Hillsborough County Public Schools (HCPS) is a large public school system near Tampa, Florida. With over 200,000 students enrolled, HCPS is the third largest district in Florida and the eighth largest district in the United States. According to the Florida Department of Education (2012–2013), 38% of the students are White, 33% are Hispanic, 21% are African American, 3% are Asian, and 4% are multiracial. Additionally, 57% of students qualify for free or reduced-price lunch and 12% of students are English learners.
Six middle schools in the district participated in the study. Three schools were assigned as the comparison schools and three schools were assigned as the treatment schools. In the treatment schools, MATH 180 replaced their previous mathematics intervention program. The control schools continued providing mathematics intervention as they had previously. At both the comparison and the MATH 180 schools, the mathematics intervention class was taught in addition to students’ core grade-level math class.
MATH 180 is a blended learning math intervention program designed to help struggling middle school students with the foundational math skills needed to become algebra ready. The program encourages students to develop an understanding that the ability to acquire knowledge is flexible and can increase with additional effort (Growth Mindset), a practice shown in research to promote learning (Dweck, C. S. (2007). Mindset: The New Psychology of Success. New York, NY: Ballantine Books). MATH 180 covers multiple years of course content by focusing on rebuilding a set of core elements (representing foundational skills that students need to become successful in mathematics). Course content is broken down into nine instructional blocks with three topics in each block. MATH 180 focuses on building understanding with multiplication, division, fractions, decimal operations, and integers. MATH 180 classes are 45–50 minutes long and meet daily. Students spend the first five minutes of class time working on and then discussing a Do Now problem. Next, students are divided into two groups. One group receives approximately 20 minutes of instruction directly from their teacher while the other group works through instruction at their own pace on the MATH 180 software. After about 20 minutes, the two groups switch.
MATH 180 teachers received two days of start-up training at the end of summer and one additional day of training in the winter on the use of data for instructional practices. Instructors from Math Solutions^{®} visited the MATH 180 classes monthly to provide feedback and additional personalized coaching.
MATH 180 was released in the fall of 2013. This study took place during the program’s first year of implementation.
All participants were in Grade 6 during the 2013–2014 school year. The participants were selected by the schools as being in need of mathematics intervention. The schools based these assignments on previous mathematics performance, including state assessments, and prior teachers’ feedback. The MATH 180 schools consisted of 151 participants. Fifty-one percent were female and 49% were male. Fourteen percent were White, 53% Hispanic, 30% African American, 1% Asian, and 2% were classified as other. Additionally, 33% were classified as special education students, 36% as English learners, and 77% were eligible to receive free or reduced-price lunch. The comparison schools consisted of 136 participants. Fifty-two percent were females and 49% were males. Twenty-one percent were White, 64% Hispanic, 13% African American, and 2% Asian. Additionally, 36% were classified as special education students, 46% as English learners, and 82% were eligible to receive free or reduced-price lunch.
In order to measure the potential effects of the MATH 180 program on students participating in the program, it was important to determine their levels of progress. Progress through the program provides valuable context with which to view student performance outcomes.
MATH 180 offers a multifaceted view of a student’s experience with the program, including progress in the adaptive software instruction and progress in the teacher-facilitated group instruction. When a MATH 180 class completes a block of teacher-facilitated instruction, every student completes an mSkills assessment. mSkills are curriculum-embedded assessments completed on the software individually. They consist of 20 automatically scored questions and two constructed-response questions.
The Math Inventory^{®} is a computer-adaptive test (CAT) that provides information on a student’s readiness for mathematics instruction. As a computer-adaptive test, Math Inventory delivers test items targeted to a students’ ability level across six content strands (Numbers Sense, Numerical Operations, Geometry, Algebra and Algebraic Thinking, Data Analysis and Probability, and Measurement). The Math Inventory quantifies a students’ path up through high school mathematics using a vertical scale aligned to the Quantile^{® }Framework for Mathematics. The Quantile (Q) scale on the Math Inventory ranges from 0 to over 1,500 Quantile measures. The test takes approximately 20 to 40 minutes to complete. Scores on the Math Inventory can be used for progress monitoring and as a component for placement decisions.
The Northwest Evaluation Association-Measures of Academic Progress (NWEA-MAP^{®}) was an additional independent measure used to examine growth for this study. NWEA-MAP is a computer-adaptive assessment consisting of 40 to 50 items. The assessment is expected to take students 45 to 60 minutes to complete. The assessment measures students’ skills in four areas: Operations and Algebraic Thinking, Real and Complex Number Systems, Geometry, and Statistics and Probability. Students completed NWEA-MAP assessments in the fall and spring. Proctors were brought into the schools while students completed the assessment.
By the end of the school year most MATH 180 students had completed five mSkills assessments. Therefore, it can be determined that the MATH 180 classes completed five blocks of the teacher-facilitated instruction.
Students spent an average of 20 minutes on the software per session, completing an average of 78 sessions. Student completion of software varied considerably. This range reflects the self-paced nature of the MATH 180 software program. However, on average, students had completed Topic 8 and were actively working in Block 3 at the end of the study.
Students from the MATH 180 and comparison groups completed the Math Inventory in the fall of 2013 and spring of 2014. The two groups began with similar Quantile measures: 484Q for the MATH 180 students and 493Q for the comparison group. Both groups experienced significant growth over the 2013–2014 school year, a change in 134Q for the MATH 180 students and 38Q for the comparison students, but the MATH 180 students experienced significantly greater growth than the students in the comparison group. Figure 1 shows the difference in growth between these two groups. The effect size for this difference was .51 using Cohen’s d.
As seen in Figure 2, the MATH 180 students outpaced the students from the comparison group on the NWEA-MAP assessment. Although both groups experienced growth over the year, the MATH 180 students demonstrated significantly more growth than the comparison group. The effect size for this difference in growth was .32 using Cohen’s d. The MATH 180 students also demonstrated greater gains on all four sub scores of the assessment: Operations and Algebraic Thinking, Real and Complex Number Systems, Geometry, and Statistics and Probability.
Although the differences in growth using Math Inventory as an outcome versus MAP seem large, they are actually reasonably consistent. Math Inventory performance is reported on a larger score range of over 1,500 Quantile measures compared to a MAP RIT score range that tends to be less than 100 units. Therefore, smaller differences in actual RIT scores can still correspond to significant indications of change relative to the scale.
After completing five blocks of teacher-facilitated instruction and working through an average of three blocks on the self-paced student software, MATH 180 students showed significantly greater growth on both Math Inventory and NWEA-MAP assessments. MATH 180 students increased their Math Inventory scores by almost 100 Quantile measures more than the comparison group and saw across-the-board growth on the NWEA-MAP assessment.
This performance speaks to MATH 180’s emphasis on building students’ mathematics vocabulary and making students feel confident with mathematics. The instructors from Math Solutions visited MATH 180 classes throughout the year, providing ongoing training to MATH 180 teachers. During these meetings, MATH 180 teachers and students’ core grade-level mathematics teachers reported MATH 180 students gaining confidence and a voice in their math courses.
MATH 180 was introduced in the fall of 2013. The growth discussed in this study reflects the potential impact of the MATH 180 program in its first year of implementation.