# 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.

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

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

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

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

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

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

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

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.

Brucker, E. L. (2008). Journey into a Standards-based mathematics classroom. *Mathematics Teaching in the Middle School, 14*(5), 300-303.

ABSTRACT: A standards-based approach to mathematics involves using story problems to allow students to investigate a solution. This approach emphasizes an understanding of concepts and processes and assumes mastery of basic computation skills. This article will encourage teachers to continue teaching standards-based mathematics and to take advantage of available training to produce students who are better prepared in mathematics and who enjoy the process.

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).

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.

Collins, A. M. (2000). Yours is not to reason why. *Education Week, 20*(1), 60.

Keller, B. A., Martin, W. G., & Hart, E. W. (2001). *Illuminating NCTM’s Principles and Standards for School Mathematics.* School Science and Mathematics, 101(6), 292 304.

ABSTRACT: Describes electronic resources designed to illuminate the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics". Provides a vehicle for further discussion of the vision put forth in the Standards.

Kendrick, D. G. (2004). *High school algebra teachers' beliefs and attitudes about the mathematics reform movement and high-stakes testing: Implications for staff development.* (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(7). (ProQuest ID No. 775169461)

ABSTRACT: This study attempts to define urban teacher quality, understand teacher learning, and gauge the success of efforts to develop urban teacher competencies in implementing mathematics education reform in high school algebra classrooms. The Professional Standards for Teaching Mathematics (NCTM, 1991) includes two underlying premises of mathematics education reform: that teachers are the primary facilitators of change, and that teachers need adequate support to make changes. The study focuses on: (a) the extent to which reform-oriented practices are being implemented in high school algebra classrooms; (b) the relationship between teacher preparation and reform-oriented practices; and (c) the effects of teacher beliefs, school-level environment, and staff development on the mathematics education reform practices in high school algebra classrooms. The research includes examination of the responses of high school algebra teachers on a self-administered survey as well as the responses of high school algebra teachers and mathematics chairpersons in one-on-one interviews. The subjects were asked about their beliefs, actions, and needs as related to the NCTM Standards.

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.

Kulm, G., Capraro, R. M., & Capraro, M. M. (2007). Teaching and learning middle grades mathematics with understanding. *Middle Grades Research Journal, 2*(1), 23-48.

ABSTRACT: This study addresses the nexus of two critical challenges for today's mathematics teacher. On the one hand, teaching for understanding for all students is the goal of most mathematics teachers. However, many teachers also must acknowledge and address the requirement that students do well on high stakes tests. This study analyzed data on 6th grade students' performance and achievement after a year-long implementation of Connected Mathematics (CMP). Texas Assessment of Academic Skills (TAAS) data were analyzed, comparing students' achievement from 5th to 6th grade. The variables of at-risk, socio-economic status, and ethnicity were analyzed to determine the nature and practical importance of adopting CMP. The results indicated that the overall gain from using CMP materials over the previous year's mathematics achievement was four points (p less than 0.01). The at-risk students demonstrated a mean 10-point gain (p less than 0.01) while the non at-risk students demonstrated a mean 2-point gain.

Kulm, G., Wilson, L. D., Kitchen, R. (2005). Alignment of content and effectiveness of mathematics assessment items. *Educational Assessment, 10*(4), 333-356.

ABSTRACT: Alignment has taken on increased importance given the current high-stakes nature of assessment. To make well-informed decisions about student learning on the basis of test results, assessment items need to be well aligned with standards. Project 2061 of the American Association for the Advancement of Science (AAAS) has developed a procedure for analyzing the content and quality of assessment items. The authors of this study used this alignment procedure to closely examine 2 mathematics assessment items. Student work on these 2 items was analyzed to determine whether the conclusions reached through the use of the alignment procedure could be validated. It was found that the Project 2061 alignment procedure was effective in providing a tool for in-depth analysis of the mathematical content of the item and a set of standards and in identifying 1 particular content standard that was most closely aligned with the standard. Through analyzing student work samples and student interviews, it was also found that students' thinking may not correspond to the standard identified as best aligned with the learning goals of the item. This finding highlights the potential usefulness of analyzing student work to clarify any additional deficiencies of an assessment item not revealed by an alignment procedure.

Lappan, G. (1997). The challenge of implementation: Supporting teachers. *American Journal of Education, 106*(1), 207-239.

ABSTRACT: Reform in mathematics education has been stimulated and propelled by the publication of standards documents by the National Council of Teachers of Mathematics. This article examines the vision of teacher decision making that is portrayed in NCTM Professional Teaching Standards: choosing worthwhile mathematical tasks, orchestrating and monitoring classroom discourse, creating an environment for learning, and analyzing one's practice. The philosophical orientation and the set of commitments to teaching and learning on which the standards are based include stances on equity, curriculum, teaching, and learning. These stances are summarized under the following headings: inclusiveness, depth over coverage, teaching for understanding, active engagement of students, curriculum investigations, applications, and connections.

Lappan, G., & Ferrini-Mundy, J. (1993). Knowing and doing mathematics: A new vision for middle grades students. *The Elementary School Journal, 93*(5), 625-639.

ABSTRACT: Research provides characteristics of effective programs for schools that want to restructure their programs to better meet the needs of students in the middle grades. Direction in revising both the curriculum and instruction in mathematics classrooms is provided by the National Council of Teachers of Mathematics in its two documents Curriculum and Evaluation Standards for School Mathematics and the Professional Standards for Teaching Mathematics. In this article we discuss mathematical tasks, classroom environments, and means of assessment that might encourage rich mathematical growth for middle grades students. Proposed changes in the mathematics content and processes emphasized in the middle grades are outlined. Shifts in the culture of the mathematics classroom that support students' development of mathematical power are described, and two problems that involve the mathematics content and processes we advocate are provided. Finally, we acknowledge the complexity of implementing such changes in tasks, environment, and assessment and point to the need for transformative research and structural shifts.

Lappan, G., & Phillips, E. (1998). Teaching and learning in the Connected Mathematics Project. In L. Leutzinger (Ed.), *Mathematics in the Middle.* Reston, VA: National Council of Teachers of Mathematics.

Lappan, G., Phillips, E. (2009). A designer speaks: Glenda Lappan and Elizabeth Phillips. *Educational Designer, Journal of the International Society for Design and Development in Education, 1*(3), 1-19. Retrieved from: http://www.educationaldesigner.org/ed/volume1/issue3/article11

ABSTRACT: The need to improve the teaching and learning of mathematics has been a focus of attention in the US over our entire careers. There have been waves of national interest in mathematics education that have attracted mathematicians and mathematics educators to the work of improving K-12 mathematics education. Today we will focus our remarks in two areas, our own curriculum development work including the story of how we came to engage in and accomplish the work and our comments on the challenges we face in future work to improve mathematics teaching and learning. We expect that many of the challenges we see are also challenges for mathematics education worldwide. First we will share relevant aspects of the work in which our research and development group have engaged for over 35 years. Many of these remarks are based on other papers that we have published about our work. But for this special audience we would like to tell you a bit of our personal stories.

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.

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.

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.