Research on CMP

Adams, L. M., Tung, K. K., Warfield, V. M., Knaub, K., Mudavanhu, B., & Yong, D. (2002). Middle school mathematics comparisons for Singapore Mathematics, Connected Mathematics Program, and Mathematics in Context. Report submitted to the National Science Foundation by the Department of Applied Mathematics, University of Washington.

Adams, R. L. (2005). Standards-based accountability: Improving achievement for all students through standards based mathematics instruction. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 66(6). (ProQuest ID No. 932378841)

ABSTRACT: The purpose of this study was to conduct evaluation research on the professional development intervention implemented to address the effectiveness of standards-based instruction in improving the mathematic achievement of all student subgroups in Yolo County schools. The question addressed in this study was "Does standards-based instruction in mathematics, coupled with professional development on the standards-based content of California State Board of Education-approved text books, lead to increases in student achievement and high school graduation rates for all subgroups in Yolo County schools?"

The Yolo County Office of Education (YCOE) university partnership designed the professional development intervention for teachers delivering math at grade levels 5th through algebra I. Twelve teachers (treatment group) participated in 40-hour institutes; follow-up sessions, and data gathering to measure the effectiveness of the training and support. Ten teachers (control group) recruited as 2005 institute participants simultaneously gathered like data.

Twelve schools participated in the study. The teacher index ranges from 0.00 teachers trained in standards-based mathematics instruction to 0.50 with a mean of 0.19 indicating that the schools hadn't implemented school-wide professional development.

There was a significant difference between the treatment group scores on the post-survey and the control group scores (p = .011) (effect size > 1.0). The treatment group results indicate that the treatment group's beliefs on standards based instruction shifted significantly into the high-reform range after the intervention.

Curriculum calibration indicates that the use of the textbook as the main teaching resource did not ensure that the instruction was on grade-level over 75% of the time. The control group used the textbook as the main teaching resource 30% of the time compared to 55% by the treatment group, yet taught on grade-level more often then the treatment group.

The implications of this program evaluation point to continued organizational improvement through reducing gaps in: content knowledge, motivation, and organization support. Based on the research cited, and the practical implications from the intervention piloted in the Yolo County schools, the county partnership must continue to build systems of support that embrace standards-based mathematic instruction.

Aisling, L. M., Friel, S. N., & Mamer, J. D. (2009). It’s a fird!: Can you compute a median of categorical data? Mathematics Teaching in the Middle School, 14(6), 344-351.

Description: Students need time and experience to develop essential understandings when they explore data analysis. In this article, the reader gains insight into confusion that may result as students think about summarizing information about a categorical data set that is attempting to use, in particular, the median. The authors highlight points to consider in helping students unpack these essential understandings.

Alibali, M. W., Stephens, A. C., Brown, A. N., Yvonne, S., & Nathan, M. J. (2014). Middle school students’ conceptual understanding of equations: Evidence from writing story problems. International Journal of Educational Psychology, 3(3), 235–264. doi:10.4471/ijep.2014.13

ABSTRACT: This study investigated middle school students’ conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations’ structures, including number of operations and position of the unknown, influenced students’ performance on both tasks. On the story-writing task, students’ performance on two-operator equations was poorer than would be expected on the basis of their performance on one-operator equations. Students made a wide variety of errors on the story-writing task, including (1) generating story contexts that reflect operations different from the operations in the given equations, (2) failing to provide a story context for some element of the given equations, (3) failing to include mathematical content from the given equations in their stories, and (4) including mathematical content in their stories that was not present in the given equations. The nature of students’ story-writing errors suggests two main gaps in students’ conceptual understanding. First, students lacked a robust understanding of the connection between the operation of multiplication and its symbolic representation. Second, students demonstrated difficulty combining multiple mathematical operations into coherent stories. The findings highlight the importance of fostering connections between symbols and their referents.

American Association for the Advancement of Science: Project 2061 (2000). Middle grades mathematics textbooks: A benchmarks-based evaluation. Evaluation report prepared by the American Association for the Advancement of Science.

Anderson, N. C. (2008). Walk the line: Making sense of y = mx + b. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics, 70th yearbook (pp. 233-246). Reston, VA: National Council of Teachers of Mathematics.

Anderson, V. J. (2010). Connected Mathematics Project, 2nd edition, implementation in Seattle: The experience of teachers and principals. Dissertation Abstracts International Section A: Humanities and Social Sciences, 71 (2-A), 432.

Arbaugh, F., Lannin, J., Jones, D. L., & Park Rogers, M. (2006). Examining instructional practices in Core-Plus lessons: Implications for professional development. Journal of Mathematics Teacher Education, 9(6), 517-550.

ABSTRACT: In the research reported in this article, we sought to understand the instructional practices of 26 secondary teachers from one district who use a problems-based mathematics textbook series (Core-Plus). Further, we wanted to examine beliefs that may be associated with their instructional practices. After analyzing data from classroom observations, our findings indicated that the teachers’ instructional practices fell along a wide continuum of lesson implementation. Analysis of interview data suggested that teachers’ beliefs with regard to students’ ability to do mathematics were associated with their level of lesson implementation. Teachers also differed, by level of instructional practices, in their beliefs about appropriateness of the textbook series for all students. Results strongly support the need for professional development for teachers implementing a problems-based, reform mathematics curriculum. Further, findings indicate that the professional development be designed to meet the diverse nature of teacher needs.

Artzt, A. F., & Curcio, F. R. with Sultan, A. & Wachter, T. (2003). Rethinking secondary mathematics teacher preparation. In D. Kaufman, D. M. Moss, & T. A. Osborn (Eds.), Beyond the boundaries: A transdisciplinary approach to learning and teaching (pp. 69-80). Westport, CT: Greenwood Publishing Group.

Asquith, P., Stephens, A.C., Knuth, E.J., Alibali, M.W. (2005). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.

ABSTRACT: This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview data were collected from 20 middle school teachers regarding their predictions of student responses to written assessment items focusing on the equal sign and variable. Teachers' predictions of students' understanding of variable aligned to a large extent with students' actual responses to corresponding items. In contrast, teachers' predictions of students' understanding of the equal sign did not correspond with actual student responses. Further, teachers rarely identified misconceptions about either variable or the equal sign as an obstacle to solving problems that required application of these concepts. Implications for teacher professional development are discussed.

Ball, D. L. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappan, 77(7), 500-508.

ABSTRACT: In order to improve mathematics education, a close examination of assumptions about teacher learning and the teaching of mathematics must be made. Teachers and others participating in the reform process will have to learn many new ideas and unlearn many previous assumptions.

Banilower, E. R. (2010). Connected Mathematics, 2nd Edition: A three-year study of student outcomes. Chapel Hill, NC: Horizon Research, Inc.

Banilower, E. R., Smith, P. S., Weiss, I. R., Malzahn, K. A., Campbell, K. M., & Weis, A. M. (2013). Report of the 2012 National Survey of Science and Mathematics Education. Chapel Hill, NC: Horizon Research, Inc.

Bay, J. M. (1999). Middle school mathematics curriculum implementation: The dynamics of change as teachers introduce and use standards-based curricula. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 60(12). (ProQuest ID No. 730586091)

ABSTRACT: Two case studies of school districts were developed to study the district-level constraints and considerations during adoption of standards-based middle school mathematics curricula. In addition, the nature of implementation within classrooms was described through six teacher case studies. The two school districts were in their third year of full implementation of a curricula, with one school district implementing the Connected Mathematics Project and the other MATH Thematics. Data collected included interviews, surveys, and classroom observations. Factors influencing teacher decision-making and district-level decision-making were analyzed.

Several themes emerged related to the district-level issues of implementation. First, teacher leadership and/or participation in the professional development and district decision-making throughout the implementation had an impact on the nature of the teachers' perceptions of the need for change. Those who were involved in professional development or provided leadership in the district had a stronger commitment to the implementation. Teacher turnover constrained the level of implementation in the classroom and the level of interaction among teachers. Perceptions of parents, expectations for students, and state/national assessments were important considerations as districts selected and implemented their curriculum.

Successful implementation of standards-based curriculum in the classroom appeared to be related to several factors. First, the extent to which teachers were involved in the process of implementation, including choosing the curriculum and participating in professional development, influenced the degree to which their classrooms were aligned with recommendations from the curricula and the NCTM Standards (1989, 1991, 1995). Collaborative relationships that were developed during the selection and first year of implementation continued to function productively in the third year of implementation, which happened to be the first year the districts were not participating in any externally-sponsored professional development. All teachers were concerned with the level of skill development that students needed beyond what was provided in the curriculum and made adjustments accordingly.

Bay, J. M., Beem, J. K., Reys, R. E., Papick, I., & Barnes, D. E. (1999). Student reactions to standards-based math-ematics curricula: The interplay between curriculum, teachers, and students. School Science and Mathematics, 99(4), 182–188.

ABSTRACT: As standards-based mathematics curricula are used to guide learning, it is important to capture not just data on achievement but data on the way in which students respond to and interact in a standards-based instructional setting. In this study, sixth and seventh graders reacted through letters to using one of two standards-based curriculum projects ("Connected Mathematics Project or Six Through Eight Mathematics. Letters were analyzed by class, by teacher, and by curriculum project. Findings suggest that across classrooms students were positive toward applications, hands-on activities, and working collaboratively. The level of students’ enthusiasm for the new curricula varied much from class to class, further documenting the critical role teachers play in influencing students’ perceptions of their mathematics learning experiences. The results illustrate that, while these curricula contain rich materials and hold much promise, especially in terms of their activities and applications, their success with students is dependent on the teacher.

Bay, J. M., Reys, B. J., & Reys, R. E. (1999). The top 10 elements that must be in place to implement standards-based mathematics curricula. Phi Delta Kappan, 80(7), 503 506.

ABSTRACT: Teachers' work with four National Science Foundation-funded curricula in the Missouri Middle-School Mathematics Project has disclosed 10 critical implementation elements: administrative support, opportunities for study, curriculum sampling, daily planning, interaction with experts, collaboration with colleagues, incorporation of new assessments, student adjustment time, and planning for transition.

Bay-Williams, J., Scott, M., & Hancock, M. (2007). Case of the mathematics team: Implementing a team model for simultaneous renewal. Journal of Educational Research, 100(4), 243-253.

ABSTRACT: Simultaneous renewal in teacher education is based on the notion that improvement at 1 level requires improvement at all levels and that all stakeholders are responsible for such improvement. The authors discuss the creation and impact of a mathematics team as a vehicle for simultaneous renewal by using the team model for simultaneous renewal for improved teacher-education courses, student achievement in an elementary school, and curriculum changes in K-16 mathematics. Participation in the mathematics team created awareness and respect for the teachers, mathematicians, and mathematics educators.

Beaudrie, B. P., & Boschmans, B. (2013). Transformations and handheld technology. Mathematics Teaching in the Middle School, 18(7), 444-450.

Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C., & Miller, J. (1997a). Development of Proportional Reasoning in a Problem-Based Middle School Curriculum. Paper presented at the Annual Meeting of the American Educational Research Association. Chicago, IL.

ABSTRACT: Contemporary constructivist views of mathematical learning have encouraged curriculum developers to devise instructional materials that help students build their own understanding and procedures for doing rational number computations, solving proportions, and applying those skills to real and whimsical problems. The Connected Mathematics Project (CMP) curriculum supports construction of rational number knowledge by presenting students with a series of units based on contextual problems that require proportional reasoning and computation. The goal of this study was to describe the character and effectiveness of proportional reasoning by students with different curricular experiences as they face problems in which ratio and proportion ideas are appropriate and useful. Performance task papers and follow-up interviews with selected students from the study indicated that, in addition to a greater frequency of correct answers and reasoning compared with control group students, CMP students appeared to have developed greater ability to articulate their thinking. Students from CMP classes had a generally broader and more flexible repertoire of strategies available for problem solving. The results suggest that problem-based curriculum and instruction can be effective in helping students construct effective personal understanding and skill in one of the core strands of middle grade mathematics.

Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C., & Miller, J. (1997b). A study of proportional reasoning among seventh and eighth grade students. Paper presented at the annual meeting of the American Educational Research Association. Chicago, IL