This symposium will explain why research found some curricular approaches in math are more effective than others at improving student achievement, describe what it takes for teachers to implement more effective approaches, and discuss the implications for math instruction.

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Conceptual/Theoretical Perspectives

Math skills are critical for success in the workplace, more so today than ever before. Scientific jobs always required a strong math foundation, and growth rates in science- and technology-related jobs are exceeding job growth in the general labor force. Moreover, service jobs that once relied on strength and endurance now require math skills. As math skills have grown in importance, so has the debate over how to improve students' math skills.

In recent years, discussions about reforming math education to meet the needs of today's labor market have focused on different approaches to improving student math achievement. Approaches include creating common standards for content and assessment, developing more effective teachers, and changing the pedagogy used to teach students. Curricula are often included in these discussions as a uniquely efficient method for implementing reform, since the majority of classrooms across the nation use a commercially available math curriculum as the basis for their instruction; however, little rigorous evidence exists on the relative effectiveness of different curricula (National Mathematics Advisory Panel, 2008; National Research Council, 2004).

Prior research has examined specific features of teaching that are effective at developing math skills. However, individual features typically function within a system, such as a curriculum, and the effects of each feature may depend on the system in which it functions (Hiebert & Grouws, 2007). The potential interdependence among teaching features points to the need to examine the effects of entire curricula, particularly a need to compare the effects of different approaches to packaging together teaching features.

Research Questions/Designs

This symposium will address three main questions:

1.      Which curricula are more effective?

2.      Why are some curricula more effective than others?

3.      What does it take to implement more effective curricula?

The first speaker will set the context for the symposium by presenting results from a large-scale, multi-year, randomized control trial that compares four early elementary school math curricula: (1) Investigations in Number, Data, and Space, (2) Math Expressions, (3) Saxon Math, and (4) Scott Foresman-Addison Wesley Mathematics. The evaluation, funded by the U.S. Department of Education (ED), provides rigorous evidence on the relative effectiveness of these curricula after two years of curriculum implementation. The curricula were selected using a competitive process and an independent study team recruited high-poverty districts and schools for the evaluation. Participating schools in each district were randomly assigned to one of the four curricula.

The second question will be addressed through three presentations. The first presentation will discuss the relationship between curriculum implementation and the study's relative curriculum effects. The second and third presentations will be given by developers of the two more effective curricula. These presentations will discuss the research base used to develop each curriculum, with a focus on specific aspects of instruction they found effective during their development efforts and that are likely contributing to the differential curriculum effects.

The third question will be addressed through the final presentation, which will discuss the curriculum effects as a measure of both teacher and curriculum capacity. The presenter will discuss relationships between curriculum design, teacher capacity, teacher interaction with materials, and curriculum implementation. Initially, the focus will be on teachers' use of curriculum materials. Then, recent research on the demands that curriculum materials place on teachers and the supports provided by each curriculum, will be discussed.

Data, Analyses, and Findings

The first presentation is based on 7 districts and 60 schools that participated in the study for two years. To measure the effects of the curricula, the study team tested students at the beginning and end of each school year using the ECLS math assessment. To interpret effects, the study team tested teacher content/pedagogical knowledge, administered two teacher surveys, and observed classroom instruction. The relative effects of the curricula were estimated using HLM techniques, which compare the average achievement of students in schools assigned to each curriculum. Two analyses were conducted to understand second-year effects of the curricula. The first examines the effects of school/teacher experience among first-graders in schools in their second year of implementation. The second examines the effects of student experience on students who experienced the curricula in both first and second grade. The results are based on a report currently under review at ED; the report will be released in Fall 2011.

The second presentation will discuss a Vygotskiian theoretical and design framework that evolved during ten years of classroom research conducted with more than 200 teachers and 5,000 students. The NSF-funded research focused on learning paths within core math content areas. Mathematically-desirable and accessible versions of the standard algorithms and visual models of problem situations were identified. In addition, research identified an effective approach that enables students to progress with understanding and fluency. Specific examples will be presented.

The third presentation will discuss the curriculum author's collaboration with teachers to research and develop a curriculum with two main goals: (1) ensure students attain mastery of each concept taught, and (2) ensure teachers can easily implement the curriculum with fidelity. The presentation will highlight specific teaching practices that research found can help students reach mastery without placing excessive burden on teachers.

The fourth presentation will draw on past and current research on teachers' use of curriculum materials (Author, 2004; Author, 2009). Prior research examined how teachers in the same school used their curriculum. The analysis showed different curriculum uses led to different opportunities for student and teacher learning. Ongoing NSF-funded research is assessing the kind of knowledge and capacities necessary for teachers to use curriculum resources effectively – the research and findings will be summarized.

Organization

This symposium will include four 15-minute presentations, followed by 30 minutes for questions. Presenters will use several questions to stimulate discussion:

1.      Are student-centered or teacher-directed instructional approaches more effective?

2.      What supports do teachers need to help students make meaningful mathematical connections?

3.      How does teacher capacity to use curricula affect curriculum effectiveness?

References

Author (2004). 

Author (2009).

Hiebert, J.C., & Grouws, D.A. The effects of classroom mathematics teaching on students' learning. In F.K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 371-404). New York: Information Age Publishing, 2007.

National Mathematics Advisory Panel. “Foundations for Success: The Final Report of the National Mathematics Advisory Panel.” Washington, DC: U.S. Department of Education, 2008.

National Research Council. On Evaluating Curricular Effectiveness: Judging the Quality of K–12 Mathematics Evaluations. Washington, DC: National Academies Press, 2004.