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Annotated
Bibliography of Research and
Other Publications about Core-Plus Mathematics
Last Updated: 23
June 2005Research
Articles in Journals
Other Peer-Reviewed Journal Articles
Book Chapters Reporting Research
Other Book Chapters
Papers Presented at Research Conferences
CPMP Field-Test Reports
Dissertations
Other Publications
| Research Articles in Journals | |
|---|---|
| Schoen, H. L., & Hirsch, C. R. (2003). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, (110)2, 109-123. | |
| This article briefly discusses the recent history of mathematics reform in high school, and then reports on research evidence for one of the new NSF-funded curriculum projects, the Core-Plus Mathematics Project (CPMP). Implications for collegiate mathematics are also discussed. A summary of the results of several studies using a range of achievement measures comparing CPMP students to comparable students in more traditional high school mathematics curricula is given on page 114: "Thus, research to date indicates that CPMP students perform particularly well [and better than the comparison students] on measures of conceptual understanding, interpretation of mathematical representations and calculations, and problem solving in applied contexts. Their performance is also relatively strong in content areas like statistics and probability that are emphasized in the curriculum. On measures of algebraic manipulative skills, CPMP students usually, but not always, score as well as students in more traditional curricula." A study of student performance on a mathematics placement test used at a major university is summarized on page 116: "On the algebra subtest, the means of the [traditional] precalculus students and the CPMP Course 4 students were virtually identical. On the intermediate algebra subtest, the mean of the precalculus group was greater than that of the Course 4 group. The only statistically significant difference in means was on the calculus readiness subtest (t = 4.93, p < 0.01). That difference favored the CPMP students." |
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| Schoen, H. L., Finn, K. F., Cebulla, K. J., & Fi, C. (2003). Teacher variables that relate to student achievement when using a standards-based curriculum. Journal for Research in Mathematics Education, (34)3, 228-259. | |
| This article reports results from a study of instructional practices that relate to student achievement in high school classrooms in which a standards-based curriculum (Core-Plus) was used. Regression techniques were used to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26 schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical expectations were positively related to growth in student achievement. | |
| Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Sangtong, J., & Fey, J. T. (2000). Effects of Standards-based mathematics education: a study of the Core-Plus Mathematics Project algebra and functions strand. Journal for Research in Mathematics Education. (31)3, 328-361. | |
| Students in CPMP Course 3 and those in more traditional Algebra II classes, matched on measures of eighth-grade mathematics achievement, were administered a researcher-developed test of algebraic understanding, problem solving and procedural skill at the end of the school year. CPMP students scored significantly better on the subtests of understanding and problem solving, and Algebra II students scored significantly better on the subtest of paper-and-pencil procedures. Scores and student work are discussed by item in this paper. | |
| Wilson, M. R., & Lloyd, G. M. (2000). The Challenge to Share Mathematical Authority with Students: High School Teachers Reforming Classroom Roles and Activities through Curriculum Implementation. Journal of Curriculum and Supervision, 15, 14-169. | |
| This article explores the experiences of three mathematics teachers as they implemented a nontraditional high school curriculum (Core-Plus Mathematics Project). During their implementation of the new curriculum, all three veteran teachers struggled with their own and their students' expectations about what constitutes appropriate mathematical activity in the classroom; in particular, re-negotiation of mathematical authority. | |
| Lloyd, G. M. (1999). Two teachers' conceptions of a reform-oriented curriculum: Implications for mathematics teacher development. Journal of Mathematics Teacher Education, 2, 227-252. | |
| This paper describes the ways in which two high school teachers experienced the Core-Plus mathematics curriculum. In elaborating how the teachers experienced the curriculum, the focus is on the teachers' conceptions of cooperative explorations of mathematical situations. The results elaborate how the curriculum materials were experienced as a challenging vision of instructional practice for one teacher, and as a constraint of a personal vision for another teacher. Discussion of the contrasting ways the two teachers experienced the curriculum advances and illustrated the notion that it does not make sense to view the curriculum "as such" - for it is always a curriculum experienced by some person in some way. | |
| Lloyd, G. M., & Wilson, M. R. (1998). Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education. 29(3), 248-274. | |
| This case study investigates the content conceptions of an experienced high school mathematics teacher and links those conceptions to their role in the teacher's first implementation of reform-oriented curricular materials during a 6-week unit on functions. | |
| Hirsch, C. R. & Coxford, A. F. (1997). Mathematics for all: Perspectives and promising practices. School Science and Mathematics, 97(5), 232-241. | |
| This article describes CPMP perspectives on a new curriculum organization for high school mathematics, identifies implications of these perspectives for promoting access and equity for all students, and reports some of the supporting oral data from the ongoing formative evaluation of the curriculum. The focus is on diversity issues related to ability, prior knowledge, gender, interests, and learning styles. | |
Other Peer-Reviewed Journal Articles |
|
| Harris, K., Marcus, R., McLaren, K., & Fey, J. (2001). Curriculum materials supporting problem-based teaching. School Science and Mathematics, 101(6), 310-318. | |
| This article describes ways in which a curriculum can support the teaching of mathematics through problem solving. Several examples are drawn from the Core-Plus Mathematics curriculum. | |
| Martin, T. S., Hunt, C. A., Lannin, J., Leonard Jr., W., Marshall, G. L., & Wares, A. (2001). How reform secondary mathematics textbooks stack up against NCTM's Principles and Standards. Mathematics Teacher, 94(7), 540-545, 589. | |
| The authors examine five reform high school mathematics textbook series, including the Core-Plus Mathematics Project texts, Contemporary Mathematics in Context (CMIC), to determine how well they are aligned with the NCTM's Principles and Standards for School Mathematics (PSSM). CMIC was rated highest among the four programs in each of the process standards, that is, problem solving, reasoning and proof, communication, connections, and representations. CMIC was also rated a '+' for inclusion of all content topics from PSSM. | |
| Ziebarth, S. W. (2001). PRIME-TEAM: The University of Iowa local systemic change project. Mathematics Teacher, 94(4), 336. | |
| This article describes the three-year PRIME-TEAM project, a teacher enhancement project that focused on helping 65 Iowa teachers in 25 schools prepare for and deliver the CPMP curriculum in their classrooms. Each summer the participants attended a one-week workshop on implementing the CPMP course that they would be teaching in the following school year. During the academic year, participants met four times to discuss issues that had arisen locally and to look more deeply at the curriculum. Counselors and administrators from the participating schools attended one of these annual meetings. Participants were very positive about their overall experience in PRIME-TEAM, and the academic year support meetings were judged to be particularly helpful. | |
| Van Zoest, L. R., & Ritsema, B. E. (1998). Fulfilling the call for mathematics education reform. NCSM Journal of Mathematics Education Leadership, 1(4), 5-15. | |
| This article addresses the implementation challenges created by adoption of innovative curricula and provides information regarding a professional development effort based on the Core-Plus Mathematics curriculum. | |
| Ziebarth, S. W. (1998). Iowa Core-Plus Mathematics Project is evaluated as a success. ICTM Journal 26, 12-21. | |
| This article reports some of the main results of an evaluation of the University of Iowa Modeling Innovation in Mathematics Education Project (MIME) involving nine Iowa high schools that adopted Core-Plus Mathematics in the 1996-1997 school year. The evaluation focused on two main questions: the effectiveness of both the teacher training model and implementation of the Core-Plus Mathematics material. The article summarizes results on the implementation of Core-Plus Mathematics and student outcomes in MIME classrooms. | |
| Schoen, H. L., & Ziebarth, S W. (1997). A progress report on student achievement in the Core-Plus Mathematics Project field test. NCSM Journal of Mathematics Education Leadership, 1(3), 15-23. | |
| This article is a shorter version of the previous one that is refocused for a mathematics education leadership audience. | |
| Coxford, A. F., & Hirsch, C. R. (1996). A common core of math for all. Educational Leadership, 53 (8), 22-25. | |
| The article describes the Core-Plus Mathematics curriculum with a focus on how it works for all students, including heterogeneous groups, in terms of race, educational background, gender, and ability. A curriculum overview and samples from a model lesson are provided, together with a brief description of achievement results. | |
| Schoen, H. L., Fey, J. T., Hirsch, C. R., & Coxford, A. F. (1999). Issues and options in the math wars. Phi Delta Kappan, 80(6), 444-453. | |
| This article revisits the historical background for the development of the 1989 NCTM Curriculum and Evaluation Standards, including the attempts at gaining a consensus among professional organizations with interest in mathematics and its related fields. Specific features of a 9-12 curriculum developed by the Core-Plus Mathematics Project that is aligned with the NCTM Standards are described. Finally, some results from the evaluation of the CPMP curriculum that have a bearing on some of the main issues raised by critics of the NCTM reform effort are presented and discussed. | |
| Hirsch, C. R., Coxford, A. F., Fey, J. T., & Schoen, H. L. (1995). Teaching sensible mathematics in sense-making ways with the CPMP. Mathematics Teacher, 88(8), 694-700. | |
| The article gives an overview of the Core-Plus Mathematics curriculum, focusing on mathematics as "sense-making." Included are the organization of the curriculum, the mathematical strands, the four-phase instructional model, the three-year "core" program accommodating all students, the curriculum-embedded assessment, and lesson samples from a Course 1 unit. | |
Book Chapters Reporting Research |
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| Schoen, H. L., & Hirsch, C. R. (2003). The Core-Plus Mathematics Project: Perspectives and student achievement. In S. Senk and D. Thompson (Eds.), Standards-Oriented School Mathematics Curricula: What Are They? What Do Students Learn? pp. 311-344. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. | |
| This chapter provides an overview of the CPMP curriculum in terms of its design and theoretical framework and a profile of student outcomes. Achievement results are reported from the three-year Core-Plus field test (1994-97) on the standardized Ability to Do Quantitative Thinking (ATDQT) test for each subtest and for students who had scored in the top, middle, and bottom third on the ATDQT pretest. Results on measures of students' understanding of algebraic and geometric concepts and methods and of statistics, probability and discrete mathematics are also presented. Students' perceptions and attitudes about mathematics and about their mathematics course are summarized. Finally, SAT and ACT scores of students in CPMP are compared to those in more traditional curricula. On all measures except paper-and-pencil algebra skills, students in CPMP do as well as or better than those in traditional curricula. | |
| Schoen, H. L., & Ziebarth, S. W. (1998). High school mathematics curriculum reform: Rationale, research, and recent developments. In P. S. Hlebowitsh & W. G. Wraga (eds.), Annual Review of Research for School Leaders. Pp. 141-191. New York: Macmillan Publishing Company. | |
| The present mathematics curriculum reform effort is examined in light of research on the process of changing curriculum and instruction. Extended discussions of four of the most important and perhaps the most ambitious goals are included: (1) mathematical literacy; (2) core high school mathematics curriculum; (3) technological tools in mathematics instruction; and (4) assessment alternatives. Related research as well as examples and evaluation results from the Core-Plus Mathematics curriculum are included for each goal area. | |
Other Book Chapters |
|
| Hirsch, C. R. (2001). The Core-Plus Mathematics Project (CPMP). In L. S. Grinstein and S. I. Lipsey (eds.), Encyclopedia of Mathematics Education. (Pp. 159-161). New York, NY: Routledge Falmer. | |
| An overview of the Core-Plus Mathematics curriculum highlights the alignment with the NCTM Standards in terms of a core mathematics program for all students, connectedness of topics, and use of various assessment alternatives. | |
| Hirsch, C. R. & Weinhold, M.L. W. (1999). Everybody counts - including the mathematically promising. In L. Sheffield (ed.), Developing Mathematically Promising Students. (Pp. 233-241). Reston, VA: National Council of Teachers of Mathematics. | |
| The article examines curricular and instructional issues of teaching mathematically promising students, and draws from experiences of teachers using the Core-Plus Mathematics Project curriculum materials with promising students in heterogeneous classes, in accelerated classes, and in special mathematics and science centers. | |
| Hart, E. W. (1998). Algorithmic problem solving in discrete mathematics. In L. Morrow and M. J. Kenney (eds.), Teaching and Learning of Algorithms in School Mathematics, 1998 Yearbook of the National Council of Teachers of Mathematics. (pp. 251-267). Reston, VA: The Council. | |
| The article discusses algorithmic problem solving and how it is developed in the discrete mathematics strand of the Core-Plus Mathematics curriculum. Included are two model lessons. | |
| Hart, E. W., & Stewart, J. (1998). Reflections on high school reform and implications for middle schools. In L. Leutzinger (Ed.), Mathematics in the Middle Grades. (pp. 65-71). Reston, VA: National Council of Teachers of Mathematics. | |
| The authors describe some of the changes in content, teaching, and assessment that are common to the new reform high school programs, with examples from the Core-Plus Mathematics Project. They also consider implications for the role that middle school mathematics education plays in the development of common themes. | |
| Hart, E. W. (1997). Discrete mathematical modeling in the secondary curriculum: Rationale and examples from the Core-Plus Mathematics Project. In J. Rosenstein and F. Roberts (eds.), Discrete Mathematics in the Schools. Providence, RI: DIMACS Series in Theoretical Computer Science and Discrete Mathematics, American Mathematical Society. | |
| The article defines discrete mathematics, describes which areas of discrete math should be incorporated into the high school curriculum, and suggests methods for integrating these topics. Included are two examples from the discrete mathematics strand of the Core-Plus Mathematics curriculum. | |
| Schoen, H. L., Bean, D. L., & Ziebarth, S. W. (1996). Embedding communication throughout the curriculum. In P. C. Elliott and M. J. Kenney (eds.), Communication in Mathematics: K-12 and Beyond, 1996 Yearbook of the National Council of Teachers of Mathematics. (Pp. 170-179). Reston, VA: The Council. | |
| The main theme of this article is that students learn to communicate mathematically by being in an environment where such communication is a regular, natural, and valued occurrence. Examples of curriculum-embedded communication from the Core-Plus Mathematics curriculum materials highlight communication in group investigations, written reflections, quizzes and examinations, and extended projects. | |
Papers Presented at Research Conferences |
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| Ziebarth, S. W. (2003). A report on advances in secondary mathematics curriculum development in the United States and imminent new directions: Core-Plus Mathematics as a case study. Paper presented at the Proceedings of the International Conference on Education. Honolulu, HI. | |
| This report uses the Core-Plus Mathematics Project (CPMP) as a case-study example of how new high school mathematics curricula have developed in the United States over the last decade since the publishing of the first NCTM Standards documents (1989, 1991). Beginning with a description of both the curriculum itself and the rationale used to guide its development, the report highlights the associated research and evaluation results that have emerged in terms of student achievement data on a variety of measures. The report concludes by documenting the growth of CPMP-related professional development activities that are an integral part of successful implementation. A consistent theme throughout is the notion that, in general, curriculum development is an ongoing process and specifically that those results highlighted in this report are used to inform a new revision of Core-Plus Mathematics currently underway. | |
| Schoen, H. L., Cebulla, K. J., & Winsor, M. S. (2001). Preparation of students in a Standards-oriented mathematics curriculum for college entrance tests, placement tests, and beginning mathematics courses. Paper presented at the Annual Meeting of the American Educational Research Association. Seattle, WA. ERIC: ED 453 217. | |
| This paper examines the level of preparation for college entrance tests, university mathematics placement tests, and beginning college mathematics courses of students who complete the CPMP curriculum. Compared to similar students completing a traditional high school curriculum, CPMP students score as well as or better on the SAT I Mathematics Test. They score better on the ACT Science Reasoning Test. On ACT Mathematics, they score as well after Course 4 but not as well after Course 3. On a typical university mathematics department placement test, CPMP students score essentially the same on algebraic skills and significantly better on concepts and applications that underlie calculus. Four years of data from two similar high schools in the same school district, one using a traditional curriculum and one using CPMP, shows that CPMP students attending the same major university earn slightly higher grades in beginning mathematics courses. In the CPMP high school, students' mathematics grades increased across most courses including Calculus I following the adoption of CPMP. | |
| Schoen, H. L., Finn, K. F., Griffin, S. F., & Fi, C. (2001). Teacher variables that relate to student achievement in a Standards-oriented curriculum. Paper presented at the Annual Meeting of the American Educational Research Association. Seattle, WA. ERIC: ED 453 265. | |
| This paper describes the classroom practices of 20 teachers during the CPMP Course 1 field test. Ten of these teachers comprise the top quartile of field-test teachers and the other ten the bottom quartile with respect to their students' growth in mathematical achievement over the one-year course. Teachers in the top quartile had strong professional development to prepare them to teach the CPMP curriculum. For the most part, the teachers in the top quartile followed the CPMP guidelines for teaching the CPMP curriculum with understanding while those in the bottom quartile deviated from these guidelines in various ways. For example, the first-quartile teachers used more small group problem explorations. They also did less supplementing with practice worksheets and more skill-oriented test items. Finally teachers in the first quartile tended to have higher expectations of their students as evidenced by homework and grading policies. | |
| Lloyd, G. M., & Wilson, M. R. (1998). Context, representation, and authority: Illustrations of reform-oriented learning about mathematical functions. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego. | |
| Schoen, H. L., Hirsch, C. R., & Ziebarth, S. W. (1998). An emerging profile of the mathematical achievement of students in the Core-Plus Mathematics Project. Paper presented at the Annual Meeting of the American Educational Research Association. San Diego, CA. ERIC: ED 421 351. | |
| Achievement results are reported for the three-year Core-Plus field test (1994-97) on the Standardized Ability to Do Quantitative Thinking (ATDQT) test for all schools with school means as the statistical unit. ATDQT results are also reported by school setting (urban, rural, or suburban), by make-up of classes (heterogeneous, high ability, low ability, and so on), by gender, by English or non-English first language, and for three classrooms of students with exceptionally high mathematical aptitudes. Results are also given for the various subtests of both the CPMP Posttest, an open-ended assessment instrument, and a test comprised of released items from the 1992 National Assessment of Educational Progress. | |
| Schoen, H. L., & Pritchett, J. (1998). Students' perceptions and attitudes in a standards-based high school mathematics curriculum. Paper presented at the Annual Meeting of the American Educational Research Association. San Diego, CA. ERIC: ED 420 518. | |
| This paper presents the results from an attitude scale called Attitude Toward Your Mathematics Course during the three-year Core-Plus field test (1994-97). This scale contains 15 likert-type items and an open-ended writing prompt. Comparisons are made between Core-Plus students and students in more traditional college preparatory mathematics curricula in the same field test schools. Students perceive the Core-Plus curriculum as difficult, at least as challenging as traditional college-prep mathematics courses, but Core-Plus students were more positive about various aspects of the curriculum and of their experience in the classroom than were students in traditional mathematics classes. | |
| Lloyd, G. M., & Wilson, M. R. (1997). The impact of teachers' beliefs about student cooperation and exploration on their interpretations of a secondary mathematics curriculum. In J. Dossey (ed.), Proceedings of the Nineteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 371-376). Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education. | |
| This paper describes two high school teachers' interpretations of and classroom experiences with a reform-oriented mathematics curriculum (Core-Plus Mathematics Project). The study focuses on the teachers' conceptions of cooperative explorations of mathematical situations. The results elaborate how the curriculum materials presented a challenging vision of instructional practices for one teacher, and a constraint to the fulfillment of a personal vision for another teacher. | |
| Lloyd, G. M., & Wilson, M. R. (1997). Teaching and learning through curriculum implementation: Teachers' beliefs about student learning in mathematics. Paper presented at the Annual Meeting of the Eastern Educational Research Association, Hilton Head, South Carolina. | |
| This paper describes the conceptions and experiences of two veteran high school teachers attempting to implement a reform-oriented mathematics curriculum (Core-Plus Mathematics Project) that explicitly supports the goals of the Standards (National Council of Teachers of Mathematics [NCTM], 1989). It focuses on the teachers' beliefs about the meaning and importance of certain mathematical activities, specifically cooperation and exploratory problem-solving. And, it reveals how teachers' beliefs about these issues relate to their interpretations of innovative curricula. | |
| Lloyd, G. M. (1996). Change in teaching about functions: Content conceptions and curriculum reform. In E. Jakubowski, D. Watkins, & H. Biske (Eds.), Proceedings of the Eighteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 200-206). Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education. | |
| A high school mathematics teacher was studied as he taught the Core-Plus curriculum for two years, and this paper focuses primarily on year two findings about the subtle but meaningful changes in his conceptions and instruction evidenced as he gained comfort with the new curriculum. In particular, the paper illustrates how the teacher revised his pedagogical content conceptions through complex interaction of his mathematical conceptions and classroom experiences with students. | |
| Lloyd, G., & Wilson, M. R. (1996). One veteran mathematics teacher's experiences with curriculum reform: Transforming instruction about functions. Paper presented at the Annual Meeting of the American Educational Research Association, New York. | |
| Lloyd, G., & Wilson, M. R. (1996). The experiences of teachers reforming mathematics instruction. In H. Schoen (Chair), Combining large-scale evaluation with focused research in reformed mathematics classrooms. Symposium conducted at the Research Presession of the National Council of Teachers of Mathematics, San Diego. | |
| Lloyd, G., & Wilson, M. R. (1995). The role of one teacher's mathematical conceptions in his implementation of a reform-oriented functions unit. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 233-239). Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education. | |
| Wilson, M. R., & Lloyd, G. (1995). High school teachers' experiences in a student-centered mathematics curriculum. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 162-167). Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education. | |
| This paper describes three mathematics teachers and ten of their ninth grade students as they implemented student-centered and exploration-based curriculum materials (Core-Plus Mathematics Project). The observations and interviews were conducted over a six-week period. One teacher claimed that her main challenge involved student ability to make the right connections without her explanations. Another teacher struggled with the dynamics of operating both small-group and whole-class discussions and ultimately decided not to hold whole-class discussions. A third teacher achieved a more equal balance between teacher-directed and student-centered activities. All three teachers demonstrated more difficulty than did students in changing their expectations about appropriate mathematical activity. | |
CPMP Field-Test Reports |
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| Core-Plus Mathematics Project. (2000). Contemporary Mathematics in Context evaluation results. Chicago, IL: Everyday Learning Corporation. | |
| This booklet summarizes the methodology and main results of the national field tests of Courses 1-4 of the Core-Plus Mathematics Project curriculum. Included are results of studies reporting the performance of CPMP students and comparable students in more traditional curricula on the ITED Ability to Do Quantitative Thinking subtest, a NAEP-based test, the SAT, the ACT, and a university mathematics department placement test, and in beginning college mathematics courses. Also reported are findings from a study of attitudes and beliefs of CPMP students and comparable students in more traditional curricula at the end of their second year of high school mathematics. | |
| Core-Plus Mathematics Project. (1998). Contemporary Mathematics in Context student achievement reports, volume I. Chicago, IL: Everyday Learning Corporation. | |
| This booklet consists of eight reports. The first report summarizes results from the national field test of Courses 1-3 of the Core-Plus Mathematics Project curriculum. The remaining reports contain firsthand accounts by teachers of how the curriculum was implemented in their schools. These reports focus on the positive experiences that teachers and students enjoyed as a result of their use of the Contemporary Mathematics in Context curriculum materials. They also comment on issues of implementation, community involvement, tracking, test results, student and teacher attitudes, and enrollment patterns. | |
| Schoen, H. L., & Ziebarth, S. W. (1998). Assessment of students' mathematical performance: A Core-Plus Mathematics Project field test progress report. Unpublished manuscript, University of Iowa. | |
| This report focuses on standardized achievement test results aggregated across 33 field test schools who were on a regular two-semester schedule. On the Ability to Do Quantitative Thinking, the mathematical subtest of the Iowa Tests of Educational Development, CPMP students in both Course 1 and Course 2 performed better across the distribution than comparison students in more traditional mathematics classes. CPMP students also grew more from the beginning of grade 9 to the end of each of grades 9, 10, and 11 than the nationally representative norm group for this test. At the end of Course 3, CPMP students performed particularly well on NAEP-developed measures of data analysis, probability and statistics and on measures of conceptual understanding. Their performance was somewhat lower in some other content areas and on items assessing procedural outcomes, but still considerably higher than a nationally representative sample of twelfth-grade students. | |
| Schoen, H. L., & Ziebarth, S. W. (1998). Mathematical achievement on standardized tests: A Core-Plus Mathematics Project field test progress report. Unpublished manuscript, University of Iowa. | |
| This report focuses on performance assessments of student achievement aggregated across 33 field test schools who were on a regular two-semester schedule. On project-developed open-ended posttests of mainly algebraic and geometric content, CPMP students in both Course 1 and Course 2 performed significantly better on conceptual, application and problem-solving tasks than comparison students in more traditional mathematics classes. At the end of Course 1, the comparison students performed somewhat better on tasks assessing algebraic procedures, but that difference had disappeared by the end of Course 2. Problem-based interviews were used to gain a better insight into the differences in the mathematical understanding of the CPMP and comparison students. | |
| Schoen, H. L., & Ziebarth, S. W. (1997). A progress report on student achievement in the Core-Plus Mathematics Project field test. Unpublished manuscript, University of Iowa. | |
| Achievement results based on standardized tests (ITED) and CPMP tests compare traditionally tracked students and Core-Plus Mathematics students. Results from both Course 1 and Course 2 are discussed. | |
Dissertations |
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| Cebulla, Kristin J. (2002). High school students' conceptions of correlation after instruction. Unpublished doctoral dissertation, University of Iowa. | |
| This study examines the understandings of high school students about correlation and explores how the use of context in mathematics curricula relates to these understandings. Students were in four groups depending upon their academic year (sophomore or juniors), school, and mathematics course enrolled in during the year of the study (Course 2 or Course 3 of the CPMP curriculum or Algebra II). Overall, students were successful on tasks involving interpretation of scatterplots and estimating correlation coefficients. Students performed better on descriptive tasks than on numeric and analytic tasks. Students used both statistical and non-statistical arguments when drawing and evaluating conclusions and tended to focus on the direction of association rather than the strength of association. Between group differences favoring CPMP students were found in some content categories. | |
| Wyberg, Terrence R. (2002). The relationships among teachers' understanding of mathematical functions, a reform curriculum, and teaching. Unpublished doctoral dissertation, University of Minnesota. | |
| This study
investigated teacher content knowledge related to the concept of
function and how that knowledge influenced their teaching. Twenty-four
CPMP teachers participated in a content knowledge interview. This
interview allowed participants to demonstrate their knowledge of
various features of the function concept including modeling, rates
of change, representation, univalence, and arbitrariness. Based
on the assessment of this interview, sixteen of these teachers participated
in a follow-up interview investigating teaching approaches related
to the same seven features. A theoretical framework was developed
using the work of Dienes, Lesh, and Sfard to analyze both the CPMP
curriculum and the responses provided by the sixteen CPMP teachers.
Classroom observations were also completed on four participants.
All of the data was collected in the spring of 2001. The results
of the study indicate that there is a positive relationship between
mathematical content knowledge and teaching approaches that are
consistent with the intended CPMP curriculum. The teachers with
higher content knowledge provided descriptions of teaching that
emphasized operational understandings while teachers with lower
content knowledge made more mathematical mistakes in their descriptions. The modeling approaches used by the CPMP teachers and the teaching approaches for situations involving modeling are described using the strategies developed by Zbiek. The results of this study indicate that the strategy types are useful for describing both modeling strategies and teaching approaches. The use of graphing calculator technology in the process of modeling and teaching of modeling is also studied. |
|
| Breyfogle, M. L. (2001). Changing mathematical discourse: A case study of a secondary mathematics teacher. Unpublished doctoral dissertation, Western Michigan University. | |
| This study investigated the notion of change that occurred in both teaching and reflection practices of one teacher as he taught Course 1 of the Core-Plus Mathematics curriculum. Data included audiotaped pre-, mid-, and post-interviews, and collaboration sessions that used a Discourse Reflection Tool (DRT) in conjunction with the viewing of videotaped episodes, and videotaped classroom observations. Analysis of transcripts from interviews, collaboration sessions, and selected episodes from the videotaped observations led to a series of findings. Among the findings were the teacher exhibited a shift from explaining away or defending his practices to openly reflecting and considering alternative ways of thinking; the teacher shifted from using general terms while talking about the "natural" development of the discourse to more clearly identifying and articulating the role the teacher plays in developing meaningful mathematical discussions; there was a shift in talking from teacher to student; and there was a shift in the teacher's talk from merely eliciting answers to probing student thinking. | |
| Latterell, C. M. (2000). Assessing NCTM Standards-oriented and traditional students' problem-solving ability using multiple-choice and open-ended questions. Unpublished doctoral dissertation, University of Iowa. | |
| This study investigated how the measured problem-solving ability differs by students' curriculum, traditional or CPMP. Four tests were administered to approximately 550 ninth-graders. The ITED-Q was used in multiple-choice format and as a parallel form with open options. Another test was constructed to test the placement of students in CPMP and was administered in multiple-choice and open-ended format. Questionnaires were administered to determine students' opportunity to learn and the classroom environment. Results indicated that students had the opportunity to learn. The classroom environments were similar. There were no significant differences between the CPMP schools and traditional schools on paper-and-pencil measures. In class observations of students solving challenging, open-ended problems, CPMP students engaged more enthusiastically and tried more solution strategies than traditional students. | |
| Kahan, J. A. (1999). Relationships among mathematical proof, high-school students, and a reform curriculum. Unpublished doctoral dissertation, University of Maryland. | |
| This study assessed proof competence and approaches to proof of 315 end-of-year juniors in three high school sites. In each site, roughly half of the students were enrolled in CPMP Course 3 and the other half in traditional Advanced Algebra. In each site, proof was very difficult for most students, and no significant difference for demonstrated overall competence with proof or for perceiving the need for mathematical proof was found between the groups. Analysis of written answers and interview data suggested several student misconceptions regarding proof and provided some insight into how the teaching of proof could be improved. | |
| Walker, R. K. (1999). Students' conceptions of mathematics and the transition from a Standards-based reform curriculum to college mathematics. Unpublished doctoral dissertation, Western Michigan University. | |
| This research examined students' conceptions about learning, knowing, and doing mathematics after studying four years of CPMP and how those conceptions influenced college mathematics experiences. Upon graduation from high school the students (n = 256) believed that mathematical concepts, principles, and generalizations were slightly more important that facts, formulas, and algorithms, that learning mathematics was more about constructing understanding than memorizing, that doing mathematics was more about making sense out of situations than just solving problems and that mathematics was useful. Case studies of six students', from five different high schools, experiences and thinking throughout the first semester of mathematics at two major midwestern universities are also reported. Among the findings were that none of the six students had difficulty making the transition from the CPMP Standards-based curriculum to college mathematics. | |
| Truitt, B. D. (1998). How teachers implement the instructional model in a reformed high school mathematics classroom. Unpublished doctoral dissertation, University of Iowa. | |
| This study involved the analysis of two experienced Core-Plus teachers' understanding of the CPMP instructional model and how they implemented this model in actual lessons in the classroom. The method of research is a descriptive study involving classroom observations, interviews, and data triangulation. One teacher was successful with the Core-Plus instructional model, while the other teacher stated a belief in the inherent value of the model but exhibited some contradictions in the way his class was conducted. | |
| Kett, J. R. (1997). A portrait of assessment in mathematics reform classrooms. Unpublished doctoral dissertation, Western Michigan University. | |
| Using a case study design, this research documents the assessment practices of four teachers using the Core-Plus Mathematics curriculum in ninth- and tenth-grade classrooms with diverse student populations. Data from teacher interviews, classroom observations, field journals, assessment documents, and teacher journals related to a year-end Capstone assessment identified five major domains into which assessment practices were divided. For each teacher, these domains were analyzed from the perspectives of learning environment, forms of communication, student feedback, and time investment. | |
| Tyson, V. (1995). An analysis of the differential performance of girls on standardized multiple-choice mathematics achievement tests compared to constructed response tests of reasoning and problem solving. Unpublished doctoral dissertation, University of Iowa. | |
| This study involved the analysis of gender differences on performance tests administered to Core-Plus Mathematics students. Boys performed significantly better on pretests, but no significant gender differences were found on posttests. Tyson notes that this result is consistent with the goals of the Core-Plus Mathematics curriculum and its compatibility with female learning styles. | |
Other Publications |
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| Core-Plus Mathematics Project. (1998). A balanced approach to mathematics education: Contemporary Mathematics in Context. Chicago, IL: Everyday Learning Corporation. | |
| This brochure describes how the Contemporary Mathematics in Context (CMIC) curriculum provides a balanced approach to mathematics education. Each section of the brochure identifies one important issue in contemporary mathematics education and describes how it is addressed by CMIC. Section topics include integrated mathematics, algebra, basic skills, practice, logic and proof, theory and applications, technology, effective teaching methods, access and challenge, and preparation for college. A brief summary of research results is given. | |