Using curriculum-specific tools for measuring fidelity of implementation is an essential yet often overlooked aspect of examining relationships among textbooks, teaching, and student learning. This “Brief Report” describes the variety of ways that curriculum implementation is measured and argues that there is an urgent need to develop curriculum-sensitive tools for analyzing classroom practice. The report outlines the use of the Concerns-Based Adoption Model (CBAM) theory to develop analytical tools for measuring implementation of two middle-grades reform mathematics curricula: Connected Mathematics and MathThematics. The report also presents next steps in this program of research.
Mary Ann Huntley
This article describes one student teacher's interactions with mathematics curriculum materials during her internship in a kindergarten classroom. Anne used curriculum materials from two distinct programs and taught lessons multiple times to different groups of children. Although she used each curriculum in distinct ways, her curriculum use was adaptive in both cases. Anne's specific ways of reading, evaluating, and adapting the curriculum materials contrast with previous results about beginning teachers' curriculum use. Several key factors appeared to contribute to Anne's particular ways of using the curriculum materials: features of her student-teaching placement, her personal resources and background, and characteristics of the materials. Directions for future research about student teachers' and other teachers' curriculum use are suggested in accord with these factors.
Robert Reys, Barbara Reys, Richard Lapan, Gregory Holiday and Deanna Wasman
This study compared the mathematics achievement of eighth graders in the first three school districts in Missouri to adopt NSF-funded Standards-based middle grades mathematics curriculum materials (MATH Thematics or Connected Mathematics Project) with students who had similar prior mathematics achievement and family income levels from other districts. Achievement was measured using the mathematics portion of the Missouri Assessment Program (MAP) administered to all 8th graders in the state annually beginning in the spring of 1997. Significant differences in achievement were identified between students using Standards-based curriculum materials for at least 2 years and students from comparison districts using other curriculum materials. All of the significant differences reflected higher achievement of students using Standards-based materials. Students in each of the three districts using Standards-based materials scored higher in two content areas (data analysis and algebra), and these differences were significant.
Beth A. Herbel-Eisenmann
In this article, I used a discourse analytic framework to examine the “voice” of a middle school mathematics unit. I attended to the text's voice, which helped to illuminate the construction of the roles of the authors and readers and the expected relationships between them. The discursive framework I used focused my attention on particular language forms. The aim of the analysis was to see whether the authors of the unit achieved the ideological goal (i.e., the intended curriculum) put forth by the NCTM's Standards (1991) to shift the locus of authority away from the teacher and the textbook and toward student mathematical reasoning and justification. The findings indicate that achieving this goal is more difficult than the authors of the Standards documents may have realized and that there may be a mismatch between this goal and conventional textbook forms.
Janine T. Remillard and Martha B. Bryans
This study was prompted by the current availability of newly designed mathematics curriculum materials for elementary teachers. Seeking to understand the role that reform-oriented curricula might play in supporting teacher learning, we studied the ways in which 8 teachers in the same school used one such curriculum, Investigations in Number, Data, and Space (TERC, 1998). Findings revealed that teachers had orientations toward using curriculum materials that influenced the way they used them regardless of whether they agree with the mathematical vision within the materials. As a result, different uses of the curriculum led to different opportunities for student and teacher learning. Inexperienced teachers were most likely to take a piloting stance toward the curriculum and engage all of its resources fully. Findings suggest that reform efforts might include assisting teachers in examining unfamiliar curriculum resources and developing new approaches to using these materials.
Harold L. Shoen, Kristen J. Cebulla, Kelly F. Finn and Cos Fi
We report results from a study of instructional practices that relate to student achievement in high school classrooms in which a standards-based curriculum (Core-Plus) was used. We used regression techniques to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26 schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical expectations were positively related to growth in student achievement.
Jeannie C. Hollar and Karen Norwood
In this study, we extended O'Callaghan's computer-intensive algebra study by using his component competencies and the process-object framework to investigate the effects of a graphingapproach curriculum employing the TI-82 graphing calculator. We found that students in the graphing-approach classes demonstrated significantly better understanding of functions on all 4 subcomponents of O'Callaghan's Function Test, including the reification component, than did students in the traditional-approach classes. Additionally, no significant differences were found between the graphing-approach and traditional classes either on a final examination of traditional algebra skills or on an assessment of mathematics attitude.
Daniel F. McGaffrey, Laura S. Hamilton, Brian M. Stecher, Stephen P. Klein, Delia Bugliari and Abby Robyn
A number of recent efforts to improve mathematics instruction have focused on professional development activities designed to promote instruction that is consistent with professional standards such as those published by the National Council of Teachers of Mathematics. This paper describes the results of a study investigating the degree to which teachers' use of instructional practices aligned with these reforms is related to improved student achievement, after controlling for student background characteristics and prior achievement. In particular we focus on the effects of curriculum on the relationship between instructional practices and student outcomes. We collected data on tenth-grade students during the 1997–98 academic year. Some students were enrolled in integrated math courses designed to be consistent with the reforms, whereas others took the more traditional algebra and geometry sequence. Use of instructional practices was measured through a teacher questionnaire, and student achievement was measured using both the multiple-choice and open-ended components of the Stanford achievement tests. Use of standards-based or reform practices was positively related to achievement on both tests for students in integrated math courses, whereas use of reform practices was unrelated to achievement in the more traditional algebra and geometry courses. These results suggest that changes to instructional practices may need to be coupled with changes in curriculum to realize effects on student achievement.
Douglas A. Grouws, James E. Tarr, Óscar Chávez, Ruthmae Sears, Victor M. Soria and Rukiye D. Taylan
This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. The study involved 2,161 students in 10 schools in 5 states. Within each school, approximately 1/2 of the students studied from an integrated curriculum (Course 1) and 1/2 studied from a subject-specific curriculum (Algebra 1). Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.
James E. Tarr, Douglas A. Grouws, Óscar Chávez and Victor M. Soria
We examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. We constructed 3-level hierarchical linear models of scores on 3 end-of-year outcome measures: a test of common objectives, an assessment of problem solving and reasoning, and a standardized achievement test. Students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the standardized achievement test. Significant student-level predictors included prior achievement, gender, and ethnicity. At the teacher level, in addition to Curriculum Type, the Opportunity to Learn and Classroom Learning Environment factors demonstrated significant power in predicting student scores, whereas Implementation Fidelity, Teacher Experience, and Professional Development were not significant predictors.