) prevalence was lower among tutored students compared to low-study-entry control at the end of first grade and at the end of second grade. As with the reading study, MD prevalence and severity depended on the definition of unresponsiveness employed, with some definitions functioning better than others. Cognitive predictors of math outcome differed depending on the area of mathematics.