Average-performing students in classrooms using Math Expressions and Saxon Math saw an improvement in their percentile rank of 5-7 points, according to the U.S. Department of Education’s Institute of Education Science report (Achievement Effects of Four Early Elementary School Math Curricula: Findings for First and Second Graders). The other two programs included in the study were Investigations in Number, Data, and Space and Scott Foresman-Addison Wesley Mathematics (SFAW).
The study of 8,060 students in 110 schools is the largest of its kind to use an experimental design. Previous findings, published in February 2009, were based on results for 1st-grade students in 39 schools during the 2006-2007 school year. This report is based on results from the first cohort of 39 schools and another cohort of 71 schools that joined the study during the 2007-2008 school year. The curricula were implemented in both grade 1 and grade 2 in the cohort of 70 schools.
These findings suggest that educators should choose their elementary math curriculum wisely,” says Roberto Agodini, senior economist and associate director at Mathematica who served as the study’s director and principal investigator. “As we continue to grapple with how to boost math achievement during the critical early years, particularly among disadvantaged students, this study offers compelling evidence to inform future research and help educators make decisions about which curricula best suit their needs and environment.”
Saxon teachers reported spending 1 more hour on math instruction per week than they did in the other curriculum groups. First-grade teachers reported an average of 6.1 hours per week compared with an average of 5.1 hours for the other curricula. Second-grade teachers using Saxon reported an average of 6.9 hours per week compared with 5.5 hours averaged by teachers using other curricula.
The additional time that Saxon teachers reported spending on math instruction appears to be consistent with the publisher recommendations for instructional time, the report says. The recommendations are 60-85 minutes per day for 1st grade and 60-90 minutes per day for 2nd grade. Publishers of other curricula recommend 60-70 minutes per day, according to the report.
Currently K-2 educators (91%) choose one of 7 math curricula for their classrooms. The 4 programs selected for the study account for 32% of the curricula used by K-2 educators, although market share is difficult to estimate because Math Expressions is a newer curriculum, the study says.
Researchers write that examining the effectiveness of curricula is especially important because teachers rely heavily on them for math instruction.
“Another reason for studying entire math curricula is that districts and schools tend to use a commercial math curriculum that provides not only content and resources for instruction but also specific pedagogical guidance for delivering the content to students,”
The schools in the study are geographically dispersed in four states and three regions of the country. They are not a representative sample of all elementary schools in the U.S., but have a higher percentage of students eligible for free or reduced-price meals than the average elementary school.
Curricula were randomly assigned to participating schools. All teachers received training from the publishers and used the curriculum regularly throughout the school year. Initial training lasted 1-2 days. The study team did not mandate a particular level of implementation but instead sought to establish a supportive environment for the level of implementation that publishers and districts set out to achieve.
Students took the math assessment developed for the Early Childhood Longitudinal Study-Kindergarten Class of 1998-99 (ECLS-K) so that researchers could measure the achievement effects of the curricula. To help interpret achievement results, researchers also surveyed teachers about curriculum implementation and conducted classroom observations. Together, the survey and observation data helped researchers assess teacher training, use of the curriculum and of supplemental materials.
The ECLS-K assessment administered to students included questions in 5 math content areas:
- number sense, properties and operations
- geometry and spatial sense
- data analysis, statistics and probability
- patterns, algebra and functions
The 4 curricula vary in the extent to which they emphasize student-centered or teacher-directed approaches. Saxon and SFAW emphasize teacher-directed instructional approaches such as explicit instruction while Investigations and Math Expressions emphasize student-centered activities such as peer collaboration, according to the report.
Here are the study’s characterizations of the 4 curricula based on publishers’ own descriptions.
Investigations in Number, Data, and Space (Investigations) is published by Pearson Scott Foresman (Russell et al. 2006) and uses a student-centered approach encouraging metacognitive reasoning and drawing on constructivist learning theory. The lessons focus on understanding, rather than on “correct answers,” and build on students’ knowledge and understanding. Students are engaged in thematic units of 3-8 weeks in which they first investigate, then discuss and reason about problems and strategies. Students frequently create their own representations.
Math Expressions is published by the Houghton Mifflin Company (Fuson 2006a) and blends student-centered and teacher-directed approaches to mathematics. Students question and discuss mathematics, but are explicitly taught effective procedures. There is an emphasis on using multiple specified objects, drawings, and language, to represent concepts, and an emphasis on learning through the use of real-world situations. Students are expected to explain and justify their solutions.
Saxon Math (Saxon) is published by Harcourt Achieve (Larson 2004) and is a scripted curriculum that blends teacher-directed instruction of new material with daily distributed practice of previously learned concepts and procedures. The teacher introduces concepts or efficient strategies for solving problems. Students observe and then receive guided practice, followed by distributed practice. Students hear the correct answers and are explicitly taught procedures and strategies. Frequent monitoring of student achievement is built into the program. Daily routines are extensive and emphasize practice of number concepts and procedures and use of representations.
Scott Foresman-Addison Wesley Mathematics (SFAW) is published by Pearson Scott Foresman (Charles et al. 2005) and is a basal curriculum that combines teacher-directed instruction with a variety of differentiated materials and instructional strategies. Teachers select the materials that seem most appropriate for their students, often with the help of the publisher. The curriculum is based on a consistent daily lesson structure, which includes direct instruction, hands-on exploration, the use of questioning, and practice of new skills.
“Achievement Effects of Four Early Elementary School Math Curricula” by Roberto Agodini et al, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, September 2010.