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.
Aisling, L. M., Friel, S. N., & Mamer, J. D. (2009). It’s a fird!: Can you compute a median of categorical data? Mathematics Teaching in the Middle School, 14(6), 344-351.
Description: Students need time and experience to develop essential understandings when they explore data analysis. In this article, the reader gains insight into confusion that may result as students think about summarizing information about a categorical data set that is attempting to use, in particular, the median. The authors highlight points to consider in helping students unpack these essential understandings.
Asquith, P., Stephens, A.C., Knuth, E.J., Alibali, M.W. (2005). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
ABSTRACT: This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview data were collected from 20 middle school teachers regarding their predictions of student responses to written assessment items focusing on the equal sign and variable. Teachers' predictions of students' understanding of variable aligned to a large extent with students' actual responses to corresponding items. In contrast, teachers' predictions of students' understanding of the equal sign did not correspond with actual student responses. Further, teachers rarely identified misconceptions about either variable or the equal sign as an obstacle to solving problems that required application of these concepts. Implications for teacher professional development are discussed.
Ball, D. L. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappan, 77(7), 500-508.
ABSTRACT: In order to improve mathematics education, a close examination of assumptions about teacher learning and the teaching of mathematics must be made. Teachers and others participating in the reform process will have to learn many new ideas and unlearn many previous assumptions.
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., 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., Keret, Y., & Ilany, B-S. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education (pre- and in-service mathematics teachers of elementary and middle school classes). Rotterdam, The Netherlands: Sense Publishers.
Bouck, M., Keusch, T., & Fitzgerald, W. (1996). Developing as a teacher of mathematics. The Mathematics Teacher, 89(9), 769-73.
ABSTRACT: This study investigated the impact of mathematics curriculum (standards based vs. traditional) on the performance of sixth and seventh grade students with disabilities on multiple-choice and open-ended assessments aligned to one state’s number and operations and algebra standards. It also sought to understand factors affecting student performance on assessments: ability status (students with and without disabilities), curriculum (standards based vs. traditional), and assessment type (multiple choice vs. open ended). In all, 146 sixth grade students and 149 seventh grade students participated in the study. A linear mixed model for each grade revealed students with disabilities did not perform better in either curriculum. Furthermore, curriculum type was not a significant factor affecting student performance; however, ability status, time, and assessment type were. The implications of these results are discussed.
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.
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.
Choppin, J. (2006). Studying a curriculum implementation using a communities of practice perspective. Paper presented at the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mèrida, Mèxico.
ABSTRACT: The publication of the 1989 NCTM Standards (NCTM, 1989) marked the launch of extensive efforts to reform mathematics teaching and learning. These efforts have included the development and publication of curricula which implicate constructivist instructional practices. Implementing reform curricula in a way that changes core teaching practices has proven to be a difficult endeavor (Spillane & Zeuli, 1999), especially so in urban settings, which are typically stressed in terms of teacher turnover, lack of material resources, and funding for professional development. A number of researchers have noted the importance – if not necessity – of professional community in facilitating and sustaining teacher change towards constructivist-based pedagogy (Cobb, McClain, Lamberg, & Dean, 2003; Secada & Adajian, 1997; Stein, Silver, & Smith, 1998). In this study I use Wenger’s (1998) three dimensions of community of practice (CoP) to analyze the extent to which core learning principles exist within the professional communities in my study. I focus on the learning principles of collaboration, reflection, recognition, and autonomy, which have been identified as characteristics of effective learning in communities of practice (Gee, 2003; Schon, 1983; Secada & Adajian, 1997; Wenger, 1998). This study describes characteristics of CoP’s in an urban school system implementing the Connected Mathematics Project (CMP) (Lappan, Fey, Fitzgerald, Friel & Phillips, 1998) curriculum.
Choppin, J. (2011). The impact of professional noticing on teachers’ adaptations of challenging tasks. Mathematical Thinking and Learning, 13(3), 175-191.
ABSTRACT: This study investigates how teacher attention to student thinking informs adaptations of challenging tasks. Five teachers who had implemented challenging mathematics curriculum materials for three or more years were videotaped enacting instructional sequences and were subsequently interviewed about those enactments. The results indicate that the two teachers who attended closely to student thinking developed conjectures about how that thinking developed across instructional sequences and used those conjectures to inform their adaptations. These teachers connected their conjectures to the details of student strategies, leading to adaptations that enhanced task complexity and students' opportunity to engage with mathematical concepts. By contrast, the three teachers who evaluated students' thinking primarily as right or wrong regularly adapted tasks in ways that were poorly informed by their observations and that reduced the complexity of the tasks. The results suggest that forming communities of inquiry around the use of challenging curriculum materials is important for providing opportunities for students to learn with understanding.
Choppin, J. M., Callard, C. H., & Kruger, J. S. (2014). Interpreting Standards as Sense-Making Opportunities. Mathematics Teaching in the Middle School, 20(1), 24-29.
Description: “The authors are a team of two teachers and a researcher who for several years have studied the teachers’ enactment of Accentuate the Negative, a unit on rational numbers that is part of the Connected Mathematics Project (CMP) curriculum (Lappan et al. 2006). We show how allowing students to create algorithms provided opportunities for them to reason about rational number addition and subtraction.”
Choppin, J. M., Cancy, C. B., & Koch, S. J. (2012). Developing formal procedures through sense-making. Mathematics Teaching in the Middle School, 17(9), 552-557.
ABSTRACT: The eight mathematical practices explored in the Common Core Math Standards are the following: (1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure.; and (8) Look for and express regularity in repeated reasoning. If teachers are going to take the Common Core Math Standards seriously, they need to think of them as more than simply a reordering of content. That means focusing on the practices they associate with mathematical understanding. A major implication is that "developing practices" rather than "covering content" requires a focus on task sequences rather than singular lessons; these sequences provide repeated opportunities for students to reason about ideas before they are formalized. Most students can reason mathematically but few get the opportunity to publicly test ideas and conjectures as they are forming. Participation in such practices leads not only to increased understanding but also to the development of mathematical dispositions that are valuable as students move to more advanced mathematics.
Collins, A. M. (2002). What happens to student learning in mathematics when a multifaceted, long-term professional development model to support Standards-based curricula is implemented in an environment of high stakes testing? (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(2). (ProQuest ID No. 765336031)
ABSTRACT: Assessment and accountability have created a high-stakes environment for districts, schools, teachers, and students. Assessment is driving most educational decisions. In Massachusetts graduation is contingent upon passing the mathematics and English language arts subtests of the Massachusetts Comprehensive Assessment System (MCAS). Teachers in schools where 30% or more students fail MCASare required to take a mathematics proficiency test. Middle schools not exhibiting improvement in their mathematics scores are identified as under-performing and are subject to interventions by the Department of Education. Not surprisingly, students in urban districts score significantly lower than those in more affluent suburban districts. To date only urban schools have been declared under-performing. It is within this environment of high-stakes testing and As repercussions that this study was undertaken.
In an effort to change the unsuccessful experiences of many urban students, the Noyce Foundation and Raytheon Company made a commitment to funding a long-term professional development intervention. This study investigates the impact of that sustained professional development program in one urban district. The professional development was designed to support the implementation of The Connected Mathematics Project (CMP) and to assess its impact on student learning. This dissertation presents a quantitative comparison between student scores on two standardized tests in schools whose teachers availed themselves of all available professional development surrounding the implementation process for CMP with schools whose teachers chose only to participate in contractually mandated district professional development.
Results indicate that students in schools whose teachers received sustained professional development designed to meet the needs of the participating teachers performed significantly higher on both the MCAS and a nationally normed achievement test, Terra Nova, than did those students whose teachers had not participated in consistent professional development. Evidence is included to document the positive impact on student achievement as a result of changing teacher practice and beliefs through mentoring and coaching in teachers' own classrooms.
DeBoer, G., Morris, K., Roseman, J. E., Wilson, L., Capraro, M. M., Capraro, R., & Manon, J. (2004). Research Issues in the Improvement of Mathematics Teaching and Learning through Professional Development. Paper presented at the American Educational Research Association, San Diego, CA.
ABSTRACT: The purpose of this paper is to describe a study we are conducting on the improvement of mathematics teaching and learning at the middle school level through professional development and to discuss some of the research issues that we have encountered in conducting the study. The paper will lay out the various rationales for our initial design and for the adjustments that we made along the way. We are nearing the end of year two of a five-year study, so this is very much a work in progress. The study is not large in terms of the number of teachers involved (approximately 50 teachers and 1,000 students per year in the early stages of the study), but it is a complex study involving many interconnected elements. In Part I we lay out the design of the study, and in Part II we discuss some of the issues that we are facing as we progress through our work.
Grunow, J. E. (1998). Using concept maps in a professional development program to assess and enhance teachers’ understanding of rational numbers. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 60(3). (ProQuest ID No. 734420161)
ABSTRACT: This professional-development institute was designed to look at a little researched component, adult learning in a specific content area. Rational-number understanding was the domain addressed. Teachers were selected to participate in a two-week institute and were supported the following year with on-line mentoring.
Assessment of teacher rational-number knowledge was done using concept maps, tools chosen because of their congruence with the domain. Concept maps, as an alternative assessment measure, had potential to satisfy another need, authentic assessment of the professional-development experience.
The study investigated three questions: (1) Will middle-school teachers' understanding of rational number, as reflected on concept maps, be enhanced as a result of participation in a professional-development institute designed specifically to develop understanding of a domain? (2) Will middle-school teachers' understanding of interrelationships among concepts and awareness of contexts that facilitate construction of conceptual knowledge, as assessed through concept maps, be increased as a result of participation designed with a focus on reform curricula, authentic pedagogy, and learner cognitions to facilitate decision-making? (3) Will middle-school teachers communicate knowledge growth through well-elaborated graphic displays using concept maps?
The research design used was both qualitative and quantitative. Participants designed preinstitute concept maps of rational-number understanding. Following instruction, participants designed postinstitute concept maps to reflect their learning. Quantitative analysis of the concept maps was achieved by scoring participant maps against an expert criterion map and a convergence score was used. Qualitative analysis of the maps was done using holistic techniques to determine overall proficiency.
The Wilcoxon Signed-Ranks Test was used to analyze the data obtained from scoring the concept maps. Three areas were examined: (a) knowledge of concepts and terminology; (b) knowledge of conceptual relationships; and (c) ability to communicate through concept maps. Results of scoring in all areas yielded significant gains. Holistic scoring showed all participants attaining proficiency with regard to rational-number understanding.
It was concluded that teacher knowledge of a content domain can be enhanced significantly in a professional-development experience designed to concentrate on such growth, that teachers can become aware of contexts that facilitate development of content knowledge, and that concept maps can be valid, reliable measures.
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.
Hull, L. S. H. (2000). Teachers' mathematical understanding of proportionality: Links to curriculum, professional development, and support. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 62(2). (ProQuest ID No. 727942411)
ABSTRACT: The Proportional Relationship Study was designed to investigate whether using a standards-based middle school mathematics curriculum, together with professional development and followup support, can lead to increased teacher content knowledge and pedagogical content knowledge of proportionality. From the literature, it is clear that what teachers do in the classroom affects what students learn, and that what teachers know affects their actions in the classroom. Teachers need strong personal content knowledge and pedagogical content knowledge in order to teach mathematics well; therefore, the question is an important one.
Seven sites participated in a statewide implementation effort during 1996-1999 that included Connected Mathematics Project (CMP) curriculum professional development experiences for teachers plus additional district and/or campus support. As part of this study, the Proportional Reasoning Exercise (PRE) was given to seventh-grade teachers three times: before CMP professional development, after a year of teaching with CMP materials, and again after a second year of teaching with the materials. Teacher responses were coded for correctness and for problem-solving strategy; group responses were compared for all three PREs. In addition, group and individual interviews were conducted with CMP teachers.
Data from the three PREs anti group and individual interviews of seventh-grade teachers showed growth in performance and understanding of proportional relationships over the two-year period. Analysis of each of the PRE problems revealed an increase in the percent of teachers who correctly answered the problems and a tendency toward using more sophisticated proportional relationship strategies. However, choice of strategy appeared to depend on the context of the problem. Participants also tended over time to record multiple and more diverse strategies, increase the depth and detail of their written explanations, and include units along with numbers.
Interviews after the first year confirmed that experienced teachers placed in a new situation, with new curriculum and expectations of using new instructional approaches, often revert to "novice" status, concerned primarily with survival (Borko & Livingston, 1989). However, individual interviews conducted after the second year showed that teachers were then ready to focus on student understanding of mathematics and were themselves learning new and important mathematics.
Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2015). Investigating the development of mathematics leaders’ capacity to support teachers’ learning on a large scale. ZDM, 47, 93–104. doi:10.1007/s11858-014-0652-5.
ABSTRACT: A key aspect of supporting teachers’ learning on a large scale concerns mathematics leaders’ practices in designing for and leading high-quality professional development. We report on a retrospective analysis of an initial design experiment aimed at supporting the learning of three math leaders who were charged with supporting the learning of middle-grades mathematics teachers across a large US school district. Initial goals for the math leaders’ learning included: (a) viewing teachers’ improvement of their classroom practices as a progression;(b) designing supports for teachers’ learning that were informed by assessments of teachers’ current practices, were oriented towards long-term goals for teachers’ practices, and would enable teachers to attain short-term goals that constituted reasonable next steps; and (c) facilitating professional development by pressing on teachers’ ideas differentially and building on their contributions. Findings suggest that the math leaders increasingly viewed teachers’ improvement of their classroom practices as a developmental progression and began to design connected sequences of activities. However, they struggled to facilitate the activities in ways that would meet their ambitious goals for teachers’ learning. Based on our findings, we indicate potential improvements to our design for supporting math leaders’ learning. More generally, we provide the field with a set of potentially revisable learning goals for math leaders’ learning, a set of principles to guide the design of supports for their learning, and a provisional design to support the development of their practices
Keiser, J. M. (2000). The role of definition. Mathematics Teaching in the Middle School, 5(8), 506–511.
ABSTRACT: The writer examines the role that mathematical definitions can play in the middle grades math classroom, focusing on the concept of angle as it was introduced to sixth-grade students.
Keiser, J. M. (2010). Shifting our computational focus. Mathematics Teaching in the Middle School, 16(4), 216-223.
ABSTRACT: Through professional development activities involving action research, middle-grades teachers at this author's school learned how to honor students' prior knowledge and experience by finding out about their K-5 computational development. Rather than complaining about what their students did not know, they learned to appreciate results from their K-5 instruction. These results seem to indicate more conceptual understanding, a strong number sense, and increased computational flexibility than they had seen in the past. In this article, the author shares the data and the process that middle-grades teachers undertook to learn about their students. She describes how middle-grades teachers used the Connected Mathematics Project (CMP) for mathematics instruction. Overall, the process of learning about the computational knowledge that students bring to middle school has highlighted the importance of flexibility.
Krebs, A. S. (1999). Students' algebraic understanding: A study of middle grades students' ability to symbolically generalize functions. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 60(6). (ProQuest ID No. 733526481)
ABSTRACT: The publication of the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards in 1989 was pivotal in mathematics reform. The National Science Foundation funded several curriculum projects to address the vision described in the Standards. After these materials were developed and implemented in classrooms, questions arose surrounding students' learning and understanding. This study investigates students' learning in a reform curriculum. Specifically, "What do eighth grade students know about writing symbolic generalizations from patterns which can be represented with functions, after three years in the Connected Mathematics Project curriculum?"
The content, the curriculum, the data, and the site chosen define the study. Initially, the study surrounded students' algebraic understanding, but I focused it to investigate students' ability to symbolically generalize functions. Although this selection is a particular slice of algebra it represents a significant piece of the discipline.
I selected the Connected Mathematics Project (CMP) as the curriculum. I supported the authors' philosophy that the teaching and learning of algebra is an ongoing activity woven through the entire curriculum, rather than being parceled into a single grade level.
The data surrounded the solutions of four performance tasks, completed by five pairs of students. These tasks were posed for students to investigate linear, quadratic, and exponential situations. I collected and analyzed students' written responses, video recordings of the pairs' work, and follow-up interviews. The fourth choice determined the site. I invited Heartland Middle School, a pilot site of the CMP to participate in this study. I approached a successful teacher, Evelyn Howard, who allowed her students to participate. Together, we selected ten students who were typical students in her classroom to participate in this study.
In conclusion, I present two major findings of this study surrounding students' understanding of algebra. First, students who had three years in the Connected Mathematics Project curriculum demonstrated deep understanding of a significant piece of algebra. And second, teachers can learn much more about students' understanding in algebra by drawing on multiple sources of evidence, and not relying solely on students' written work.
Lachance, A., & Confrey, J. (2003). Interconnecting content and community: A qualitative study of secondary mathematics teachers. Journal of Mathematics Teacher Education, 6(2), 107- 37.
ABSTRACT: The publication of the National Council of Teachers of Mathematics initial Standards(1989) has acted as a catalyst to begin reforming the way mathematics is taught in the USA. However, the literature regarding reform movements suggests that changing our educational systems requires overcoming many barriers and is thus difficult to achieve. Reform in mathematics education, like reform movements in other areas of education, has thus been slow to take hold. One structure that has been shown to support educational reform, particularly instructional reform, has been teacher community. This paper discusses a professional development intervention that attempted to start a professional community among a group of secondary mathematics teachers through in-service work on mathematical problem solving and technology. The results of this study suggest that the use of mathematical content explorations in professional development settings provides a means to help mathematics teachers build professional communities. Together, these two components –mathematical content explorations and teacher community – provided these secondary mathematics teachers with a strong foundation for engaging in the reform of their mathematics classes.
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.
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, R. A. (2004). Generation of mathematical knowledge through teacher practice: Study of a novice elementary teacher. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(12). (ProQuest ID No. 845705381)
ABSTRACT: Research on teachers' knowledge has shown that elementary teachers often lack the deep, flexible, and conceptual mathematical understandings necessary for reform efforts in mathematics education to be realized in classroom practice. In order to meet the complex demands of developing a reform-oriented teacher practice, a considerable amount of teacher learning must take place through participation in the activity of teacher practice.
Using case study methods, this research analyzed the practice of one 1st-year elementary teacher as she implemented a reform-based curriculum program (Connected Mathematic Project) and participated in the school, classroom, and reform (i.e., curriculum materials and professional development) communities of practice. Data were collected from observations of three units of instruction, professional development sessions, concept maps, and interviews with the case study teacher and members of the school community. Analysis revealed the key role curriculum materials played in the generation of mathematical knowledge. The classroom and reform communities acted as catalysts in the teacher's participatory practices, which generated expanded, connected, and unresolved mathematical knowledge.
Pradere, S. (2007). Effective staff development connected to increased student achievement. (Doctoral dissertation). Dissertation Abstracts International, 68(3). (ProQuest ID No. 1310415901)
ABSTRACT: School districts expend considerable resources to establish effective staff development opportunities that lead to increased student achievement. This research project focused on the development, implementation, and evaluation of a school based staff development project built around four distinct instructional elements: teacher instructional practices, student engagement, stating the objective, and developing a literacy rich environment. Specifically, the study addressed the following research questions: (1) Did teachers' instructional practices change as a result of participating in the professional development program? (2) If teachers adopted the new instructional practices, did the changes have an impact on student performance as calculated on the Measures of Academic Progress (MAP) assessment? The study was established within a mixed methodology design in which changes in teacher performance were measured using qualitative research methods including survey, interview, and classroom observation data sets. To measure changes in student performance, traditional univariate and multivariate statistical techniques were utilized including a t-test, analysis of variance, and K-means cluster analysis. To conduct the study the researcher: (1) facilitated the design of the staff development model; (2) provided or facilitated foundation staff development on four key instructional elements to both teachers and administrators; (3) provided guidance to administrators on gathering key data; (4) provided support to teacher leaders and administrators on methods for coaching teachers adopting new practices; (5) observed teachers utilizing skills in practice; (6) gathered both perception and observation data related to teacher implementation of four key elements; (7) gathered and processed student academic performance data; and (8) studied the results measuring the impact of staff development on both teacher practices and student performance. The results of the study verified: (1) that teachers adopted or maintained teacher skill levels related to key instructional practices; (2) students' actual mean growth rates on MAP assessment exceeded projected mean growth rates in reading and language but not mathematics; and (3) students whose teachers exceeded proficient skill levels in instructional practices and student engagement demonstrated higher performance levels in reading and language on the MAP assessment than those students whose teachers met or approached desired skill levels in those two areas.
Wilt, B. J. (2007) Preservice teachers to inservice teachers: Teaching for social justice. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 68(10). (ProQuest ID No. 1251814391)
ABSTRACT: The purpose of this research project was to explore how preservice teachers, who are now currently inservice teachers, who took an undergraduate secondary education course with a focus on teaching for social justice, currently, make sense of what it means to teach for social justice. The participants in this study took the same secondary education course for preservice teachers which focused on critical consciousness raising experiences in order to promote teaching for social justice in classrooms. My participants took this course when they were working on their undergraduate degrees in education. This course was the one course in the education program that brought together students in each of the content specific discipline areas of the program--mathematics, science, social studies, language and literacy, and world languages (Bullock, 2004). The course was taken the semester prior to student teaching and occurred during the first 10 weeks of the semester followed by a five-week practicum (Bullock, 2004). In order to conduct my research project I solicited sixteen secondary education teachers, who were previously enrolled in the same undergraduate teacher education program (mentioned above) at a major university in the Mid-Atlantic region of the United States to volunteer to participate in this study. The inservice teachers all took the same secondary education course as preservice teachers which focused on teaching for social justice.
There were many factors that influenced the participant's perspectives about teaching for social justice as well as the degree to which they taught for social justice. All these factors--the undergraduate course rooted in critical consciousness raising experiences, sociocultural structures, political structures, contextual influences, hidden curriculum, teaching stance, teaching praxis--connected to power, privilege, and oppression through issues such as race, ethnicity, class, culture, sexual preference, language, ability, etc.
Both participants self-admittedly teach for social justice, however, the degree to which this takes place varies depending on their respective perspectives on what it means to teach for social justice. Jim does not teach for social justice and is less inclined to trouble and challenge dominant perspectives because he is uncomfortable with difference. He also does not understand the sociocultural mechanisms that reproduce hegemony and is part of the complicit process rather than part of the solution. Neil teaches for social justice to a certain degree and is more inclined to trouble and challenge the status quo and hegemonic mechanisms. However, he does this by teaching for the other (Kumashiro, 2002) and teaching about the other (Kumashiro, 2002) but does not teach in a manner that is critical of privileging and Othering (Kumashiro, 2002).
This study suggests that more research is needed in order to explore and understand how teachers who have an awareness of teaching for social justice actually teach for social justice. This exploration and understanding needs to look at the broad scope of the influences on teachers and how these influences impact teaching for social justice. In addition, teacher education programs must emotionally and structurally embrace curricula rooted in social justice in order to promote teaching for social justice in a way that preservice teachers can also embrace and incorporate in to their teaching praxis. If preservice teachers are to do this they need to understand approaches like education for the Other, education about the Other, education that is critical of privileging and Othering, and education that changes students and society (Kumashiro, 2002) in order to teach for social justice.