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.
Banilower, E. R. (2010). Connected Mathematics, 2nd Edition: A three-year study of student outcomes. Chapel Hill, NC: Horizon Research, Inc.
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.
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.
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.
Cavanagh, J. M. (2012). An organizational case study: The impact of an initiation, implementation, and institutionalization of a curricular change (Doctoral dissertation). Available from ProQuest Dissertations and Theses data-base. (UMI No. 1015379520)
ABSTRACT: Successful change in schools is planned, expected and managed with the objective focused on benefiting the students, not just converting the staff. This investigation is a case study of a public school district that opted to implement curricular change following an examination of the district's performance toward adequate yearly progress. This case study utilized a quantitative design to address: the process and impact of an initiation, implementation and institutionalization of a district level curricular change, the roles that emerged among participants in this process, the influence of stakeholders, the dynamics and processes of change, and the impact of the curricular change on student achievement. Surveys were distributed to 18 teachers, three middle level administrators and four central office personnel in order to analyze the organizational processes and the perceived roles of stakeholders in the curricular change process. The overall participation rate was 68%. Surveys were analyzed to examine three themes: if the curricular change process was triggered by external stakeholders that had legitimate claims on the operation of the organization, if the curricular change process was initiated and dictated by the high level district stakeholders, and if the curricular change process was implemented and carried through by high level internal stakeholders. Additionally, Pennsylvania System of School Assessment math scores for eighth grade were collected and analyzed comparing four groups based upon the amount of Connected Mathematics Project instruction the students received. Analysis of Pennsylvania System of School Assessment eighth grade math scores revealed that scores increased progressively with each additional year of Connect Mathematics Project completion. Further research involving the surveying of high school teachers, as well as review of eleventh grade Pennsylvania System of School Assessment math scores may be helpful. Review of additional performance indicators, such as classroom mathematics grades may also be beneficial.
De Groot, C. (2000). Three female voices: The transition to high school mathematics from a reform middle school mathematics program. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 61(4). (ProQuest ID No. 731933601)
ABSTRACT: In this ethnographic study, the transition experiences and coping mechanisms of three female students are reported. These students were members of a cohort in grades 6, 7, and 8 (ages 12-14) that participated in the field testing of the Connected Mathematics Project (1990-1995), a middle school curriculum closely reflecting recommendations of the National Council of Teachers of Mathematics. The participants of the study were in the same mathematics class during their grade 8 experience, but went to different high schools.
Two interviews were conducted toward the end of their grade 9 experience and six interviews were conducted during their grade 10 experience. Middle school mathematics teachers and high school mathematics teachers were interviewed as well as one parent. One observation of each of their tenth grade mathematics classes was conducted. The reported characteristics of transition in this study focus mainly on changes or discontinuities in the learning of mathematics. Data were analyzed by coding processes and presented in narratives and Qualitative Schematics of Dimensions of Transition in Learning Mathematics Thematic interpretations are given with respect to coping mechanisms that were revealed.
One of the major findings of this study is that early in grade 9 these three students related their learning of mathematics in high school closer to their (traditional) elementary experience, which was termed as regular mathematics, than to their reform middle school experience, which was more constructivist in design. In grade 10 they seemed to connect more with their middle school experience, for example, while doing proofs and related this to "explaining your thinking." Another major finding was that these three students experienced a gradual individualization during this transition together with increased in-class competition among students, particularly for attention from the teacher. In high school, they appeared to cope with this lack of student-to-student discourse by forming out of-class support networks.
Suggestions for future research are made regarding the transition discontinuity from learning in a reform environment to learning in a traditional environment, as well as the need to investigate how transitional standards-based curricula, steeped in problem solving, supports students' development of mathematical proof.
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.
Garrison, A. L. (2013). Understanding teacher and contextual factors that influence the enactment of cognitively demanding mathematics tasks. (Unpublished doctoral dissertation). Vanderbilt University, Nashville, TN.
ABSTRACT: The level of challenge, or cognitive demand, of the tasks students solve is the foundation for their learning opportunities in mathematics classrooms. Unfortunately, it is difficult for teachers to effectively use cognitively demanding tasks (CDTs). I seek to understand how to support and improve mathematics teachers’ enactment of CDTs at scale. The purpose of this three-paper dissertation is to address some of the key unresolved questions and to set a direction for future research.
In paper 1, based on a comprehensive literature review, I identify 13 potentially relevant factors and elaborate a method for building on results from small-scale studies to better understand the enactment of CDTs across large samples of teachers.
Paper 2 investigates how teachers’ mathematical knowledge for teaching and their beliefs about teaching and learning mathematics are related to their enactment of CDTs. I found that aspects of teachers’ knowledge and beliefs are interconnected and are significantly related to their enactment of CDTs.
Paper 3 investigates changes in teachers’ enactment of CDTs over time and whether their interactions with colleagues (e.g., work with a math coach, advice-seeking interactions) are related to these changes. I found that the mere occurrence of interactions was generally not sufficient to support teachers’ development, and expertise available within interactions did not influence the productivity of those interactions. However, advice-seeking interactions were significantly related to teachers’ development. Further, the lack of expertise within interactions might have contributed to these findings.
These three studies suggest that there is much more to be understood about supporting teachers’ enactment of CDTs. There is, however, evidence that teachers’ mathematical knowledge for teaching and their beliefs about teaching and learning mathematics are integral to their enactment of CDTs, and that they are interrelated. In addition, it is clear that in designing supports for teachers’ enactment of CDTs, schools and districts should go beyond policies that provide only opportunities for interaction, and should specifically plan productive activities and enhance the available expertise within those interactions.
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.
Heck, D. J., Banilower, E. R., Weiss, I. R., & Rosenberg, S. L. (2008). Studying the effects of professional development: The case of the NSF's local systemic change through teacher enhancement initiative. Journal for Research in Mathematics Education, 39(2), 113-152.
ABSTRACT: Enacting the vision of NCTM's Principles and Standards for School Mathematics depends on effective teacher professional development. This 7-year study of 48 projects in the National Science Foundation's Local Systemic Change Through Teacher Enhancement Initiative investigates the relationship between professional development and teachers' attitudes, preparedness, and classroom practices in mathematics. These programs included many features considered to characterize effective professional development: content focus, extensive and sustained duration, and connection to practice and to influences on teachers' practice. Results provide evidence of positive impact on teacher-reported attitudes toward, preparedness for, and practice of Standards-based teaching, despite the fact that many teachers did not participate in professional development to the extent intended. Teachers' perception of their principals' support for Standards-based mathematics instruction was also positively related to these outcomes.
Hodges, T. & Cady, J. A. (2012). Negotiating contexts to construct an identify as a mathematics teacher. The Journal of Educational Research, 105(2), 112-122.
ABSTRACT: The authors focused on 1 middle-grades mathematics teacher's identity and her efforts to implement standards-based instructional practices. As professionals, teachers participate in multiple professional communities and must negotiate and manage conflicting agendas. The authors analyze how the contexts of these communities influence the teacher's identity and thus her teaching of mathematics.
Hoffmann, A. J. (2004). Middle school mathematics students' motivations for participating in whole-class discussions: Their beliefs, goals, and involvement. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(9). (ProQuest ID No. 795927881)
ABSTRACT: Whole-class discussions in mathematics classrooms are considered to foster active sense-making and intellectual autonomy among students. Through participating in these discussions, students have the opportunity to develop skills of mathematical communication, reasoning, and justification. However, middle school students may resist participating in whole-class discussions if they perceive social consequences resulting from this activity.
Research on mathematics classroom discourse typically focuses on the role of the teacher in discourse, examining student variables as outcomes to measure the effectiveness of the teachers' strategies. Alternatively, in this study, students' beliefs and goals are examined for how they influence students' participation in classroom discourse rather than as outcomes.
I assessed beliefs and goals of 15 target students from two seventh grade mathematics classrooms through one-on-one interviews and a Likert-scale survey instrument. Students' talk in interviews was analyzed through the use of a framework that included imperative verbs to capture idealized states, repetition to capture emphasis, and connections to affect to capture relative importance to the student. This framework allowed for a more rigorous analysis of students' beliefs in contrast to reporting any and all of their responses to interview questions.
Students' involvement in classroom discourse was described based on an analyses of videotaped classroom discussions about four investigation problems from the Connected Mathematics Project Standards-based mathematics curriculum.
Results from this study indicate that students' involvement in classroom discussions is influenced by their social goals and epistemological beliefs. Students who believed they learned mathematics through a process of negotiation and associated a low level of risk with participating in discussion were more likely to extend their participation during an interaction, critique the thinking of their classmates, and talk about mathematics at a high level of explicit meaning. There were also differences in students' involvement between the target students based on their classrooms.
This study illustrates how adolescence intersects with the mathematics reform movement by taking into account students' perspectives. Future research investigating how beliefs and goals relate to students' involvement in discussions may explain how a classroom of students together supports the development of effective classroom discussions.
Jansen, A. (2006). Seventh graders’ motivations for participating in two discussion-oriented mathematics classrooms. Elementary School Journal, 106(5), 409–428.
ABSTRACT: In this study I examined the self-reported motivational beliefs and goals supporting the participation of 15 seventh graders in whole-class discussions in 2 discussion-oriented Connected Mathematics Project classrooms. Through this qualitative investigation using semistructured interviews, I inductively identified and described the students' motivational beliefs and goals and relations among them. Results demonstrated beliefs that constrained students' participation and ones that supported their participation. Students with constraining beliefs were more likely to participate to meet goals of helping their classmates or behaving appropriately, whereas students with beliefs supporting participation were more likely to participate to demonstrate their competence and complete their work. Results illustrated how the experiences of middle school students in discussion-oriented mathematics classrooms involve navigating social relationships as much as participating in opportunities to learn mathematics.
Jansen, A. (2008). An investigation of relationships between seventh-grade students' beliefs and their participation during mathematics discussions in two classrooms. Mathematical Thinking and Learning, 10(1), 68-100.
ABSTRACT: As mathematics teachers attempt to promote classroom discourse that emphasizes reasoning about mathematical concepts and supports students' development of mathematical autonomy, not all students will participate similarly. For the purposes of this research report, I examined how 15 seventh-grade students participated during whole-class discussions in two mathematics classrooms. Additionally, I interpreted the nature of students' participation in relation to their beliefs about participating in whole-class discussions, extending results reported previously (Jansen, 2006) about a wider range of students' beliefs and goals in discussion-oriented mathematics classrooms. Students who believed mathematics discussions were threatening avoided talking about mathematics conceptually across both classrooms, yet these students participated by talking about mathematics procedurally. In addition, students' beliefs about appropriate behavior during mathematics class appeared to constrain whether they critiqued solutions of their classmates in both classrooms. Results suggest that coordinating analyses of students' beliefs and participation, particularly focusing on students who participate outside of typical interaction patterns in a classroom, can provide insights for engaging more students in mathematics classroom discussions.
Katwibun, D. (2004). Middle school students' mathematical dispositions in a problem-based classroom. (Doctoral dissertation). Dissertation Abstracts International, 65(5). (ProQuest ID No. 766026571)
ABSTRACT: The purpose of this study was to describe middle school students' mathematical dispositions in a problem-based learning [PBL] classroom. Eight volunteer students from one 6th grade mathematics classroom participated in this study. The curriculum used was the Connected Mathematics Project [CMP]. The main sources for data collection were classroom observations, the Attitudes and Beliefs questionnaire, teacher interviews, and student interviews. The CMP class routine consisted of four phases: Warm-up, Launch, Explore, and Summarize. The teacher in this study had her students investigate mathematics problems within cooperative small groups and share their ideas in large group discussions. The teacher acted as a facilitator and encouraged her students to try new ideas without fear of making mistakes. The findings revealed that almost all of the students in this study demonstrated positive mathematical dispositions. They volunteered and shared their ideas, both in small cooperative group investigations and in large group discussions. They believed mathematics was about "learning new ideas" and mathematics was "life" because it was everywhere in their lives. They also mentioned the usefulness of numbers, measurement, and geometry in their daily lives. All eight participants liked hands-on activities and working on a mathematics project. Most of them agreed that they liked mathematics because it was fun and interactive. Most also saw themselves as good at mathematics. All of them agreed that mathematics was useful, and that one's mathematics ability could be increased by effort. They also believed that there were no gender differences in mathematics, even though in their class, they realized that boys outperformed girls. Most of the students agreed that they could solve time-consuming mathematics problems and that it was important to understand mathematical concepts. None of them had negative feelings about group work; they learned from each other.
Finally, an analysis of the participants' mathematical dispositions was discussed. Based on the Taxonomy of Educational Objects: Affective Domains by Krathwohl, Bloom, and Masia (1964), the participants were categorized into three disposition levels: Level 1: "receiving;" Level 2: "responding;" and Level 3: "valuing." Half of the participants demonstrated dispositions at the high level (Level 3: "valuing") because of their willingness to pursue and/or seek to do mathematics outside the classroom. Three of them were in mathematics disposition Level 2.3: "satisfaction in response" because they usually participated in the class activities. They were satisfied and enjoyed doing mathematics. One of them demonstrated mathematical disposition Level 1.2: "willingness to receive" because she listened to the whole class and group discussions without sharing any ideas or asking for help when she needed it.
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.
Kilman, T. (2015). The relationship between students’ applied mathematics skills and students’ attitudes towards mathematics. (Doctoral Dissertation). Retrieved from The Aquila Digital Community, Paper 54. (Proquest ID No. 1664611515).
ABSTRACT: Mathematics is a subject with which many students struggle. It has been noted that students’ attitudes towards mathematics can often affect their performance in related courses. The goal of this research is to explore the relationship between students’ basic applied mathematics skills and students’ attitudes towards mathematics. That is, do students, as they learn how to use mathematics in the real world, tend to develop a more favorable outlook towards mathematics? Or, on the other hand, do the attitudes towards mathematics of students remain unaffected as their ability to use mathematics in the real world increases? The current research seeks to clarify these propositions in an effort to improve mathematics instruction by providing educators with a better understanding of students’ attitudes towards mathematics.
Multiple linear regression analysis found that attitude toward mathematics was indeed significantly related to students’ basic applied mathematics skill. Attitude toward mathematics explained 29.7% of the variance observed in basic applied mathematics skill. Attitudinal subscales were also analyzed. Student self-confidence and motivation were both significant predictors of basic applied mathematics skill. In a separate analysis, attitude toward mathematics was found not to be significantly related to mathematical achievement in the college classroom.
Lehrer, R., Kobiela, M., & Weinberg, P. J. (2012). Cultivating inquiry about space in a middle school mathematics classroom. ZDM Mathematics Education, 45(3), 365-376.
ABSTRACT: During 46 lessons in Euclidean geometry, sixth-grade students (ages 11, 12) were initiated in the mathematical practice of inquiry. Teachers supported inquiry by soliciting student questions and orienting students to related mathematical habits-of-mind such as generalizing, developing relations, and seeking invariants in light of change, to sustain investigations of their questions. When earlier and later phases of instruction were compared, student questions reflected an increasing disposition to seek generalization and to explore mathematical relations, forms of thinking valued by the discipline. Less prevalent were questions directed toward search for invariants in light of change. But when they were posed, questions about change tended to be oriented toward generalizing and establishing relations among mathematical objects and properties. As instruction proceeded, students developed an aesthetic that emphasized the value of questions oriented toward the collective pursuit of knowledge. Post-instructional interviews revealed that students experienced the forms of inquiry and investigation cultivated in the classroom as self-expressive.
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.
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.
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.