A large new federal study that takes sides in the “math wars” may make it easier in the future for educators to choose among math curricula for the elementary grades. The study of 1,309 1st graders from 39 elementary schools is thought to be the largest experimental test of some of the nation’s most widely used commercial math programs.

Of the 4 math curriculum programs that were tested, 2 programs, Saxon Math, and a newer program called Math Expressions, emerged as the clear winners. The study wasÂ commissioned by the Institute of Education Sciences.

In classrooms that used Math Expressions or Saxon, a student at the 50th percentile in math achievement would score 9 to 12 points higher than if he or she were in a classroom that used one of the other two programs in the study, Investigations in Number, Data, and Space and Scott Foresman-Addison Wesley Mathematics, according to researchers.

The schools participating in the study were in 4 states in 3 regions of the country. Two districts are in urban areas, 1 is in a suburban area and the other is in a rural area.

Currently K-2 educators (91%) choose one of 7 math curricula for their classrooms without much independent scientific evidence of how the curricula compare in on-the-ground effectiveness. The study was conducted by an independent research group, Mathematica Policy Research Inc. of Princeton, N.J.

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.

To examine achievement differences among subgroups, the researchers studied math curriculum effects across the following 6 characteristics:

- Participating districts
- School fall achievement
- School free/reduced-price meals eligibility
- Teacher education
- Teacher experience
- Teacher math content/pedagogical knowledge.

The pattern of higher student performance with Math Expressions and Saxon students was consistent across most subgroups, the researchers write. Math Expressions and Saxon students had higher average adjusted spring scores than Investigations and Scott Foresman-Addison Wesley Mathematics students.

### Selection of 4 programs

A panel of outside experts in math and math instruction reviewed 8 programs from developers who applied to participate in the study. Six criteria were used to review the programs:

- research support for the curriculum’s conceptual framework
- empirical evidence of effectiveness
- objectives of the curriculum
- quality of training and materials
- institutional capability to train the num- ber of teachers in the study, and
- appropriateness for grades one, two, and three in Title I schools.

Below are the study’s descriptions of the different approaches of the final four curricula.

**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.

The 4 programs were each randomly assigned to 10 schools each for use over the 2006-07 school year. All teachers received initial training from the publishers and 96% received follow-up training. Training varied by curriculum, ranging from 1.4 days for Saxon to 3.9 days for Investigations. On average, Saxon teachers reported spending 1 more hour on math instruction per week than did teachers of the other curricula.

The study analyzed student achievement based on testing in both the fall and spring. Students were assessed with an adaptive measure developed for the National Center for Education Statistics’ Early Childhood Longitudinal Study-Kindergarten Class of 1998-99(ECLS-K). The nationally normed test begins with a routing test that broadly measures each examinee’s achievement level and then, depending on the score, assigns the student to one of 3 longer tests: an easy test, a middle-difficulty test or a difficult test.

“Adaptive tests are useful for measuring achievement because they limit the amount of time children are away from their classrooms and reduce the risk of ceiling or floor effects in the test score distribution–something that can have adverse effects on measuring achievement gains,” the study says.

Researchers said the report is the first of 3 that will be issued on the study. Seventy-one more schools joined in the 2007-08 academic year and researchers plan to continue to analyze results on students’ mathematical progress through the 2008-09 school year.

*“Achievement Effects of Four Early Elementary School Math Curricula, Findings from First Graders in 39 Schools,” by Roberto Agodini et al, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, February 2009.*