Across the country, students are struggling with mathematics. Nearly two-thirds of our nation’s eighth graders do not meet current mathematics standards (National Center for Education Statistics, 2015). These standards define the skills students need to master in order to succeed in algebra, a known gatekeeper to college and career readiness. Struggling students often need additional mathematics support to fill in gaps in mathematics knowledge. Norfolk Public Schools identified this need among its struggling students, including those who did not pass the state assessment in the prior year.
No students included in this study passed the Virginia Standards of Learning (SOL) assessment at the end of the previous school year. After using MATH 180 Course I, nearly half (46%) of the Grade 6 students passed the SOL.
MATH 180 is an intervention program for struggling students in Grades 5 and up. MATH 180 Course I focuses on rebuilding students’ understanding of multiplicative thinking, division, fractions, and decimals as students progress toward algebra readiness. Built around nine blocks of instruction, each covering three topics, MATH 180 uses a blended learning model of instruction to build reasoning and elicit student thinking. In this blended model students rotate between teacher-facilitated instruction and personalized software that adapts to their needs.
Students in the Norfolk School district were enrolled in MATH 180 in addition to their regular grade-level mathematics courses. These students were identified as struggling through multiple assessments, including performance in previous mathematicsclasses, state assessment results, recommendations from previous mathematics teachers, and Math Inventory® results.No student taking MATH 180 passed the math portion of the Virginia Standards of Learning (SOL) assessment in the previous year.Students in grades 6 through 8 used MATH 180 Course I for 90 minutes a day. The program was implemented as intended—with daily teacher-led instruction and software rotations. Students took the Math Inventory in the fall and spring and the SOL in the spring.
Serving more than 32,000 students, Norfolk Public Schools is one of the largest school districts in Virginia. According to data from the 2013–2014 school year, approximately 61% of students were identified as African American, 23% as White, and 7% as Hispanic. Approximately 63% of students in the district were eligible to receive free or reduced-price lunches.
Students in this study were enrolled in MATH 180 Course I during the 2014–2015 school year. Only students with at least 20 software sessions and two Math Inventory scores captured at least 120 days apart were retained for analysis. This resulted in a sample size of 217 students with 32% in Grade 6, 37% in Grade 7, and 31% in Grade 8. Approximately 88% of students were African American, and 5% of students were White.
In terms of increases in overall math achievement, students grew an average of 117 Quantile measures (Q) over the school year, starting the program at 564Q and ending the school year at 681Q.
The effectiveness of MATH 180 was investigated using four outcome measures. The first, progress through the program (or number of topics completed), was used as an indicator of content exposure and mastery within the program. The second investigation included changes in performance on addition and multiplication fact screeners that are embedded in the Math Inventory assessment. These screeners assess math fact fluency, including fact recall and the ability to respond to missing addend, missing sum, and equivalency problems for addition and a similar mix of tasks for multiplication. The third set of outcomes included changes in Quantile® measures over the course of the year. Math Inventory provides an independent, adaptive measure of mathematical knowledge and understanding across a range of mathematical content, not just what is included in the program. These findings were broken out by grade level and learning disability (LD) designation. Finally, performance on the Virginia Standards of Learning (SOL) assessment was analyzed for changes in student passing rates. These are grade-level assessments with expectations and requirements that vary by grade level.
Students completed an average of nine topics over an average of 44 sessions. The range of completed topics was widely distributed, reflecting the self-paced nature of the software. The average software session was 28 minutes. These metrics are consistent with the implementation model.
The content covered in the early blocks of MATH 180 addresses foundational skills that struggling students often lack. Students who don’t learn these skills can have difficulty later with more advanced content. Although acquiring knowledge and developing skills such as math fact fluency are critical for later success, the content can be significantly below grade level and, therefore, can be overlooked on grade-level state or local assessments. Math Inventory addresses this issue by using an adaptive algorithm to deliver test items below grade level in order to gauge students’ understanding of foundational knowledge.
The early blocks of MATH 180 focus on multiplicative thinking and the distributive property. In order to obtain a more proximal impact of this early content and skills on student outcomes, the fact fluency student data was initially examined over three time periods. Testing to gather the first set of fluency data occurred in the fall. The second administration occurred an average of 61 days later, followed by end-of-year testing, which occurred an average of 180 days later. Figure 1 summarizes the percentage of students who were able to pass the screener during the school year. At the beginning of the school year students were passing the fluency screener at a rate of 31% for addition and 17% for multiplication. These percentages increased dramatically throughout the school year, ending with 70% and 60% for addition and multiplication, respectively.
In terms of increases in overall math achievement, students grew an average of 117Q over the school year, starting the program at an average of 564Q and ending the school year at an average of 681Q. Figure 2 portrays this growth broken out by grade level. As expected, the starting scores for students gradually increased with grade level. Growth was fairly consistent for Grades 6 and 7 but dropped off slightly in the 8th grade. Growth for all three grades was statistically significant.
In addition to taking the Math Inventory at the beginning and end of the year, students also took the Virginia Standards of Learning assessment during the spring of their MATH 180 year as well as during the spring prior to their MATH 180 year. The availability of this data allowed for a year-to-year comparison of their state assessments results. Performance on the SOL was a major factor in determining placement into the MATH 180 program. No students included in this study passed the SOL assessment at the end of the previous school year. After using MATH 180 Course I, nearly half (46%) of the Grade 6 students passed the math section of the SOL. Of the 81 Grade 7 students who used the program, 28% passed the math section of the SOL, and of the 66 Grade 8 students who used the program, 36% passed the math section of the SOL (see Figure 3).
Students in a typical MATH 180 Course I setting will come from diverse backgrounds, including students classified with some form of learning disability (LD). In an effort to understand whether the program has any differential impact on students with disabilities, a comparison was made between students classified as learning disabled compared to those with no disability classification. Results indicated students who were classified as LD completed an average of eight topics, while students with no classification completed an average of 10 topics. Results also indicated that although students classified as LD started the year significantly lower than the non-classified students, they still maintained an identical level of growth (116Q). This finding seems to indicate that the program is able to meet the needs of individual students in the classroom.
District implementation of the program was consistent with best practices for program implementations. Over the course of the school year, students’ overall mathematical knowledge grew based on the increase in Quantile scores. The MATH 180 Course I fluency screener is designed to target skills that should have been mastered by the end of third grade. Fluency represents a fundamental skill in the efficiency by which students solve math problems and is a key to whole number competency (Russell, 2000). As fluency is increased, finite cognitive resources are made available to address more complex problem activities. Most students did not demonstrate mastery of these foundational elements at the beginning of the year, but most did pass the screener by the end of the year. The SOL assessment measures grade-level expectations. The early content of MATH 180 Course I was closer to the grade level expectations for sixth-grade students, and nearly half of them passed the SOL after having failed the prior year’s SOL. Approximately 28% of seventh graders and 36% of eighth graders also passed the SOL.
Students who are typically placed in MATH 180 are struggling with mathematics and come from a variety of backgrounds. The current study examined students in the MATH 180 program who were identified by the district as learning disabled (LD). The LD group represented approximately 12% of the study sample. When their growth in mathematics achievement was measured against those students not classified as LD, the results indicated that their starting score in Quantile measures was significantly below that of the non-LD group. Results indicated that although they seemed to be struggling to a greater degree at the start of the study, their growth on the Math Inventory was comparable to the non-LD group. In addition, the LD students averaged slightly fewer topics completed, indicating they were able to capitalize on the efficiency of the program’s pacing to better suit their individual needs (see Figure 4).
Russell, S. J. (2000). Developing computational fluency with whole numbers. Teaching Children Mathematics, 7, 154–158.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Department of Educational Progress (NAEP), 2015 MathematicsAssessment.