Reform efforts in mathematics have lead to the creation of curricular materials that focus on strengthening the mathematical knowledge of all students and are guided by instructional practices that promoted problem solving, communication, reasoning, and creating mathematical connections (Senk & Thompson, 2003). However, it is difficult to discuss the impact of these curricula when teachers are not provided with necessary support. Implementing reform mathematics curricula represents a challenging transition for many teachers (Ziebarth, 2003). Teachers’ beliefs and backgrounds greatly influence how they implement curricula, potentially causing the implemented curricula to be significantly different from the developers’ intended curricula (Ball & Cohen, 1996; Remillard, 2000) and from a teacher’s own intentions (Stein, Remillard, & Smith, 2007; Stein & Smith, 2010). We cannot expect curricula to be tossed into the hands of teachers without a structure for supporting them in their use of the materials.

While studies of curricular evaluation may report on professional development experiences, and the NRC (2004) argues for the importance of gathering such data, few studies provide adequate detail to position those treatments in light of research on effective professional development. As a result, this study provides an account of the impact different components of a professional development, designed around the Core-Plus curriculum, have on students’ state test scores and on teachers’ implementation of the curricular materials. The research conducted in this paper is guided by the recommendations of the NRC and the ongoing work of the COSMIC project (Tarr, et al., 2010).

The North Carolina Integrated Mathematics (NCIM) project was developed to create and support a community of teachers using the Core-Plus curricular materials particularly in high needs schools. The model of professional development included: summer workshops, visits from instructional coaches, and a collaborative website. Its aim was to educate teachers about the content and pedagogy of using integrated mathematics. Spread throughout rural parts of the state, the seven partner schools were identified as low-performing and joined the project.

Research Questions

1. Among teachers using the Core-Plus curricular materials, what evidence of systematic differences is there on the effects of student learning based on varying levels of teacher participation in the NCIM project?
2. Among teachers using the Core-Plus curricular materials, to what extent and how can the variance in student outcomes be explained by teacher implementation? 

To address the research questions, this study used a mixed methods design due to the relative importance of the quantitative findings and the ability of the qualitative data analysis to refine the statistical results by exploring teachers’ implementation in greater detail. The first question was answered using a quasi-experimental matched group design, while the second question was analyzed utilizing qualitative methods. First, 2009-2010 student state testing data was compared for teachers exposed to different components of the NCIM professional development. Hierarchical linear modeling (Raudenbush & Bryk, 2002) was utilized to model variation in student achievement, using student and teacher level data. Second, field-notes from the researcher’s classroom observations, teacher interviews, and instructional coach reports combined with the textbook implementation data to provide a detailed account of the teachers’ implementation of Core-Plus.

The sample included four target populations. Group A consisted of 7 teachers from the NCIM project schools who receive instructional coach visits each month following the summer workshops. Two Group F teachers had an instructional coach only and no summer support, Group B teachers (n=6) only participated in the summer workshops, and Group D teachers (n=6) were not involved in any aspect of the NCIM project.

This study found significant differences in teachers’ implementation of Core-Plus textbook content, analyzed factors that correlated to student Algebra I and II achievement among groups with varying levels of NCIM professional development experience, examined themes that influenced teachers’ instructional practices, and drew on multiple forms of analysis to detail how these various data sources and results combine to provide a rich picture for teachers implementation of Core-Plus.

First, an analysis of textbook implementation showed significant differences between teachers that attended the NCIM workshop and those that had not. This suggests that workshop attendance can increase teachers’ trust for the curriculum or knowledge about how to implement it with students. Next, these implementation indices were used to model student Algebra achievement. These models underscored the importance that teacher content knowledge and experience teaching a curriculum had on student achievement. Further, differences in student achievement among the groups was only prevalent on the Algebra II exam when controlling for teacher variables.  

Qualitative data indicated that teachers’ beliefs about how students learn mathematics, their trust for the curriculum, and systemic factors influenced decisions teachers made about textbook implementation. Teacher beliefs about how students learn mathematics had an impact on teachers’ use of collaborative groups, supplements they provided to students, and their ability to let students struggle through mathematics. Teachers’ trust for the curriculum was a barometer for how frequently they utilized reform or traditional instructional practices. Participation at the NCIM summer workshop helped Group A and B teachers feel more confident and trusting of the Core-Plus curriculum and instructional practices, and the instructional coaches supported these ideas throughout the year for Group A teachers. Systemic factors within a school or system also had an impact on teachers’ implementation of Core-Plus. The constraints and affordances of the system (access to materials, scheduling, and student adjustment to Core-Plus) contributed to the variance among teachers’ implementation of the textbook materials.

Using a mixed methods approach provided a deeper understanding for differences in the implementation indices, for the lack of significant differences among groups when modeling Algebra I achievement, and for the varying degree of differences among groups in the Algebra II sample. Analyzing teacher interviews, instructional coach reports, and field-notes from classroom observations helped to detail instructional practices teachers used in their classrooms and decisions they made about supplementing the textbook.

The presenters will speak for approximately 10 minutes. Audience members will have 10 minutes to review findings from the analysis and the final 10 minutes will be devoted to audience questions and discussion.

References

Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is - or might be - the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-14.

Raudenbush, S., & Bryk, A. (2002). Hierarchical linear models: Applications and data analysis methods (Second ed.). Thousand Oaks, CA: Sage Publications.

Remillard, J. T. (2000). Can curriculum materials support teachers' learning? Two fourth-grade teachers' use of a new mathematics text. The Elementary School Journal, 100(4), 331-350.

Senk, S., & Thompson, D. (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahway, NJ: Lawrence Erlbaum.

Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 319-369).

Stein, M. K., & Smith, M. S. (2010). The influence of curriculum on students' learning. In B. J. Reys, R. E. Reys & R. Rubenstein (Eds.), Mathematics curriculum: Issues, tends, and future directions. Reston, VA: National Council for Teachers of Mathematics

Tarr, J. E., Ross, D., McNaught, M. D., Chávez, O., Grouws, D. A., Reys, R., et al. (2010, April). Identification of student– and teacher–level variables in modeling variation of mathematics achievement data. Paper presented at the Annual Meeting of the American Education Research Association, Denver.

Ziebarth, S. W. (2003). A report on advances in secondary mathematics curriculum development in the united states and imminent new directions: Core-plus mathematics as a case study. Paper presented at the Hawaii International Conference on Education, Honolulu, HI.