Mathematics Curricula
The decision to conduct an evaluation of the effectiveness of mathematics curricula resulted from a series of discussions with and recommendations from the IRP, the Office of Elementary and Secondary Education, and an expert panel convened to provide advice on policy-relevant questions that would be important to address in an impact evaluation focused on mathematics. Information on the effectiveness of mathematics curricula is crucial to improving performance on state mathematics assessments under NCLB. There is considerable controversy about what mathematics children should learn and how it should be taught, but there is very little reliable information available to educators and policy makers about which curricula are most likely to improve mathematics achievement.8
This evaluation is focusing on early elementary grades because disadvantaged children are behind their more advantaged peers in basic mathematics competencies even before entering elementary school. If basic concepts are not mastered in early elementary grades, students have great difficulty understanding more advanced mathematics concepts in upper elementary grades. The evaluation will compare different approaches to teaching early elementary mathematics since there are many mathematics curricula that are being widely implemented without evidence of their effectiveness.
The major evaluation questions are:
- What is the relative effectiveness of different math curricula on student achievement for early elementary school students in disadvantaged schools?
- Which math curricula result in sustained impact on student math achievement?
These questions are being addressed through an experimental methodology in which schools are randomly assigned to selected math curricula. The study design calls for recruitment of 10-15 school districts with a total of 100 schools across all sampled districts. Within each sampled district, each sampled school has been randomly assigned to one of the four curricula. Since all schools have a core mathematics curriculum, including the curricula being tested in the study, there will not be a no-treatment control group. For some of the schools, the intervention curriculum is their regular curriculum. The difference in math achievement among the schools using each math curricula will be the measure of the relative effectiveness of each math curriculum on student achievement.
- What is the relationship between teacher knowledge of math content and pedagogy and the effectiveness of math curricula?
Teacher knowledge of mathematics content and pedagogy is being assessed prior to training on the curriculum that their school is implementing allowing for a subgroup analysis of the impact of the curricula on student achievement taught by teachers with varying expertise. It is hypothesized that some math curricula may require higher levels of teacher knowledge than others for successful implementation. The teacher assessment being used is "Learning Mathematics for Teaching" developed by the Consortium for Policy Research in Education for the Study of Instructional Improvement.
- Under what conditions is each math curriculum most effective?
This question will be addressed by correlational analyses. Fidelity of implementation of each curriculum will be measured, as well as characteristics of students, teachers, schools, and districts. These measures will be correlated with the relative impacts of the math curricula on student achievement.
Four commercially-available mathematics curricula were competitively selected by an expert panel to represent a variety of approaches to teaching mathematics. Selection of the interventions was based on existing evaluation evidence, extent of use of curricula in schools, capability to implement the intervention, and appropriateness of the intervention for the target population. These curricula represent varying approaches to mathematics instruction and include widely used curricula. The curricula are:
- Investigations in Number, Data, and Space (Pearson Scott Foresman) is a child-centered approach to teaching mathematics through activities, discussions, and problem solving. Students are involved in meaningful mathematical problems, and teachers engage in ongoing learning about mathematics content and how children learn mathematics.
- Math Expressions (Houghton Mifflin) combines conceptual understanding with opportunities to develop fluency with problem solving and computation. Both reform and traditional mathematics approaches are incorporated along with new teaching strategies.
- Saxon Math (Harcourt Achieve) provides a multi-sensory approach designed to enable all children to develop a solid foundation in the language and basic concepts of mathematics. This is accomplished through hands-on activities that actively engage students. Concepts are reviewed and practiced over time leading to mastery and fluency.
- Scott Foresman-Addison Wesley Mathematics (Pearson Scott Foresman) provides explicit instruction of essential mathematics skills and concepts, using concrete manipulatives and pictorial and abstract representations. Ongoing assessment and diagnosis are coupled with strategic intervention to meet the needs of individual students.
The evaluation began in the 2006-07 school year with curricula being implemented in the first grade. The curricula will be implemented in the first and second grades during the 2007-08 school year and extended to the third grade in the 2008-09 school year.
Four school districts with forty schools have agreed to implement the curricula in all first grade classrooms during the 2006-07 school year. Data will be collected on student mathematics achievement at the beginning and end of the 2006-07 school year and on implementation of each curriculum in the spring of 2007. The student mathematics assessment developed for the Early Childhood Longitudinal Study will be used in this study. This assessment is individually-administered and computer adaptive.
Additional districts with approximately 60 schools are being recruited to begin participation in the study in the 2007-08 school year. The additional schools will implement the curricula in their first and second grades. The original 40 schools will continue implementation of the curricula in their first grade classrooms as well as in their second grade classrooms. Data will be collected on the implementation of each curriculum and student mathematics achievement for first- and second-graders during the 2007-08 school year. The first report on the relative effectiveness of the mathematics curricula is planned for Spring 2009.
8 The National Academy of Sciences (2004). On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations. Washington, DC: The National Academies Press.