All Published Research and Evaluation on CMP
A large body of literature exists that focuses on or is related to the Connected Mathematics Project. Here, you will find articles on CMP that we have compiled over the past thirty years. These include research, evaluation and descriptions from books, book chapters, dissertations, research articles, reports, conference proceedings, and essays. Some of the topics are:
- student learning in CMP classrooms
- teacher's knowledge in CMP classrooms
- CMP classrooms as research sites
- implementation strategies of CMP
- longitudinal effects of CMP in high school math classes
- students algebraic understanding
- student proportional reasoning
- student achievement
- student conceptual and procedural reasoning and understanding
- professional development and teacher collaboration
- comparative studies on different aspects of mathematics curricula
- the CMP philosophy and design, development, field testing and evaluation process for CMP
This list is based on thorough reviews of the literature and updated periodically. Many of these readings are available online or through your local library system. A good start is to paste the title of the publication into your search engine. Please contact us if you have a suggestion for a reading that is not on the list, or if you need assistance locating a reading.
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.
Banilower, E. R. (2010). Connected Mathematics, 2nd Edition: A three-year study of student outcomes. 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.
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. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247-273.
ABSTRACT: Contextual problems involving rational numbers and proportional reasoning were presented to seventh grade students with different curricular experiences. There is strong evidence that students in reform curricula, who are encouraged to construct their own conceptual and procedural knowledge of proportionality through collaborative problem-solving activities, perform better than students with more traditional, teacher-directed instructional experiences. Seventh grade students, especially those who study the new curricula, are capable of developing their own repertoire of sense-making tools to help them to produce creative solutions and explanations. This is demonstrated through analysis of solution strategies applied by students to a variety of rate problems.
Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71–80. doi:10.1016/j.ijer.2013.06.005
ABSTRACT: Over the past two decades, standards documents have emphasized the importance of developing students’ abilities to generate and critique mathematical arguments across all grade levels. However, little is known about the opportunities elementary textbooks provide for students to learn mathematical argumentation. We analyzed seven upper elementary (ages 9–11) mathematics textbooks published in the U.S., focusing specifically on reasoning-and-proving opportunities in written tasks, and found that the average percentage of such tasks was 3.7%. Further, analyses of the task purpose and type of justification warranted revealed distinctions between the text materials in terms of the kinds of reasoning-and-proving activities prompted and the placement of tasks in the lesson sections. Specifically, textbooks developed based on research and written to align with curriculum and instruction standards were more likely to have reasoning-and-proving tasks within the narrative and student exercise sections than other texts. We discuss implications for the opportunities to learn reasoning-and-proving in elementary classrooms.
Bledsoe, A. M. (2002). Implementing the Connected Mathematics Project: The interaction between student rational number understanding and classroom mathematical practices. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 63(12). (ProQuest ID No. 765115471)
ABSTRACT: The Research Advisory Council (RAC, 1991) of the National Council of Teachers of Mathematics (NCTM) called for research on the effects of Standards -based (NCTM, 1989, 1991, 2000) curricula. Following a qualitative design, this dissertation study provides insight into what it means to know and do mathematics in one seventh-grade classroom in which one such curriculum was implemented. More specifically, this study provides a thick description of the teaching and learning of rational number concepts in a classroom where the Bits and Pieces I unit (Lappan, Fey, Fitzgerald, Friel, & Phillips, 1997) from the Connected Mathematics Project (CMP) was used.
Through the lens of the Emergent Perspective (Cobb & Yackel, 1996), this study investigates the relationship between students' initial and developing understandings and the evolving classroom mathematical practices. Results indicate that students' rational number understandings and the teacher's proactive role contributed to the establishment of the classroom mathematical practices. These mathematical practices serve to document the development of the collective understandings as the students engaged in activities from Bits and Pieces I (Lappan et al., 1997). Findings suggest that students did make significant growth in their rational number understandings as a consequence of engaging in these activities and participating in these mathematical practices. In particular, results indicate that participation in conceptually-based mathematical practices provided greater opportunities for students' to advance in their rational number understandings than participation in those that were procedurally-based. In fact, participation in procedurally-based mathematical practices actually constrained some students' advance in their rational number understandings.
Bray, M. S. (2005). Achievement of eighth grade students in mathematics after completing three years of the Connected Mathematics Project. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 66(11). (ProQuest ID No. 1031063341)
ABSTRACT: The purpose of this study was to examine the three-year effect of the Connected Mathematics Project (CMP) on the mathematics achievement of middle school students in a southeastern Tennessee public school district. This was accomplished by (1) comparing the mathematics achievement of eighth graders who have completed three years of CMP with their mathematics achievement after completing one and two years of CMP; (2) comparing the achievement of male and female students during the same period of time; and (3) comparing the mathematics achievement of historically underrepresented students after completing one, two, and three years of CMP.
In order to provide for a richer analysis of the CMP experience, the overall design employed quantitative and qualitative methodologies. The quantitative section of the study examined the mathematical achievement of almost 2,900 of the 2001-2002 eighth graders, over 3,000 of the 2000-2001 seventh graders, and over 3,100 1999- 2000 sixth graders as evidenced by their Tennessee Comprehensive Assessment Program (TCAP) test scores. The qualitative segment of the study explored the experiences of the textbook adoption committee members, teachers, administrators, and parents.
Using the Tennessee Comprehensive Assessment Program mathematics total battery test score as the dependent variable, there was no significant difference between the mathematics achievement of students completing one or two years of CMP. However, there was a significant difference in the mathematics achievement between students completing three years of CMP when compared to their mathematics scores after one and two years. There was also a significant difference between male and female students after completing one and two years of CMP but no significant difference was detected after the completion of three years. Though there was a significant difference revealed in the achievement between African Americans and Non African Americans after completing one, two, and three years of CMP the gap closed slightly after completing three years. Overall, CMP students performed better on the state achievement assessment the longer they were being instructed using the standards based curriculum.
Burdell, C., & Smith III, J. P. (2001). “The math is different, but I can deal”: Studying students’ experiences in a reform-based mathematics curriculum. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA.
ABSTRACT: The research reported in this paper describes the mathematical experiences of 9 students who moved from a traditional mathematics program in junior high school to a high school mathematics program structured by current reforms in curriculum and teaching. We will refer to the high school site of this work as Logan High (though the name is fictitious). Logan has for some years implemented the Core-Plus Mathematics Project materials for most of its grade 9–12 students, including some (but not all) students who come out of the “advanced” mathematics track in the junior high school. We recruited 24 Logan student volunteers starting in January 2000 and have tracked these students in their mathematics work for 2.5 semesters.
We report on the experiences of 9 of these students, drawing on a maximum of 3 semesters of mathematics coursework (Spring 2000, Fall 200, and Spring 2001). We have analyzed their mathematical experiences along 4 dimensions: (1) performance in mathematics, (2) disposition towards the subject, (3) approach to learning the subject, and (4) differences students see between traditional and Core-Plus mathematics curricula and teaching. All of our 9 students reported differences between their past and present mathematics programs as they moved into Core-Plus, but in only 2 cases was there any significant change in performance across the curricular shift.
Cady, J. A., Hodges, T. E., & Collins, R. L. (2015). A comparison of textbooks’ presentation of fractions. School Science & Mathematics, 115(3), 105–116. doi:10.1111/ssm.12108.
ABSTRACT: In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that teaching and learning of fractions is a complex process, and that fraction understanding is the foundation for later topics such as proportionality, algebra, and probability, makes it important to examine the variation in presentation of fraction concepts in U.S. textbooks, especially the difference between traditional and standards-based curricula. The purpose of this study is to determine if differences exist in the presentation of fractions in conventional and standards-based textbooks and how these differences align with the recommendations of National Council of Teachers of Mathematics, Common Core State Standards, and the research on the teaching and learning of fractions.
Cai, J. (2014). Searching for evidence of curricular effect on the teaching and learning of mathematics: Some insights from the LieCal project. Mathematics Education Research Journal, 26, 811-831.
ABSTRACT: Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics Project (CMP) in the USA on teachers' teaching and students' learning. Using a three-level conceptualization of curriculum (intended, implemented, and attained), a variety of evidence from the LieCal Project is presented to show the impact of mathematics curriculum reform on teachers' teaching and students' learning. This paper synthesizes findings from the two longitudinal studies spanning 7 years of the LieCAl Project both to show the kind of impact curriculum has on teachers' teaching and students' learning and to suggest powerful but feasible ways researchers can investigate curriculum effect on both teaching and learning.
Cai, J. (2015). Curriculum reform and mathematics learning: Evidence from two longitudinal studies. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 71–92). Gewerbestrasse, Switzerland: Springer International Publishing.
ABSTRACT: Drawing on longitudinal evidence from the LieCal Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics Project (CMP) in the United States on teachers’ teaching and students’ learning. Using a three-level conceptualization of curriculum (intended, implemented and attained), a variety of evidence from the LieCal Project is presented to show the impact of mathematics curriculum reform on teachers’ teaching and students’ learning. The findings from the two longitudinal studies in the LieCal Project serve both to show the kind of impact curriculum has on teachers’ teaching and students’ learning and to suggest powerful ways researchers can investigate curriculum effect on both teaching and learning.
Cai, J., & Moyer, J. C. (2006). A conceptual framework for studying curricular effects on students’ learning: Conceptualization and design in the LieCal project. Poster presented at the 2006 Annual Meeting of the International Group of Psychology of Mathematics Education, Prague, Czech Republic.
Cai, J., Hwang, S., & Moyer, J.C. (2016) Mathematical problem posing as a measure of curricular effect on students’ learning: A response. Educational Studies in Mathematics, 91(1), 9–10.
Cai, J., Moyer, J. C., Wang, N., & Nie, B. (2011). Examining students’ algebraic thinking in a curricular context: A longitudinal study. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialog from multiple perspectives (pp. 161-186). New York: Springer.
ABSTRACT: This chapter highlights findings from the LieCal Project, a longitudinal project in which we investigated the effects of a Standards-based middle school mathematics curriculum (CMP) on students’ algebraic development and compared them to the effects of other middle school mathematics curricula (non-CMP). We found that the CMP curriculum takes a functional approach to the teaching of algebra while non-CMP curricula take a structural approach. The teachers who used the CMP curriculum emphasized conceptual understanding more than did those who used the non-CMP curricula. On the other hand, the teachers who used non-CMP curricula emphasized procedural knowledge more than did those who used the CMP curriculum. When we examined the development of students’ algebraic thinking related to representing situations, equation solving, and making generalizations, we found that CMP students had a significantly higher growth rate on representing-situations tasks than did non-CMP students, but both CMP and non-CMP students had an almost identical growth in their ability to solve equations. We also found that CMP students demonstrated greater generalization abilities than did non-CMP students over the three middle school years.
The research reported in this chapter is part of a large project, Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal Project). The LieCal Project is supported by a grant from the National Science Foundation (ESI-0454739). Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69.
ABSTRACT: In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed.
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garger, T. (2012). Mathematical problem posing as a measure of the curricular effects on students’ learning. Educational Studies in Mathematics, 83(1), 57-69.
ABSTRACT: In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed.
Cai, J., Moyer, J., Nie, B., & Wang, N. (2009). Learning mathematics from classroom instruction using Standards-based and traditional curricula: An analysis of instructional tasks. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 692-699). Atlanta, GA: Georgia State University.
ABSTRACT: The LieCal Project longitudinally investigates the effects of the Connected Mathematics Program (CMP) and more traditional middle school curricula (non-CMP) on students’ learning of algebra. To ascertain the curricular effects, we must attend to aspects of teaching that influence students’ learning opportunities. In this paper, we particularly focused on the mathematical tasks to understand the instructional experiences provided when using CMP and Non-CMP curricula. We found that teachers in CMP classrooms implemented significantly more cognitively demanding tasks than teachers in Non-CMP classrooms. Also, teachers are much more likely to encourage multiple strategies in CMP classrooms than in Non-CMP classrooms.
Cai, J., Nie, B., & Moyer, J. (2010). The teaching of equation solving: Approaches in Standards-based and traditional curricula in the United States. Pedagogies: An International Journal. 5(3), 170-186.
ABSTRACT: This paper discusses the approaches to teaching linear equation solving that are embedded in a Standards-based mathematics curriculum (CMP) and in a traditional mathematics curriculum (Glencoe Mathematics) in the United States. Overall, the CMP curriculum takes a functional approach to teach equation solving, while Glencoe Mathematics takes a structural approach to teach equation solving. The functional approach emphasizes the important ideas of change and variation in situations and contexts. It also emphasizes the representation of relationships between variables. The structural approach, on the other hand, requires students to work abstractly with symbols, and follow procedures in a systematic way. The CMP curriculum may be regarded as a curriculum with a pedagogy that emphasizes predominantly the conceptual aspects of equation solving, while Glencoe Mathematics may be regarded as a curriculum with a pedagogy that emphasizes predominantly the procedural aspects of equation solving. The two curricula may serve as concrete examples of functional and structural approaches, respectively, to the teaching of algebra in general and equation solving in particular.
Cai, J., Nie, B., Moyer, J. C., & Wang, N. (2014). Teaching mathematics using standards-based and traditional curricula: A case of variable ideas. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 391–415). Dordrecht, Netherlands: Springer Netherlands.
ABSTRACT: This chapter discusses approaches to teaching algebraic concepts like variables that are embedded in a Standards-based mathematics curriculum (CMP) and in a traditional mathematics curriculum (Glencoe Mathematics). Neither the CMP curriculum nor Glencoe Mathematics clearly distinguishes among the various uses of variables. Overall, the CMP curriculum uses a functional approach to teach equation solving, while Glencoe Mathematics uses a structural approach to teach equation solving. The functional approach emphasizes the important ideas of change and variation in situations and contexts. The structural approach, on the other hand, avoids contextual problems in order to concentrate on developing the abilities to generalize, work abstractly with symbols, and follow procedures in a systematic way. This chapter reports part of the findings from the larger LieCal research project. The LieCal Project is designed to investigate longitudinally the impact of a Standards-based curriculum like CMP on teachers’ classroom instruction and student learning. This chapter tells part of the story by showing the value of a detailed curriculum analysis in characterizing curriculum as a pedagogical event.
Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal project in the United States. International Journal of Educational Research, 50(2), 117–136.
ABSTRACT: In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditionalmathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills).
Cai, J., Yujing N., & Hwang, S. (2015). Measuring change in mathematics learning with longitudinal studies: Conceptualization and methodological issues. In J. Middleton, J. Cai, & S. Hwang (Eds.), Large-scale studies in mathematics education (pp. 293–309). Gewerbestrasse, Switzerland: Springer International Publishing.
ABSTRACT : Learning is fundamentally about growth and change. Longitudinal studies of mathematics learning must therefore conceptualize, measure, analyze, and interpret changes in students’ mathematical thinking. This chapter provides a perspective on how researchers can deal with issues entailed in researching such change over time, drawing on the authors’ experiences with two longitudinal projects in the USA and China. Both the LieCal (Longitudinal Investigation of the Effect of Curriculum on Algebra Learning) project and the China project studied the effects of curriculum on student learning. Based on these projects, several challenges are discussed, including the complexity of conceptualizing and measuring change in mathematical thinking, the importance of appropriate analytic techniques, the need to consider long-term change, and critical concerns when interpreting the correlates or causes of observed change.
Cain, J. S. (2002). An evaluation of the Connected Mathematics Project. Journal of Educational Research, 95(4), 224-33.
ABSTRACT: Evaluated the Connected Mathematics Project (CMP), a middle school reform mathematics curriculum used in Louisiana's Lafayette parish. Analysis of Iowa Test of Basic Skills and Louisiana Education Assessment Program mathematics data indicated that CMP schools significantly outperformed non-CMP schools. Surveys of teachers and students showed that both groups believed the program was helping students become better problem solvers.
Castro, A. M. (2006). Planning for mathematics instruction: A study of the teacher guide as a resource. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 67(10). (ProQuest ID No. 1251814391)
ABSTRACT: Planning is an important, and often underappreciated, phase of teaching, during which teachers make decisions and draw upon a variety of resources, such as curriculum materials, that shape students' opportunities to learn. The teacher guide (TG) is a particularly important curricular resource be cause it is designed to assist teachers in making decisions that affect these opportunities. Prior research has established that teachers' use of curriculum materials is affected by a range of factors, such as state level policies, knowledge of mathematics, and the nature and extent of their teaching experience. What is less clear, and far less examined, in prior research is the role that the TG may play in mediating the influence of these and other factors on teachers' decisions and actions during planning and instruction. Accordingly, this study examines how four experienced 6th grade teachers use the TG from Connected Mathematics Project (CMP) as a resource in making planning and enactment decisions, and factors associated with patterns of TG use.
Using interpretive case study methodology, the author examined teachers' use of the CMP TG in planning for and implementing an entire unit. In addition to observing their implementation of the unit, teachers were interviewed prior to and immediately following each observation to understand how they used the TG to plan for and enact different mathematical tasks. The author then developed case studies of teachers' use of the TG in implementing the unit.
Through cross-case analysis, the author found that teachers seemed to draw largely from their personal resources when making planning and enactment decisions related to mathematical tasks, and not particularly from the TG. For example, when faced with certain planning and instructional challenges, such as anticipating how students would work on a task or students struggling with the content, teachers tended to rely on their particular conceptions of mathematics teaching to address these challenges. Despite the fact that the TG provided suggestions for teachers as to how address such challenges, it was not extensively used as a resource by the teachers in this study in their planning and enactment of classroom lessons. Based on these and other findings the author identifies important questions and potential implications for curriculum developers, teacher educators, and researchers.
Charalambos, C. Y., & Hill, H. C. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Unpacking a complex relationship. Journal of Curriculum Studies, 44(4), 443- 466.
ABSTRACT: The set of papers presented in this issue comprise a multiple-case study which attends to instructional resources—teacher knowledge and curriculum materials—to understand how they individually and jointly contribute to instructional quality. We approach this inquiry by comparing lessons taught by teachers with differing mathematical knowledge for teaching who were using either the same or different editions of a US Standards-based curriculum. This introductory paper situates the work reported in the next four case-study papers by outlining the analytic framework guiding the exploration and detailing the methods for addressing the research questions.
Charalambos, C. Y., Hill, H. C., & Mitchell, R. N. (2012). Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality. Journal of Curriculum Studies, 44(4), 489-513.
ABSTRACT: This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations.
Confrey, J. (2006). Comparing and contrasting the National Research Council report on evaluating curricular effectiveness with the What Works Clearinghouse approach. Educational Evaluation and Policy Analysis, 28(3), 195-213.
ABSTRACT: This article summarizes the findings of the National Research Council (NRC) report On Evaluating Curricular Effectiveness and examines the reviews in middle grades mathematics undertaken by the What Works Clearinghouse (WWC). The NRC report reviewed and assessed 147 key evaluations of 13 National Science Foundation–supported K–12 mathematics curricula and six commercially generated curricula. The report found that the evaluations overall were not sufficiently robust to permit confident judgments on individual programs, so it instead focused on how to define effectiveness in conducting future evaluations. Effectiveness was defined as “an integrated judgment based on interpretation of a number of scientifically valid evaluations that combine social values, empirical evidence, and theoretical rationales” (NRC, 2004, p. 4). The report introduced a model for curricular evaluation that includes program theory, implementation, and outcome measures, and reviewed three major methodologies found in the literature: content analysis, comparative analysis, and case study. This article then examines the What Works Clearinghouse’s exclusive emphasis on experimental and quasi-experimental designs from the perspective of an author of the NRC report. The two reports agree in recognizing the need for significant improvement in evaluation quality; however, they differ in four areas: standards for individual studies, need for multiple methods, the way to accumulate information across a set of studies, and how to communicate results with the public. This article concludes with a call for focused efforts to address several shared targets needed to make further progress on how to establish curricular effectiveness.
Covington Clarkson, L. M. (2001). The effects of the Connected Mathematics Project on middle school mathematics achievement. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 61(12). (ProQuest ID No. 727079071)
ABSTRACT: The purpose of this study was to examine the three-year effect of the Connected Mathematics Project (CMP) on the mathematics achievement of middle school students in an urban school district. This was accomplished by (1) comparing the mathematics achievement of eighth graders who have completed three years of CMP with the achievement of eighth graders who have completed three-years of a traditional curriculum; (2) comparing the interaction and communication patterns in the two types of classrooms; and (3) comparing the mathematics achievement of historically underrepresented students in both curricula. In order to provide for a richer analysis of the CMP experience, the overall design employed quantitative and qualitative methodologies. The quantitative section of the study examined the mathematical achievement of 700 of the 1999- 2000 eighth graders as evidenced by their State Basic Standards Test(BST) scores. The qualitative segment of the study explored the experiences of the primary participants, the teacher and the students.
Using the State Basic Standards Test as the dependent variable, there was no significant difference between the mathematics achievement of CMP students and that of traditional students after three years of the respective curricula. The achievement gap between CMP Caucasian students and CMP African American students was smaller than the achievement gap between these groups in the traditional curricula. The classroom interaction and communication patterns were very different. CMP classrooms provided more opportunities to learn mathematics than traditional classes. Moreover, CMP students demonstrated algebraic reasoning skills at the same level as the traditional students and demonstrated conceptual understanding through the use of multiple strategies at a higher level than traditional students. Overall, CMP students had a higher level of satisfaction and more positive experiences in their mathematics classes than did traditional students.
Danielson, C. (2005). Walking a straight line: Introductory discourse on linearity in classrooms and curriculum. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 67(2). (ProQuest ID No. 1095417771)
ABSTRACT: The current curricular reform in US mathematics education has changed many aspects of classroom teaching. Commonly, discussions about this curricular reform presume an unproblematic relationship between textbooks and classroom instruction. This study contributes to the understanding of the relationship between one published reform curriculum, Connected Mathematics (CMP) (Lappan, Fey, Fitzgerald, Friel & Phillips, 2001) and classroom instruction. The study characterizes teaching and learning in terms of communication patterns---discourse ---and analyzes the discourse of CMP, of a traditional US curriculum, Mathematics, Structure and Method (Dolciam, Sorgenfrey & Graham, 1992), and of two teachers in urban classrooms---focusing on the introductory lessons on linear relationships in each case. Results include full descriptions of the introductory discourse on linearity in the textbooks and changes that the CMP textbook discourse undergoes as the curriculum is implemented in these two classrooms.
Durkin, N. M. (2005). Using Connected Math program: Its impact on the Delaware State Testing scores of 8th-grade students at Milford Middle School. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 66(4). (ProQuest ID No. 913516241)
ABSTRACT: This study was designed to investigate the impact of the Connected Math Project curriculum on the student achievement of eighth grade students participating in the Delaware State Testing Program from 1998-2004. The study included an investigation of overall student achievement of students participating in the Connected Math Project as well as specific subgroup populations such as the Black and Special Education students
The investigation revealed that overall student performance and subgroup population performance has increased since the first administration of the Delaware State Testing Program in 1998. A pair wise comparison probability for all test years indicates the increase in mean math scale scores was significant. However, additional pair wise comparison probabilities indicate the percentages of students meeting the state math standard are significant for comparison of test year 2000 with 2003 only. This indicates that although student mean math scale scores are increasing the percentage of students meeting the standard has not increased significantly. Student scores may be approaching the standard but not meeting or exceeding the standard. Pair wise comparison probabilities for the subgroup populations Black and Special Education also indicate a significant increase in the mean math scale scores but not a significant increase in the percentage of students meeting the standard.
Eddy, R. M., Berry, T., Aquirre, N., Wahlstrand, G., Ruitman, T., & Mahajan, N. (2008). The effects of Connected Mathematics Project 2 on student performance: Randomized control trial. Claremont, CA: Claremont Graduate University Institute of Organizational and Program Evaluation Research. Pearson's CMP2 Efficacy Study
Claremont Graduate University (CGU) conducted an efficacy trial of the Connected Mathematics Project 2 (CMP2) curriculum in sixth grade classrooms (across six schools in three states including more than 1,000 students), during the 2007-08 school year. This study was funded by Pearson Education. This report provides an overall description of the study as well as a summary of results based on the major outcome measures. The results are drawn from student performance on the Iowa Test of Basic Skills (ITBS), the Balanced Assessment in Mathematics (BAM), and responses on a student attitudes survey.
Folsom, M. L. (2002). Empowering girls in math: The influence of curriculum on female beliefs about mathematics. (Doctoral dissertation). Retrieved from Masters Abstracts International, 41(2). (ProQuest ID No. 766367131)
ABSTRACT: This qualitative inquiry examines the belief systems of female students in a sixth grade mathematics classroom and explores how a middle school math curriculum influences these beliefs. Specifically, this inquiry focuses on two of four internal beliefs posited by Gilah C. Leder: confidence and usefulness of mathematics. The design of this inquiry is loosely based on the research tradition of ethnography. Data collection consisted of classroom observations, teacher surveys, standardized test scores, and student questionnaires. The inquiry found that the math curriculum had some influence on the girls' overall attitude towards and enjoyment of math classes. Despite confusing explanations with overly complicated language and editing errors, the girls' enjoyed working through the math curriculum's small group activities and experiments. The inquiry found that the Connected Mathematics Project curriculum connected with the sixth grade girls.
Genz, R. (2006). Determining high school students’ geometric understanding using Van Hiele Levels: is there a difference between Standards-based curriculum students and non-Standards-based curriculum students? (Unpublished master’s thesis). Brigham Young University, Provo, UT.
ABSTRACT: Research has found that students are not adequately prepared to understand the concepts of geometry, as they are presented in a high school geometry course (e.g. Burger and Shaughnessy (1986), Usiskin (1982), van Hiele (1986)). Curricula based on the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) have been developed and introduced into the middle grades to improve learning and concept development in mathematics. Research done by Rey, Reys, Lappan and Holliday (2003) showed that Standards-based curricula improve students’ mathematical understanding and performance on standardized math exams. Using van Hiele levels, this study examines 20 ninth-grade students’ levels of geometric understanding at the beginning of their high school geometry course. Ten of the students had been taught mathematics using a Standards-based curriculum, the Connected Mathematics Project (CMP), during grades 6, 7, and 8, and the remaining 10 students had been taught from a traditional curriculum in grades 6, 7, and 8. Students with a Connected Mathematics project background tended to show higher levels of geometric understanding than the students with a more traditional curriculum (NONcmp) background. Three distinctions of students’ geometric understanding were identified among students within a given van Hiele level, one of which was the students’ use of language. The use of precise versus imprecise language in students’ explanations and reasoning is a major distinguishing factor between different levels of geometric understanding among the students in this study. Another distinction among students’ geometric understanding is the ability to clearly verbalize an infinite variety of shapes versus not being able to verbalize an infinite variety of shapes. The third distinction identified among students’ geometric understanding is that of understanding the necessary properties of specific shapes versus understanding only a couple of necessary properties for specific shapes.
Goodman, E. (2004). Connected Mathematics Project: A constructivist view of mathematics education in the middle grades. (Masters thesis). Retrieved from Masters Abstracts International, 43(2). (ProQuest ID No. 813809801)
ABSTRACT: For decades, education critics have been debating what and how mathematics should be taught. The following Master's thesis examines a new mathematics curriculum, Connected Math Project, geared to teach mathematics from a constructivist approach. It examines whether or not the students are able to reflect knowledge or understanding of mathematical concepts as well as their ability to learn from group motivated investigation. It also looks at the view and beliefs of mathematics teachers towards a constructivist program. This thesis is founded on the notion that public school educators must introduce a mathematics curriculum that enables all children to increase their problem solving skills and abilities with regards to mathematics.
Haile, T. K. (2012). A study on the use of history in middle school mathematics: The case of Connected Mathematics Curriculum. (Unpublished doctoral dissertation). The University of Texas at Austin, Austin, TX.
ABSTRACT: This dissertation explores the use of history of mathematics in middle school mathematics. A rationale for the importance of the incorporation of historical dimensions (HD) of mathematics is provided through a review of the literature. The literature covers pedagogical, philosophical, psychological, and social issues and provides arguments for the use of history. The central argument is that history can help reveal significant aspects regarding the origins and evolutions of ideas that provide contexts for understanding the mathematical ideas. History can be used as a means to reflect on significant aspects—errors, contractions, challenges, breakthroughs, and changes—of mathematical developments. Noting recent NCTM (2000) calls for school math to include so-called process standards, I contend that incorporating the history of mathematics can be considered as part of this standard. This study examines how HD is addressed in a contemporary mathematics curriculum. Specifically, the study examines the Connected Mathematics Project (CMP) as a case. This curriculum has some historical references which triggered further exploration on how seriously the historical aspects are incorporated. The analysis and discussion focus on four CMP units and interviews with three curriculum experts, eight teachers, and 11 middle school students. The analysis of textbooks and interviews with the experts explore the nature and purpose of historical references in the curriculum. The interviews with teachers and students focus on their perspectives on the importance of HD in learning mathematics. This study examines specifically historical incorporations of the concepts of fractions, negative numbers, the Pythagorean Theorem, and irrational numbers . The analysis reveals that CMP exhibits some level of historical awareness, but the incorporation of HD was not systematically or seriously considered in the development of the curriculum. The interviews suggest that the teachers did not seriously use the limited historical aspects available in the textbooks. The experts’ and teachers’ interviews suggest skepticism about the relevance of HD for middle school mathematics. The teachers’ accounts indicate that students are most interested in topics that are related to their experience and to future applications. The students’ accounts do not fully support the teachers’ assessment of students’ interest in history. I contend that incorporating HD can complement instruction in ways that relate to students’ experiences and to applications besides adding an inquiry dimension to instruction.
Hansen-Thomas, H. (2009). Reform-oriented mathematics in three 6th Grade classes: How teachers draw in ELLs to academic discourse. Journal of Language, Identity, and Education, 8(2&3), 88-106.
ABSTRACT: Traditionally, mathematics has been considered easy for English language learners (ELLs) due to the belief that math is a "universal language." At the same time, reform-oriented mathematics curricula, designed to promote mathematical discourse, are increasingly being adopted by schools serving large numbers of ELLs. CMP, the Connected Math Project, is one such reform-oriented curriculum. Taking a community-of-practice approach, this article compares how three 6th grade mathematics teachers in a Spanish/English community utilized language to draw ELLs into content and classroom participation. Teacher use of standard language fell into 2 categories: (a) modeling and (b) eliciting student practice. In the teacher's class that regularly elicited language, ELLs were successful on academic assessments; whereas students in the other 2 classes were not. Results suggest that CMP facilitates ELLs' learning and that a focus on mathematical language and elicitation benefits the development of mathematical discourse and content knowledge.
Herbel-Eisenmann, B. A. (2007). From intended curriculum to written curriculum: Examining the "voice" of a mathematics textbook. Journal for Research in Mathematics Education, 38(4), 344-369.
ABSTRACT: 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.
Hill, H. C., & Charalambos, C. Y. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues. Journal of Curriculum Studies, 44(4), 559-576.
ABSTRACT: This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.
Hill, H. C., & Charalambos, C. Y. (2012). Teaching (un)Connected Mathematics: Two teachers’ enactment of the Pizza Problem. Journal of Curriculum Studies, 44(4), 467-487.
ABSTRACT: This paper documents the ways mathematical knowledge for teaching (MKT) and curriculum materials appear to contribute to the enactment of a 7th grade Connected Mathematics Project lesson on comparing ratios. Two teachers with widely differing MKT scores are compared teaching this lesson. The comparison of the teachers' lesson enactments suggests that MKT appears to contribute to the mathematical richness of the lesson, teacher ability to capitalize on student ideas, and capacity to emphasize and link key mathematical ideas; yet the relationship of MKT to whether and how students participated in mathematical reasoning was more equivocal. Curriculum materials seemed to contribute to instructional quality, in that the novel tasks contained in the curriculum laid the groundwork for in-depth student problem-solving experiences; they also prevented the low-MKT teacher from making a mathematical error. At the same time, these ambitious materials influenced enactment because of the difficulties they caused teachers: the lesson's tasks needed to be ‘repaired' to enable students to engage with the main mathematical ideas, and off-track student responses to these tasks required remediation. Only the higher-MKT teacher was successfully able to meet the challenge, a finding suggestive of the confluence of MKT and the curriculum materials in informing instructional quality.
Hirsch, C. R. & Reys, B. J. (2009). Mathematics curriculum: A Vehicle for school improvement. International Journal on Mathematics Education, 41(6), 749-761.
ABSTRACT: Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curriculum materials such as textbooks, instructional units, and computer software constitute the textbook curriculum, which continues to play a dominant role in teachers’ instructional decisions. These decisions influence the actual implemented curriculum in classrooms. Various curriculum policies, including mandated end-of course assessments (the assessed curriculum) and requirements for all students to complete particular courses (e.g., year-long courses in algebra, geometry, and advanced algebra or equivalent integrated mathematics courses) are also being implemented in increasing numbers of states. The wide variation across states in their intended curriculum documents and requirements has led to a historic and precedent-setting effort by the Council of Chief State School Officers and the National Governors Association Council for Best Practices to assist states in the development and adoption of common College and Career Readiness Standards for Mathematics. Also under development by this coalition is a set of common core state mathematics standards for grades K-12. These sets of standards, together with advances in information technologies, may have a significant influence on the textbook curriculum, the implemented curriculum, and the assessed curriculum in US classrooms in the near future.
Institute of Education Sciences (2010). Connected Mathematics Project (CMP). What Works Clearinghouse Intervention Report. What Works Clearinghouse.
ABSTRACT: The "Connected Mathematics Project" ("CMP") is a mathematics curriculum designed for students in grades 6-8. Each grade level of the curriculum is a full-year program and covers numbers, algebra, geometry/measurement, probability, and statistics. The curriculum uses an investigative approach, and students utilize interactive problems and everyday situations to learn math concepts. The What Works Clearinghouse (WWC) reviewed 79 studies of "CMP." No studies of "CMP" meet WWC evidence standards, and one study meets WWC evidence standards with reservations. The one study included more than 12,000 students from grades 6-8 in Texas. Based on this study, the WWC considers the extent of evidence for "CMP" to be small for math achievement. "CMP" was found to have no discernible effects on math achievement. Appended to this report are: (1) Study characteristics: Schneider, 2000 (quasi-experimental design); (2) Outcome measure for the math achievement domain; (3) Summary of study findings included in the rating for the math achievement domain; (4) Summary of cohort findings for the math achievement domain; (5) "CMP" rating for the math achievement domain; and (6) Extent of evidence by domain. (Contains 9 notes.) [The following study is reviewed in this intervention report: Schneider, C. L. (2000). "Connected Mathematics and the Texas Assessment of Academic Skills" (Doctoral dissertation, University of Texas at Austin, 2000). Dissertation Abstracts International, 62(02), 503A. (UMI No. 3004373). For previous WWC intervention reports on the "Connected Mathematics Project," see ED499297 (2007) and ED485389 (2004).
Kar, T., & Isik, C. (2015). Comparison of Turkish and American Seventh Grade Mathematics Textbooks in Terms of Addition and Subtraction Operations with Integers. Egitim ve Bilim, 40(177).
ABSTRACT: This study analyzes how addition and subtraction with integers are presented in Turkish and American mathematics textbooks. Analyses focus on how the concepts are given as well as the nature of the presented mathematical problems. It was found that both the Turkish and the American textbooks emphasized the relationships among different representations in teaching addition and subtraction with integers. It was found that the coordination among visual representation, verbal explanations and mathematical sentences was constructed in a more organized manner in the textbook named Connected Mathematics 2. It was found that operational skill oriented problems were proportionately featured more in the Turkish textbooks whereas the problems requiring high-level cognitive skills such as mathematical reasoning and problem posing were featured more in the American textbooks.
Kersaint, G. (1998). Preservice elementary teachers' ability to generalize functional relationships: The impact of two versions of a mathematics content course. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 59(5). (ProQuest ID No. 1251814391)
ABSTRACT: This study investigated the impact of two versions of a mathematics content course designed for preservice elementary teachers on their growth in algebraic understanding. One section of the course was presented a traditional approach using instructor developed or compiled materials. Another section of the course was presented a function-based approach using algebra materials developed for middle school students by the Connected Mathematics Project (CMP). Specifically, this study examined the influence these materials had on preservice teachers' ability to generalize problem situations, to represent them symbolically, and to use their representation to solve related problems. Achievement gains and obstacles experienced by the students were also analyzed.
Data collection for this study included self-reported background data, instructor and student journals, written pre-and post-assessments, interviews, and observations. Qualitative and quantitative data analysis methods were used to analyze the data. Sfard's (1991) model of conceptual development was used as a lens by which to examine, describe, and interpret the students' conceptual understandings.
Achievement gains on the post-assessment were not statistically significant. Students from both classes performed similarly. Responses from the students in both sections of this course were characterized at the interiorization and condensation phases of Sfard's model. In spite of this, results from the study show differences in the kinds of understandings developed by the students. The section using the CMP materials focused on developing students' conceptual understanding of algebra. While the other section of the course focused on developing students' procedural understanding of algebra. In addition to developing conceptual understandings, students using the CMP algebra units reported that they learned an alternate method for introducing and teaching algebra.
Kim, R. Y. (2012). The quality of non-textual elements in mathematics textbooks: An exploratory comparison between South Korea and the United States. ZDM Mathematics Education, 44(2), 175-187.
ABSTRACT: As an exploratory investigation, this study aims to analyze non-textual elements in some Korean and US mathematics textbooks using a conceptual framework whose components include accuracy, connectivity, contextuality, and conciseness. By analyzing three US textbooks and three Korean ones, the study not only shows patterns in the use of non-textual elements in mathematics textbooks in different contexts but also provides insights into how to assess the quality of non-textual elements in mathematics textbooks, which I hope will contribute to the provision of more meaningful and productive learning opportunities to school children. Overall, the results from this study show that there is significant difference across topics and textbooks, which implies different opportunities to learn through non-textual elements. This study makes a unique contribution to the conceptualization of non-textual elements in mathematics education and has implications for textbook analysis and curriculum development.
King, K. D., Mitchell, M. B., Tybursky, J., Simic, O., Tobias, R., Barriteau Phaire, C., & Torres, M. (2011). Impact of teachers’ use of Standards-based instructional materials on students’ achievement in an urban district: A multilevel analysis. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.
ABSTRACT: This effectiveness study explores the relationship between the use and adaptation of the Connected Mathematics Project instructional materials by middle grades teachers in an urban school district and their students’ achievement. All middle grades mathematics teachers in Newark, NJ Public Schools were surveyed using the Surveys of Enacted Curriculum and the CMP Implementation Survey. The 6th, 7th, and 8th grade students in these teachers’ first period classes completed the New Jersey Assessment of Knowledge and Skills for their grade. Using hierarchical linear modeling with two levels, we found that both increased use and adaptation of the instructional materials were related to increased student achievement. Implications for further research on instructional materials implementation and the design and implementation of materials are discussed.
Lloyd, G. M. (2008). Curriculum use while learning to teach: One student teacher's appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 39(1), 63-94.
ABSTRACT: 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.
Lloyd, G. M., & Behm, S. L. (2005). Preservice elementary teachers' analysis of mathematics instructional materials. Action in Teacher Education, 26(4), 48-62.
ABSTRACT: This article explores the practice of engaging prospective elementary teachers in the analysis of lessons from different textbooks. A rationale for such engagement, based on particular teacher education goals, is provided. The article focuses on a specific lesson analysis assignment given to prospective elementary teachers in which portions of mathematics textbooks were compared and contrasted. Examination of 23 preservice teachers' analysis of two textbook lessons (one fairly traditional and one more reform oriented) revealed that, with very few exceptions, the preservice teachers searched the textbook lessons for familiar, mainly traditional instructional components. The teachers' preference for traditional lesson components appeared to contribute to a tendency to make considerable misinterpretations of the two textbook lessons. These tendencies, including ways that the teachers attempted to justify differences between the two lessons, offer important insights into prospective elementary teachers' conceptions of the role of textbooks in the teaching and learning process. In addition, these findings suggest the necessity of involving prospective teachers more extensively in the analysis of textbooks, curriculum materials, and other instruction resources so that richer, more useful conceptions may develop.
Lo, J-J., Cox, D., & Mingus, T. (2006). A conceptual-based curricular analysis of the concept of similarity. In Alatorre, S., Cortina, J.L., Sáiz, M., and Méndez, A. (Eds), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, México: Universidad Pedagógica Nacional.
ABSTRACT: As they engage with activities in mathematics textbooks, students have a variety of opportunities to make sense of the concept of similarity. The nature and sequence of these activities have an impact on the development of concept images that support students as they make sense of the terms “similar figures” or “scale drawings” and the properties they hold. In this analysis of the treatment of similarity in three middle grade textbook series, the authors share their analysis of the concept definitions and concept images supported by these texts. The term “curriculum” has different meanings in different contexts. According to the Center for the Study of Mathematics Curriculum, the most familiar terms include the ideal curriculum, the intended curriculum, the enacted curriculum, the achieved curriculum and the assessed curriculum. The focus of the present study was on the intended curriculum, which typically includes teacher’s manuals, student books, and additional resources such as technology, assessment, etc.
Lowe, P. (2004). A new approach to math in the middle grades. Principal, 84(2), 34-39.
ABSTRACT: Part of a special section on mathematics teaching and learning. Suggestions for implementing reform programs such as Connected Mathematics Project in the middle grades are provided. The advantages and disadvantages of such research-based reform programs are also discussed.
Lubienski, S. T. (1997). Class matters: A preliminary exploration. In J. Trentacosta, & M. J. Kenney (Eds.), Multicultural and gender equity in the mathematics classroom, the gift of diversity, 59th Yearbook (pp. 46-59). Reston, VA: National Council of Teachers of Mathematics.
ABSTRACT: As a researcher-teacher, I examined 7th-graders' experiences with problem-centered curriculum and pedagogy, focusing on SES differences in students' reactions to learning mathematics through problem solving. Although higher SES students tended to display confidence and solve problems with an eye toward the intended mathematical ideas, the lower SES students preferred more external direction and sometimes approached problems in a way that caused them to miss their intended mathematical points. An examination of sociological literature revealed ways in which these patterns in the data could be related to more than individual differences in temperament or achievement among the children. I suggest that class cultural differences could relate to students' approaches to learning mathematics through solving open, contextualized problems.
Lubienski, S. T. (2000a). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454-482.
ABSTRACT: As a researcher-teacher, I examined 7th-graders' experiences with a problem-centered curriculum and pedagogy, focusing on SES differences in students' reactions to learning mathematics through problem solving. Although higher SES students tended to display confidence and solve problems with an eye toward the intended mathematical ideas, the lower SES students preferred more external direction and sometimes approached problems in a way that caused them to miss their intended mathematical points. An examination of sociological literature revealed ways in which these patterns in the data could be related to more than individual differences in temperament or achievement among the children. I suggest that class cultural differences could relate to students' approaches to learning mathematics through solving open, contextualized problems.
Lubienski, S. T. (2000b). A clash of social class cultures? Students’ experiences in a discussionintensive seventh-grade mathematics classroom. The Elementary School Journal, 100(4), 377–403.
ABSTRACT: Examined how a curriculum development project, aligned with current mathematics education reforms, affected 18 students in socially diverse mathematics classroom. Found that students of lower socioeconomic status preferred direct teacher intervention as opposed to open discussions among classmates. Higher socioeconomic status students displayed more comfort with abstract mathematical concepts. Findings suggest that discussion-intensive classrooms align more with middle-class cultures.
Mac Iver, M. A., & Mac Iver, D. J. (2009). Urban middle-grade student mathematics achievement growth under comprehensive school reform. Journal of Educational Research, 102(3), 223–236.
ABSTRACT: Recognizing the need to implement standards based instructional materials with school wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and the number of years schools implemented either a WSR model with National Science Foundation-supported mathematics curriculum or a WSR model without a mathematics curriculum component, from 1997 to 2000. As the authors hypothesized, mathematics achievement gains (Grades 5–8) were positively related to the number of years those schools were implementing a specific mathematics curricular reform. Additional analyses indicated that the relation held for both computation skills and ability to apply mathematics concepts.
Maccini, P., & Gagnon, J. (2002). Perceptions and application of NCTM standards by special and general education teachers. Exceptional Children, 68(3), 325-344.
ABSTRACT: This study determined teachers' perceptions related to application of and barriers to implementation of the National Council of Teachers of Mathematics (NCTM) Standards with students labeled learning disabled (LD) and emotionally disturbed (ED). A stratified random sample of 129 secondary general education math and special education teachers responded to a mail survey. A majority of special education teachers indicated they had not beard of the NCTM Standards. Respondents reported teaching mostly basic skills/general math to secondary students with LD and ED, versus higher-level math, such as algebra and geometry. Teachers identified lack of adequate materials as a considerable barrier to successful implementation of activities based on the Standards. Implications for practice and future research are also provided.
Males, L. (2011). Educative supports for teachers in middle school mathematics curriculum materials: What is offered and how is it expressed? (Unpublished doctoral dissertation). Michigan State University, East Lansing, MI.
ABSTRACT: Teaching can have a substantial impact on student learning (Darling-Hammond, 1999). However, teaching excellence depends on many factors, including the need for high quality teachers and their continued education, and high quality materials (Cohen, Raudenbush, & Ball, 2002; Putnam & Borko, 2000). This learning includes learning to plan and enact lessons that are appropriate for all students, which requires learning to interpret and understand student thinking and learning instructional routines and practices that will enable them to use student thinking productively. As we enter into the era of the Common Core State Standards for Mathematics this learning is even more critical, as the standards may require teachers to not only learn to understand and unpack the standards themselves, but may also require teachers to learn new content and learn to teach in different ways (Lappan, McCallum, Kepner, 2010).
Due to the complex nature of teaching and the myriad of demands placed on teachers, mathematics educators need to consider all possible venues for teacher learning. In this paper, I discuss my examination of the opportunities for teacher learning embedded within written curriculum materials. Research indicates that teachers can and do learn from curriculum materials. Curriculum materials, particularly educative ones, emerge as a potential source for opportunities for teacher learning in ways that set them apart from more traditional professional development, which is often criticized for being decontextualized, contrived, short-term, fragmented, discontinuous, and disconnected (Ball & Cohen, 1999; Little, 1994; Lord, 1994; Wilson & Berne, 1999). Educative curriculum materials are materials for Grades K-12 that are ?intended to promote teacher learning in addition to students‘ ? (Davis & Krajcik, 2005, p. 3).
I investigated the opportunities to learn embedded in four middle school curricular series in the areas on introduction to variables and geometric transformations, by examining the content and its expression in the teachers' guides. I developed and used two analytical frameworks; one to code the content support derived from work in science education (Beyer et al., 2009) and a second framework to describe the expression of text developed by Morgan (1996) and augmented by Herbel-Eisenmann (2007).
My results indicated that all four curricular series included opportunities for teacher learning (mostly related to Pedagogical Content Support for Practices and Curricular Knowledge, depending on the curriculum) in both the variable and the transformations units, but these opportunities were quite minimal and focused heavily on particular types of supports. This lack of support was particularly true for Rationale Guidance for teachers. In addition to the content support, my analysis of aspects of voice indicated that although these four series provided opportunities for teacher learning, they also may hinder teachers' learning by speaking "through" teachers rather than "to" teachers (Remillard, 2000), as evidenced by the ways in which personal pronouns were used and the frequencies of imperatives and modal verbs. I discuss implications for curriculum development, teacher education, and research.
Martin, T., Brasiel, S. J., & Turner, H. (2012). Effects of the Connected Mathematics Project 2 (CMP2) on the Mathematics Achievement of Grade 6 Students in the Mid-Atlantic Region. Final Report. (NCEE 2012-4017). National Center for Education Evaluation and Regional Assistance. U.S. Department of Education.
ABSTRACT: This study examines the effects of Connected Mathematics Project 2 (CMP2) on grade 6 student mathematics achievement and engagement using a cluster randomized controlled trial (RCT) design. It responds to a need to improve mathematics learning in the Mid-Atlantic Region (Delaware, Maryland, New Jersey, Pennsylvania, and Washington, DC). Findings reveal that the type of instructional activity taking place in intervention schools differed from that in control schools, and the activity observed in intervention schools was the type expected when implementing CMP2. Sixty-four percent of intervention teachers reported implementing the curriculum at a level consistent with the publishers' recommendations on the number of units completed per school year (six), and 68 percent of them reported implementing the curriculum consistent with the recommended amount of class time per week. But CMP2 did not have a statistically significant effect on grade 6 mathematics achievement as measured by the TerraNova, which answered the primary research question.12 Indeed, grade 6 mathematics students in schools using CMP2 performed no better or worse on a standardized mathematics test than did their peers in schools not using it. The results for the secondary research question were similar. There was no statistically significant difference between groups in PTV, and the small effect size is unlikely meaningful. These results were insensitive to alternative model specifications. The lack of statistically significant effects is consistent with prior research on CMP2 rated in the 2010 WWC review as meeting standards "with reservations" (Schneider 2000) and the Eddy et al. (2008) RCT. The intent-to-treat analytical approach used in this study, which analyzes participants based on how they are randomly assigned, yielded unbiased estimates of program effectiveness as implemented. To estimate the effect of CMP2 under typical conditions, teachers were provided all the typical materials and PD that a normal school adopting CMP2 would have. However, while CMP2 use was tracked, the study team did not ensure a particular amount or quality of CMP2 instruction. So, the curriculum impact reflects the effect of a school being assigned to use CMP2 or to continue use of their regular curriculum, not necessarily of actually using CMP2. The results apply to the implementation of the CMP2 curriculum, after typical PD, in schools with grade 6 students. Use of a volunteer sample limits the findings to the schools, teachers, and students that participated in the study in the Mid-Atlantic region. The conclusions drawn in this study about the effects of CMP2 on student math achievement are limited to student math achievement as measured by the TerraNova, and do not generalize to any other standardized test.
Mathis, E. (2004). A comparison of two NSF funded middle school mathematics curricula in Delaware's Appoquinimink and Caesar Rodney school districts. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(1). (ProQuest ID No. 765270181)
ABSTRACT: This evaluation compares two NSF funded middle school curricula, Math in Context and the Connected Math Project as measured by student achievement on the mathematics portion of the Delaware State Testing Program. The two groups consisted of 7th grade students from the Caesar Rodney and Appoquinimink School Districts who were not classified as receiving special education services nor services for learning English as a second language. The students took the 5th grade math portion of the DSTP in the Spring of 2000 and the 7th grade math portion of the DSTP in the Spring of 2002. The evaluation involved 295 students from the Appoquinimink School District and 291 students from the Caesar Rodney School District.
The findings of the study indicate that the use of different curricula in the Caesar and Appoquinimink School Districts, CMP and MIC, respectively, did not equivocate to a significant difference in math achievement as measured by the math portion of the DSTP. Descriptive data did show that CMP students outperformed MIC students in terms of increasing their scale scores, but again this difference was not significant. It is important to note that the factors of gender and ethnicity did not contribute to any statistically significant differences between the groups.
Meiler, J. (2006). Does a problem-centered curriculum foster positive or negative changes in students' attitude and learning in mathematics? A case study of three sixth grade students. (Masters thesis). Retrieved from Masters Abstracts International, 45(3). (ProQuest ID No. 1251814661)
ABSTRACT: This case study walks you through the educational lives of three students in sixth grade as they journey through learning by "doing" in a newly implemented, problem-centered math curriculum, Connected Math Project. The purpose of this study was to investigate how the learning strategies provided by Connected Math Project impacts students' attitudes and learning in mathematics. The overall confidence in personal mathematical ability, in how good they perceived themselves to be, in math, demonstrated an increase in positive responses over the last year for the case study students. Because of the increase in positive responses over the last year, the achievement level for the students also increased. These gains were impacted by the highly motivating problem-centered curriculum, Connected Math Project.
Monaghan, S. R. (2013). Textbooks, teachers, and middle school mathematics student achievement (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 1469609858)
ABSTRACT: The purpose of this study was to extend the research on textbook effectiveness to a situated investigation of a single large urban school district in which middle schools were given a choice in selecting from three textbooks for mathematics instruction: a reform textbook, a commercially produced textbook developed in response to mathematics standards, and a traditional textbook. Its genesis is rooted in the efforts in the mathematics education community to investigate the interaction of teachers and mathematics curriculum materials, but in light of the shift to an accountability policy climate in public education. In particular, this study sought to determine whether the type of textbook selected by a school, moderated by the human capital of the teachers teaching mathematics, and the interaction of those variables was associated with increased student mathematics achievement on the mathematics portion of the eighth grade statewide standardized test. Hierarchical linear modeling (HLM) was used to investigate models relating to textbook selection, components of teacher human capital, and their interaction. Contrary to the initial hypothesis, the interaction of textbook selection and components of human capital were not found to be significantly associated with student achievement. However, the selection of a reform mathematics textbook (CMP) over other more traditional texts was associated with student achievement, but accounted for very little of the variance in student test scores. To further explicate the interaction of textbook selection with school factors, logistic regression was used to investigate the association between school factors and the selection of a reform textbook. The demographics of the school (i.e. race, SES, ELL) were not associated with the school selecting a reform mathematics textbook. However, one component of teacher human capital, expertise (a component constructed from data about teacher certification, mathematics specialization, and participation in math focused professional development) was associated with the selection of a reform textbook. This study suggests there is a connection between teacher human capital, the use of reform texts and student achievement; however further investigation is needed to understand the mechanisms at work.
Moyer, J. C., Cai, J., Wang, N., & Nie, B. (2011). Impact of curriculum reform: Evidence of change in classroom practice in the United States. International Journal of Educational Research, 50(2), 87–99. doi:10.1016/j.ijer.2011.06.004
ABSTRACT: The purpose of the study reported in this article is to examine the impact of curriculum on instruction. Over a three-year period, we observed 579 algebra-related lessons in grades 6–8. Approximately half the lessons were taught in schools that had adopted a Standards- based mathematics curriculum called the Connected Mathematics Program (CMP), and the remainder of the lessons were taught in schools that used more traditional curricula (non- CMP). We found many significant differences between the CMP and non-CMP lessons. The CMP lessons, emphasized the conceptual aspects of instruction to a greater extent than the non-CMP lessons and the non-CMP lessons emphasized the procedural aspects of instruction to a greater extent than the CMP lessons. About twice as many CMP lessons as non-CMP lessons were structured to use group work as a method of instruction. During lessons, non-CMP students worked individually on homework about three times as often as CMP students. When it came to text usage, CMP teachers were more likely than non- CMP teachers to work problems from the text and to follow lessons as laid out in the text. However, non-CMP students and teachers were more likely than CMP students and teachers to review examples or find formulas in the text. Surprisingly, only small proportions of the CMP lessons utilized calculators (16%) or manipulatives (11%).
Moyer, J., Cai, J., Laughlin, C., & Wang, N. (2009). The effect of curriculum type on middle grades instruction. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 201-209). Atlanta, GA: Georgia State University.
ABSTRACT: In this article, we discuss differences between the mathematics instruction of CMP and non-CMP teachers in the LieCal project. There are three aspects of instruction that 200 6th grade urban classroom observations showed were strongly and differently related to the type of curriculum that teachers were using. These three aspects relate to the teachers' use of (1) group and individual work, (2) written narratives and worked-out examples, and (3) conceptually- and procedurally-focused instruction.
Newton, J. A. (2008). Discourse analysis as a tool to investigate the relationship between the written and enacted curricula: the case of fraction multiplication in a middle school standards-based curriculum. (Unpublished doctoral dissertation). Michigan State University, East Lansing, MI.
ABSTRACT: In the 1990s, the National Science Foundation (NSF) funded the development of curricula based on the approach to mathematics proposed in Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989). Controversy over the effectiveness of these curricula and the soundness of the standards on which they were based, often labeled the “math wars,” prompted a plethora of evaluative and comparative curricular studies. Critics of these studies called for mathematics education researchers to document the implementation of these curricula (e.g., National Research Council, 2004; Senk & Thompson, 2003) because “one cannot say that a curriculum is or is not associated with a learning outcome unless one can be reasonably certain that it was implemented as intended by the curriculum developers” (Stein, Remillard, & Smith, 2007, p. 337). Curriculum researchers have used a variety of methods for documenting curricular implementation, including table-of-content implementation records, teacher and student textbook use diaries, teacher and student interviews, and classroom observations. These methods record teacher and student beliefs, extent of content coverage, in-class and out-of-class textbook use, and classroom participation structures, but do little to compare the mathematics presented in the written curriculum (the student and teacher textbooks) and the way in which this mathematics plays out in the enacted curriculum (that which happens in classrooms).
In order to compare the mathematical features in the written and enacted curricula, I utilized Sfard’s Commognition framework (most recently and fully described in Thinking as Communicating: Human Development, the Growth of discourses, and Mathematizing published in 2008). That is, I compared the mathematical words, visual mediators, endorsed narratives, and mathematical routines in the written and enacted curricula. Each of these mathematical features provided a different perspective on the mathematics present in the curricula. The written curriculum in this study was represented by Investigation 3(Multiplying with Fractions) included in Bits and Pieces II: Using Fraction Operations in Connected Mathematics 2 (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2006). Videotapes of this same Investigation recorded in a sixth grade classroom in a small, rural town in the Midwest were used as the enacted curricula for this case.
The study revealed many similarities and differences between the written and enacted curricula; however, most prominent were the findings regarding objectification in the curricula. Sfard defines objectification as “a process in which a noun begins to be used as if it signifies an extradiscursive, self-sustained entity (object), independent of human agency” (Sfard, 2008, p. 412). She proposes that objectifying is an important process for students’ discursive development and that it serves them particularly well in the study of advanced mathematics. Both objectification itself and the opportunities present for objectification were more prevalent in the written curriculum than in the enacted curriculum.
Newton, J. A. (2012). Investigating the mathematical equivalence of written and enacted middle school Standards-based curricula: Focus on rational numbers. International Journal of Educational Research, 51-52, 66-85.
ABSTRACT: Although the question of whether written curricula are implemented according to the intentions of curriculum developers has already spurred much research, current methods for documenting curricular implementation seem to be missing a critical piece: the mathematics. To add a mathematical perspective to the discussion of the admittedly controversial and conceptually complex issue of “fidelity of curricular implementation,” this study proposes a method for investigating fidelity that deals with the question of mathematical equivalence of written curricula and their enactments in the classroom. The method rests on the assumption that the curricula, both written and enacted, can be treated as discourses, and that one of the ways to judge their mathematical equivalence is to compare the mathematical objects around which these discourses evolve. As an illustration for how the method works, I analyzed a part of the written Connected Mathematics Project (CMP) curriculum and its enactment in a sixth grade classroom learning about fractions. This analysis showed that the written and enacted versions of the central mathematical objects of the two curricula, rational numbers, differed in almost every aspect: in their ontology, in the relative prominence of their realizations (i.e., symbols, icons and concrete objects) and in the importance attributed to their different properties. These differences may have an impact on the nature of students’ mathematical competence.
Newton, J., Geller, R., Umbeck, L., & Kasmer, L. (2012). Reflections on teaching with a standards-based curriculum: A conversation among mathematics educators. Montana Mathematics Enthusiast, 9(1), 179–192.
Nie, B., Cai, J., & Moyer, J. (2009). How a Standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 41(6), 777-792.
ABSTRACT: Analyzing the important features of different curricula is critical to understand their effects on students’ learning of algebra. Since the concept of variable is fundamental in algebra, this article compares the intended treatments of variable in an NSF-funded standards-based middle school curriculum (CMP) and a more traditionally based curriculum (Glencoe Mathematics). We found that CMP introduces variables as quantities that change or vary, and then it uses them to represent relationships. Glencoe Mathematics, on the other hand, treats variables predominantly as placeholders or unknowns, and then it uses them primarily to represent unknowns in equations. We found strong connections among variables, equation solving, and linear functions in CMP. Glencoe Mathematics, in contrast, emphasizes less on the connections between variables and functions or between algebraic equations and functions, but it does have a strong emphasis on the relation between variables and equation solving.
Nie, B., Freedman, T., Hwang, S., Wang, N., Moyer, J. C., Cai, J. (2013). An investigation of teachers’ intentions and reflections about using Standards-based and traditional textbooks in the classroom. ZDM, 45(5), 699-711.
ABSTRACT: This study analyzed teachers’ intentions for and reflections on their use of Standards-based [Connected Mathematics Program (CMP)] textbooks and traditional (non-CMP) mathematics textbooks to guide instruction. In this investigation of the interplay between textbooks and instruction, we focused on learning goals, instructional tasks, teachers’ anticipation of students’ difficulties, and their perceptions of students’ achievement of learning goals. All of these are aspects of teachers’ intentions and reflections that have proved fruitful in comparing the roles of the CMP and non-CMP mathematics textbooks in our Longitudinal Investigation of the Effect of Curriculum on Algebra Learning project. Whereas the cognitive level of the teachers’ intended learning goals appeared generally to reflect the emphases of their respective textbooks, we found that the CMP teachers’ intended learning goals were not as well aligned with the CMP textbooks as the non-CMP teachers’ learning goals were aligned with their non-CMP textbooks. The CMP and non-CMP teachers’ implementations of the lessons seemed to reduce the degree of difference between the cognitive levels of their intended goals. Even so, we found that significantly more CMP lessons than non-CMP lessons were implemented at a high level of cognitive demand. Although the non-CMP teachers’ intended learning goals were better aligned with their textbook’s learning goals, we found that the CMP teachers were more likely than the non-CMP teachers to follow the guidance of their textbooks in designing and selecting instructional tasks for a lesson. Future research should consider other aspects of teachers’ intentions and reflections that may shed a broader light on the role of textbooks and curriculum materials in teachers’ crafting of instructional experiences for their students.
O'Clair, K. K. (2005). Impact on student achievement: Going to scale with a middle school math initiative. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 66(5). (ProQuest Id No. 921030071)
ABSTRACT: To measure the impact of a middle school math initiative on student achievement, a survey research design was used to categorize the levels of implementation by 7th -grade math teachers. The survey targeted the teachers' participation in 4 key components of the middle school math initiative, based on an expanded model of the theory of action of standards-based reform by Elmore & Rothman (1999): district-led professional development, school walkthroughs, site-based team planning, and use of standards-based Connected Mathematics program. In a western urban school district, 18 of the 21 contacted teachers from 2002-2003 completed and returned their selfadministered surveys; 26 of 33 from 2003-2004. The Year 1 teacher sample represented 29% of the total teacher population and their 1,259 students were 24% of the total student population. The Year 2 teacher sample represented 39% of the teachers and their 1,765 students were 33% of the total student population. The scale scores of these students from 18 schools were the dependent variable for analyses of variance. The independent variables were the year and the level of implementation that was determined by weighting the results from the teacher survey against a rubric of implementation created by the researcher.
The major findings showed statistically significant differences by years and by levels of implementation. The 7th -grade student math scale scores of the statewide standards-based assessment positively improved and the strength of the effect was small. Using a 2-way ANOVA to compare the 4 groups of high and low implementation in both years, there was a statistically significant difference between the students' scores who experienced higher versus lower levels of implementation in their 7th grade math classes. The students of the higher implementation group of teachers, who had less teaching experience but attended more professional development and had more team planning, had higher math scale scores.
The research results conclude that there was a statistically significant small improvement, Recommendations for further research suggest investigation of the quality of instructional delivery, not only the quantity of CMP units. More involvement with instructional leaders on-site could support scheduling efforts for grade-level planning and more walkthroughs.
Patel, N., Franco, S., Miura, Y., & Boyd, B. (2012). Including curriculum focus in mathematics professional development for middle-school mathematics teachers. School Science and Mathematics, 112(5), 300-309.
ABSTRACT: This paper examines professional development workshops focused on Connected Math, a particular curriculum utilized or being considered by the middle-school mathematics teachers involved in the study. The hope was that as teachers better understood the curriculum used in their classrooms, i.e., Connected Math, they would simultaneously deepen their own understanding of the corresponding mathematics content. By focusing on the curriculum materials and the student thought process, teachers would be better able to recognize and examine common student misunderstandings of mathematical content and develop pedagogically sound practices, thus improving their own pedagogical content knowledge. Pre- and post-mathematics content knowledge assessments indicated that engaging middle-school teachers in the curriculum materials using pedagogy that can be used with their middle-school students not only solidified teachers’ familiarity with such strategies, but also contributed to their understanding of the mathematics content.
Post, T. R., Harwell, M. R., Davis, J. D., Maeda, Y., Cutler, A., Andersen, E., Norman, K. W. (2008). Standards-based mathematics curricula and middle-grades students' performance on standardized achievement tests. Journal for Research in Mathematics Education, 39(2), 184- 212.
ABSTRACT: Approximately 1400 middle-grades students who had used either the Connected Mathematics Project (CMP) or the MATH Thematics (STEM or MT) program for at least 3 years were assessed on two widely used tests, the Stanford Achievement Test, Ninth Edition (Stanford 9) and the New Standards Reference Exam in Mathematics (NSRE). Hierarchical Linear Modeling (HLM) was used to analyze subtest results following methods described by Raudenbush and Bryk (2002). When Standards-based students' achievement patterns are analyzed, traditional topics were learned. Students' achievement levels on the Open Ended and Problem Solving subtests were greater than those on the Procedures subtest. This finding is consistent with results documented in many of the studies reported in Senk and Thompson (2003), and other sources.
Purnamasari, W. (2013). Application of the model Connected Mathematics Project (CMP) in an effort to improve students’ adaptive reasoning abilities: A quasi-experimental study in grade 45 Public VIII SMP Duo. (Unpublished doctoral dissertation). Indonesia University of Education, Bandung, Indonesia.
ABSTRACT: This study was motivated by the relatively low student achievement in adaptive reasoning ability. One of ways to help students develop adaptive reasoning ability is applying the model of Connected Mathematics Project (CMP). The aim of this study was to determine the adaptive reasoning ability improvement among students who had learning mathematic with CMP model compared with conventional model, determine the increase of adaptive reasoning ability of students in the high group and low group who get the learning of mathematic by CMP model compared with students in the high group and low group with conventional model and determine students' attitudes to learning mathematic with CMP model. The method used in this study was quasi-experimental. The population in this study is the eighth grade students of SMP Negeri 45 Bandung with two samples of the entire eighth grade class available. The instruments used were the adaptive reasoning ability test instruments, questionnaires, observation sheets and daily journals of students. The results of this study showed that the improvement of adaptive reasoning ability of students with CMP model better than students who had learning mathematic with conventional model. Furthermore, students in the high group and low group who get the learning of mathematic by CMP model have the adaptive reasoning ability better than students in the high group and low group with conventional model. In addition, students responded positively to the learning of mathematic with CMP model. Key Words: Adaptive reasoning ability, Connected Mathematics Project (CMP).
Quigley, D. (2010). Project-based learning and student achievement (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 741546820)
ABSTRACT: More evidence is needed to support the soundness of project-based learning in addressing student achievement as measured by assessments used by one northeastern U.S. state, especially since the state is creating project-focused schools. Project-based learning encompasses various strategies designed to enhance engagement and performance. This quasi-experimental, nonequivalent control-group study investigated the effectiveness of project-based instruction and of mixed strategy instruction related to changes in student achievement. Brain-based research, curriculum integration literature, and motivation theory informed this work. Forty-four 6th grade students comprised the sample. The student group was a stratified, single stage sampled, leveled mix with consideration given to age, gender, and ability level. Half of the participants were in a project-based learning environment and the other half were in an environment with a mix of collaborative and investigative strategies. Students explored concepts in the 6th grade Curriculum Frameworks in mathematics and used the aligned Connected Mathematics program. Hypotheses were tested using independent samples t test. No statistically significant difference in the students’ math performance was found. The potential for positive social change is related to a higher level of awareness of integration strategies, and more informed practice, both of which can lead to more opportunities for raising student achievement.
Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2004). Assessing the impact of Standards-based middle grades mathematics curriculum materials on student achievement: Corrections. Journal for Research in Mathematics Education, 35(2), 152.
Riordan, J., & Noyce, P. (2001). The impact of two standards-based mathematics curricula on student achievement in Massachusetts. Journal for Research in Mathematics, 32(4), 368-398.
ABSTRACT: Since the passage of the Education Reform Act in 1993, Massachusetts, has developed curriculum frameworks and a new statewide testing system. As school districts align curriculum and teaching practices with the frameworks, standards-based mathematics programs are beginning to replace more traditional curricula. This paper presents a quasi-experimental study using matched comparison groups to investigate the impact of one elementary and one middle school standards-based mathematics program in Massachusetts on student achievement. The study compares statewide standardized test scores of fourth-grade students using Everyday Mathematics and eighth-grade students using Connected Mathematics to test scores of demographically similar students using a mix of traditional curricula. Results indicate that students in schools using either of these standards-based programs as their primary mathematics curriculum performed significantly better on the 1999 statewide mathematics test than did students in traditional programs attending matched comparison schools. With minor exceptions, differences in favor of the standards-based program, remained consistent across mathematical strands, question types, and student subpopulations.
Schneider, C. (2000). Connected Mathematics and the Texas Assessment of Academic Skills. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 62(2). (ProQuest Id No. 727941391)
ABSTRACT: This study determined if the use of Connected Mathematics (CMP), a middle school curriculum based on the reform standards called for by the National Council of Teachers of Mathematics in 1989, impacted student performance measured by the state mandated Texas Assessment of Academic Skills (TAAS) test. Did Texas campuses involved in the CMP pilot from 1997 to 1999 have different TAAS results compared to similar Texas campuses that did not use CMP?
In this study campuses were not randomly selected to use the curriculum. CMP and non-CMP campuses were matched using a regression analysis of the significant variables predicting 1996 pre-CMP TAAS rates. Campus level TARS passing rates and student Texas Learning Index (TLI) scores were analyzed using mixed model methodology. There were 48 campuses represented in the campus level analysis and 19,501 students from 32 of these campuses in the student level analysis. Based upon an implementation survey, a high use subset of campuses was identified from teachers' reporting that at least one-third of the total possible curriculum at every grade and year during the pilot was taught. The data were partitioned into cohorts; Cohort 1 represented observations from sixth, seventh, and eighth grades, from 1996-97 to 1998-99. Cohort 2 included data from sixth and seventh grades, 1997-98 to 1998-99. Cohort 3 had data for sixth grade, 1998-99.
For the analyses on TAAS percent passing and student TLI for all campuses and cohorts combined there is no difference between CMP and non-CMP campuses. When disaggregating the analyses by cohort, there is no difference between CMP and non-CMP campuses for either type of data for any individual cohort using all campuses. For the high use subset of campuses with all cohorts combined there is no difference between CMP and non-CMP campuses for either TAAS passing rates or student TLI scores. For the high use subset of campuses and students disaggregated by cohort, differences may be found, but they are not consistent. Research in this study indicates that the use of the CMP curriculum does not make a difference on TAAS passing rates or student level TLI scores.
Slavin, R., Lake, C., & Groff, C. (2007). Effective programs in middle and high school mathematics: A best-evidence synthesis. Review of Educational Research, 79(2), 839-911.
ABSTRACT: This article reviews research on the achievement outcomes of mathematics programs for middle and high schools. Study inclusion requirements include use of a randomized or matched control group, a study duration of at least 12 weeks, and equality at pretest. There were 100 qualifying studies, 26 of which used random assignment to treatments. Effect sizes were very small for mathematics curricula and for computer-assisted instruction. Positive effects were found for two cooperative learning programs. Outcomes were similar for disadvantaged and nondisadvantaged students and for students of different ethnicities. Consistent with an earlier review of elementary programs, this article concludes that programs that affect daily teaching practices and student interactions have more promise than those emphasizing textbooks or technology alone.
Sleep, L., & Eskelson, S. L. (2012). MKT and curriculum materials are only part of the story: Insights from a lesson on fractions. Journal of Curriculum Studies, 44(4), 537-558.
ABSTRACT: This paper investigates the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the mathematical quality of instruction by comparing the enactment of a fractions problem taught by two teachers with differing MKT. It was found that MKT seem to support teachers’ precise use of mathematical language and to prevent errors; the curriculum materials provided a rich representational context for mathematical work. However, teachers’ orientations toward mathematics and mathematics teaching and their goals for student learning also seemed to contribute to their use of curriculum materials to engage students with rich mathematics and to support students’ participation in the development of the mathematics. Although orientations and goals made it more likely for a teacher to use multiple representations and elicit multiple solution methods, MKT was needed to productively use these elements in instruction. Based on this analysis, it is argued that there are aspects of developing orientations and goals that are related to MKT.
Smith III, J. P., & Star, J. R. (2007). Expanding the notion of impact of K-12 Standards-based mathematics and reform calculus programs. Journal for Research in Mathematics Education, 38(1), 3-34
ABSTRACT: Research on the impact of Standards-based, K-12 mathematics programs (i.e., written curricula and associated teaching practices) and of reform calculus programs has focused primarily on student achievement and secondarily, and rather ineffectively, on student attitudes. This research has shown that reform programs have competed well with traditional programs in terms of student achievement. Results for attitude change have been much less conclusive because of conceptual and methodological problems. We critically review this literature to argue for broader conceptions of impact that target new dimensions of program effect and examine interactions between dimensions. We also briefly present the conceptualization, design, and broad results of one study, the Mathematical Transitions Project (MTP), which expanded the range of impact along those lines. The MTP results reveal substantial diversity in students' experience within and between research sites, different patterns of experience between high school and university students, and surprising relationships between achievement and attitude for some students.
Spielman, L. J., & Lloyd, G. M. (2004). The impact of enacted mathematics curriculum models on prospective elementary teachers’ course perceptions and beliefs. School Science and Mathematics, 104(1), 32-44.
ABSTRACT: This paper communicates the impact of prospective teachers' learning of mathematics using novel curriculum materials in an innovative classroom setting. Two sections of a mathematics content course for prospective elementary teachers used different text materials and instructional approaches. The primary mathematical authorities were the instructor and text in the textbook section and the prospective teachers in the curriculum materials section. After one semester, teachers in the curriculum materials section (n= 34) placed significantly more importance on classroom group work and discussions, less on instructor lecture and explanation, and less on textbooks having practice problems, examples, and explanations. They valued student exploration over practice. In the textbook section (n= 19), there was little change in the teachers' beliefs, in which practice was valued over exploration. These results highlight the positive impact of experiences with innovative curriculum materials on prospective elementary teachers' beliefs about mathematics instruction.
Stancavage, F., Shepard, L., McLaughlin, D., Holtzman, D., Blankenship, C., & Zhang, Y. (2009). Sensitivity of NAEP to the effects of reform-based teaching and learning in middle school mathematics. Washington, D. C.: American Institutes for Research.
ABSTRACT: This study is a validity study of the National Assessment of Educational Progress (NAEP), intended to test the adequacy of NAEP for detecting and monitoring the effects of mathematics education reform. The current study design was intended to support a comparison of the relative effectiveness of three different types of large-scale assessments--"Balanced Assessment in Mathematics" (BAM), NAEP, and state assessments--for measuring the learning gains of students participating in a well-implemented reform mathematics curriculum. To provide a context for assessing student learning where the authors could be reasonably certain of observing substantial learning gains in mathematics over the course of a school year, they selected National Science Foundation's (NSF's) Connected Mathematics Project (CMP). Although the authors had initially hypothesized that BAM, being more closely aligned with the reform curriculum, would reveal larger gains than NAEP, they found that both assessments were equally sensitive to the gains of their sample of students in CMP classrooms, and NAEP appeared better able to detect gains in the algebra classrooms. This was true even though the BAM test required twice as much time to administer as the NAEP test. Three appendices are included: (1) Sample NAEP Items; (2) Sample BAM Task; and (3) Analyses Using Booklet Percent Correct Metric.
Stancavage, V. B., Shepard, L., McLaughlin, D., Holtzman, D., Blankenship, C., & Zhang, Y . (2009). Sensitivity of NAEP to the effects of reform-based teaching and learning in middle school mathematics. A publication of the NAEP Validity Studies Panel. Palo Alto, CA: American Institutes for Research.
Star, J. R., & Hoffmann, A. J. (2002). Assessing students' conceptions of reform mathematics. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant, & K. Nooney (Eds.), Proceedings of the twenty-fourth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 1729-1732). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
ABSTRACT: As the use of NSF-sponsored, reform-oriented mathematics curricula has become more prevalent across the US, an increasing number of researchers are attempting to study the "impact" of reform. In particular, mathematics educators are interested in determining whether reforms are having the desired effects on students, particularly with respect to the learning of mathematical content and the improvement of attitudes about mathematics. In this effort, researchers have used a variety of methods, and have looked at a variety of variables, in order to assess the impact of reform. In many cases, such research assesses reform by looking closely at students' scores on tests or their strategies for solving certain kinds of problems. For example, Riordan & Noyce (2001) assessed reform's impact by comparing students' scores on standardized achievement tests. Other researchers have used structured interviews, classroom observations, and more interpretive or ethnographic methods to assess the impact of reform (e.g., Boaler,1997). Both of these methodologies are useful in assessing the impact that reform mathematics curricula are having on students. An alternative evaluation of the impact of reform that has not been as widely used is through the use of survey instruments. Surveys have been widely and reliably used to assess students' motivation (Pintrich, Smith, Garcia, & McKeachie, 1993), beliefs and attitudes (Kenney & Silver, 1997), and interest (Köller, Baumert, & Schnabel, 2001). We propose to add to this literature by using a survey to study the impact of reform on students' conceptions of mathematics.
Star, J. R., & Hoffmann, A. J. (2005). Assessing the impact of Standards-based curricula: Investigating students’ epistemological conceptions of mathematics. The Mathematics Educator, 15(2), 25-34.
ABSTRACT: Since the advent of the NCTM Standards (1989), mathematics educators have been faced with the challenge of assessing the impact of Standards-based (or “reform”) curricula. Research on the impact of Standards-based curricula has predominantly focused on student achievement; here we consider an alternative: Students’ epistemological conceptions of mathematics. 297 participants were administered a Likert-scale survey instrument, the Conceptions of Mathematics Inventory. Of these, 163 had not experienced Standards-based curricula, while the rest had used a Standards-based curriculum for over three years. Our results indicate that students at the Standards-based site expressed more sophisticated epistemological conceptions of mathematics than those of the students from the non-Standards-based site. We interpret this result to suggest that implementation of Standards-based curricula may be having an effect on students’ epistemological conceptions of mathematics.
Star, J. R., Smith III, J. P., & Jansen, A. J. (2008). What students notice as different between reform and traditional mathematics programs. Journal for Research in Mathematics Education, 39(1), 9-32.
ABSTRACT: Research on the impact of Standards-based mathematics and reform calculus curricula has largely focused on changes in achievement and attitudes, generally ignoring how students experience these new programs. This study was designed to address that deficit. As part of a larger effort to characterize students' transitions into and out of reform programs, we analyzed how 93 high school and college students perceived Standards-based and reform calculus programs as different from traditional ones. Results show considerable diversity across and even within sites. Nearly all students reported differences, but high-impact differences, like Content, were not always related to curriculum type (reform or traditional). Students' perceptions aligned moderately well with those of reform curriculum authors, e.g., concerning Typical Problems. These results show that students' responses to reform programs can be quite diverse and only partially aligned with adults' views.
Stevens, B. B. A. (2005). The development of pedagogical content knowledge of a mathematics teaching intern: The role of collaboration, curriculum, and classroom context. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 67(9). (ProQuest ID No. 1212777591)
ABSTRACT: In this study I examined the role of collaboration, curriculum, and the classroom context in the development of pedagogical content knowledge of a mathematics teaching intern. Additionally, I investigated the nature of the collaborative process between the teaching intern and his mentor teacher as they collaborated on action (during structured planning time) and in action (while students were present). The teaching internship resided in a seventh-grade mathematics classroom during the teaching of a probability unit from a standards-based curriculum, Connected Mathematics Project.
Using existing research, a conceptual framework was developed and multiple data sources (audio taped collaborations, observations of the intern's teaching practices, semi structured interviews, and a mathematics pedagogy assessment) were analyzed in order to understand the teaching intern's development of knowledge of instructional strategies, knowledge of student understandings, curricular knowledge, and conceptions of purpose for teaching probability.
Results identified numerous dilemmas related to planning and implementing instruction. Although the teaching intern developed pedagogical content knowledge, he often experienced difficulty accessing it while teaching. Through collaboration, curriculum, and the classroom context, the teaching intern learned to incorporate his pedagogical content knowledge in instruction. Analysis revealed that as he gained new knowledge he was able to shift his focus from content to the use of instructional strategies for teaching and learning. The curriculum was the primary focus of collaboration and initiated the intern's examination of the learning-to-teach process.
Collaboration on action and collaboration in action proved to be essential elements in the development of pedagogical content knowledge.
Stylianides, G. J. (2007). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6(1), 191 -215.
ABSTRACT: Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed.
Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288.
ABSTRACT: Despite widespread agreement that the activity of reasoning-and-proving should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that teachers make about what tasks to implement in their classrooms and when and how to implement them are mediated by the textbooks they use. Yet, little is known about how reasoning-and-proving is promoted in school mathematics textbooks. In this article, I present an analytic/methodological approach for the examination of the opportunities designed in mathematics textbooks for students to engage in reasoning-and-proving. In addition, I exemplify the utility of the approach in an examination of a strategically selected American mathematics textbook series. I use the findings from this examination as a context to discuss issues of textbook design in the domain of reasoning-and-proving that pertain to any textbook series.
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle grades mathematics curricula on student achievement and the classroom learning environment. Journal for Research in Mathematics Education, 39(3), 247-280.
ABSTRACT: We examine student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher developed textbooks. Using hierarchical linear modeling (HLM), curriculum type was not a significant predictor of student achievement on the Balanced Assessment in Mathematics (BAM) or TerraNova Survey (TNS) after controlling for student-level variables. However, the Standards-Based Learning Environment (SBLE) moderated the effect of curriculum type. Students were positively impacted on the BAM by NSF-funded curricula when coupled with either Moderate or High levels of SBLE. There was no statistically significant impact of NSF- funded curricula on students in classrooms with a Low level of SBLE, and the relationship between publisher-developed textbooks and SBLE was not statistically significant. Moreover, there was no significant impact of either curriculum type when coupled with varying levels of SBLE on the TNS as the dependent measure.
Theule-Lubienski, S. A. (1996). Mathematics for all?: Examining issues of class in mathematics teaching and learning. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 58(1). (ProQuest ID No. 739654911)
ABSTRACT: Diversity and equity are popular topics in the mathematics education community today, particularly amidst current reforms intended to "empower all students." Still, little attention is given to socio-economic diversity in relation to mathematics teaching and learning.
In this study, a researcher-teacher explores the ways in which a curriculum and pedagogy aligned with current, mathematics education reforms played out with a socio-economically diverse group of seventh-grade students. Interviews, surveys, teaching journal entries, and daily audio recordings were used to document students' experiences across the 1993-94 school year. Qualitative analyses compared the lower-and higher-SES students' experiences with the whole-class discussions and contextualized, open-ended mathematics problems. The analyses revealed that while the higher-SES students tended to have confidence in their abilities to make sense of the mathematical discussions and problems, the lower-SES students often said they were "confused" by conflicting ideas in the discussions and the open nature of the problems--they desired more specific direction from the teacher and texts. Additionally, while the higher-SES students seemed to approach the problems and discussions with an eye toward the larger, abstract, mathematical ideas, the lower-SES students more often became "stuck" in the contexts of the problems.
ES students more often became "stuck" in the contexts of the problems. The study examines critical links between the current mathematics reforms and literatures on social class, which suggest there might be a mismatch between the culture of lower-SES students and the culture of the mathematics classroom advocated by current reformers. "Cultural confusion" is proposed as an explanation for the struggles the lower-and working-class students faced in the reformed mathematics classroom. The study suggests that a classroom in which taking initiative in solving problems, analyzing and discussing ideas, and abstracting mathematical ideas from contextualized problems, might be more aligned with middle-class students' preferred ways of communicating, thinking and learning.
Dilemmas involved in educating lower-and working-class students are discussed. This study contributes to our understanding of both possibilities and hazards inherent in constructivist-inspired pedagogies and curricula intended to "empower all students," in both mathematics and other fields.
Van Dyke, C. L. (2001). The shape of things to come: Mathematics reform in the middle school. (Masters thesis). Retrieved from Masters Abstracts International, 40(2). (ProQuest ID No. 727357331)
ABSTRACT: In this thesis I investigate the implementation of the Connected Mathematics Project (CMP) at Gallup Middle School in the Holbrook School District. I analyze my experiences and observations at Gallup Middle School during the 2000-2001 school year in the broad context of mathematics education reform. My observations reveal difficulties with implementing CMP. I describe several factors contributing to these problems. It is my goal to strengthen investigation-oriented mathematics by illuminating its weaknesses. I believe CMP fosters a greater understanding of mathematics among students. This understanding creates the foundation for a mathematical perspective on the world. The development of a mathematical perspective is crucial to the economic well-being of our students and, in turn, our country.v
Waite, R.D. (2000). A study of the effects of Everyday Mathematics on student achievement of third-,fourth-, and fifth-grade students in a large north Texas urban school district. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 61(10). (ProQuest ID No. 1251814391)
ABSTRACT: Data were examined in this study from student records in a large North Texas urban school district who were taught with two different mathematics curricula to determine whether or not they had different effects on student achievement. One of the mathematics curricula, Everyday Mathematics, was developed upon national mathematic standards, written by the National Council of Teachers of Mathematics. The other mathematics curriculum was district-approved, using a textbook from a large publisher, with a more traditional approach.
The students selected for the experimental group came from six schools that had implemented the Everyday Mathematics curriculum for the 1998-99 school year. An experimental group was formed from these students. Twelve schools with similar socioeconomic ratios, ethnic makeup and 1998 Iowa Test of Basic Skills mathematic score profiles were selected. A control group was formed from this population of students that was similar to the experimental group with the exception of having been taught using the district-approved mathematics curriculum.
These two groups were very similar in socioeconomic, ethnic, gender, and grade level makeup. Most importantly, the experimental group and control group were almost identical (there was no statistically significant difference) in their 1998 Iowa Test of Basic Skills mathematics scores, a gauge used to demonstrate that prior mathematics ability was equal going into the 1998-99 school year.
In the statistical analysis, almost all comparisons showed that the experimental group taught with the Everyday Mathematics curriculum had higher scores on the 1999 Texas Assessment of Academic Skills mathematics test. When compared to children with similar mathematics ability at the beginning of the 1998-99 school year, the students in this study who were taught using Everyday Mathematics showed greater achievement gains than students in classes that used the district-approved curriculum.
Wasman, D. G. (2000). An investigation of algebraic reasoning of seventh-and eighth-grade students who have studied from the Connected Mathematics Project curriculum. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 61(9). (ProQuest ID No. 727777811)
ABSTRACT: This study investigated algebraic reasoning of seventh and eighth graders' who have studied from the Connected Mathematics Project (CMP) materials. Algebraic reasoning was defined as the process of thinking logically about and applying algebraic concepts as described by NCTM's expectations for grades six through eight students described in the Patterns, Functions, and Algebra Standard outlined in the Principles and Standards for School Mathematics. The seventh and eighth graders represented 75% of the students at their grade level because the other 25% were enrolled in accelerated courses that did not use CMP. In order to document the extent and nature of the use of CMP, all sixth, seventh and eighth grade teachers completed a survey followed by researcher-conducted classroom observations. The Iowa Algebra Aptitude Test (IAAT) was administered to 100-seventh graders and 73-eighth graders. Five-seventh graders and six-eighth graders were randomly selected for individual interviews consisting of a series of twelve algebra tasks.
Students' performance on the IAAT and interview tasks demonstrated the well-developed nature of their understanding and use of algebraic ideas and strategies. Students demonstrated flexibility in their thinking and ability to describe linear relationships in a variety of representations. Students described rate of change arithmetically, algebraically, and/or geometrically in different situations. Students approached problems in a sense-making way, choosing a variety of different strategies (informal and formal) all of which led to correct solutions and reflected strong conceptual understanding of algebraic ideas. Eighth graders were more likely to use symbolic algebra methods to solve problems than the seventh graders, reflecting a natural development of more symbolic strategies. Context played an important role with regard to students' ability to interpret and symbolize mathematical ideas. Students were more likely to represent situations symbolically when they were embedded in a context-rich setting. Some students had difficulty translating from a recursive pattern to an explicit formula and interpreting a graph as a relationship between independent and dependent variables. These same weaknesses have been noted in other research studies indicating that these ideas may require more time or maturity to develop, regardless of the particular curriculum used.
Woodward, J., & Brown, C. (2006). Meeting the curricular needs of academically low-achieving students in middle grade mathematics. The Journal of Special Education, 40(3), 151.
ABSTRACT: An important component of the National Council of Teachers of Mathematics Standards is the equity principle: All students should have access to a coherent, challenging mathematics curriculum. Many in the mathematics reform community have maintained that this principle can be achieved through one well-designed curriculum. However, the extant research on equity—which focuses on either ethnic diversity or academic achievement—suggests that this principle is illusive. The current study compares the effectiveness of two curricula in teaching a range of math concepts to 53 (28 male; 25 female) middle school students at risk for special education services in math. The yearlong, quasi-experimental study involved achievement and attitudinal measures. Results indicated that students in the intervention group who used materials designed according to instructional principles described in the special education literature achieved higher academic outcomes (p < .05, p < .001) and had more positive attitudes toward math (p < .001) than did students in the comparison group.
Zvoch, K., & Stevens, J. (2006). Longitudinal effects of school context and practice on middle school mathematics achievement. The Journal of Educational Research, 99(6), 347– 357.
ABSTRACT: The authors analyzed mathematics achievement data from a longitudinally matched student cohort from a large southwestern U.S. school district to investigate school context and practice effects on the academic performance and growth of middle school students. Investigation of the degree to which aspects of the school environment related to mathematics achievement outcomes revealed 2 distinct patterns. School context, as measured by student and school demographic characteristics, related closely to mathematics performance levels but had little relationship with mathematics growth rates. The opposite was true for aspects of school practice. Teacher educational attainment and the mathematics curricula delivered to students were not related to student performance levels but were moderately associated with mathematics growth rates. These results suggest that the effect of some policy-relevant school variables may be difficult to identify when student achievement is studied at a single point in time. However, investigation of school impacts on student achievement may be facilitated when an analytic strategy that takes into account the time-dependent and cumulative nature of schooling is adopted.