Annotated Bibliography of Research and
Other Publications about Core-Plus Mathematics

Last Updated: 11 June 2014


Download the Reduced Annotated Bibliography
PDF listing the most helpful items for those
considering adopting Core-Plus Mathematics.


Choose a section for complete bibliography entries:
Research Articles in Journals
Other Peer-Reviewed Journal Articles
Books and Book Chapters Reporting Research
Other Book Chapters
Papers Presented at Research Conferences
CPMP Technical Reports
Dissertations
Other Publications

Research Articles in Journals
Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. Educational Studies in Mathematics, 85(2), 241–263.
  This study reports a content analysis of the development of quadratic equations in national Korean and Core-Plus Mathematics textbooks. The number of topics, contents, and mathematics items were analyzed. The results show that in Korean textbooks some topics are developed relatively earlier than in Core-Plus Mathematics. However, the Core-Plus Mathematics textbooks include more problems requiring explanations and various representations and problems requiring higher-level cognitive demand.
Chávez, Ó., Tarr, J. E., Grouws, D. A., & Soria, V. M. (2013, December). Third-year high school mathematics curriculum: Effects of content organization and curriculum implementation. International Journal of Science and Mathematics Education. Retrieved from http://link.springer.com/article/10.1007%2Fs10763-013-9443-7
  This study examined the effect of curriculum organization in U.S. high schools where students could freely choose to study mathematics from textbooks that employed one of two types of content organization: an integrated approach or a (traditional) subject-specific approach (published by Glencoe, Holt, McDougal Littell, or Prentice Hall). The study involved 2,242 high school students, enrolled in either Core-Plus Mathematics Course 3 or Advanced Algebra, in 10 schools in 5 geographically dispersed states. Taking into account curriculum implementation and students' prior mathematics learning, we analyzed two end-of-year outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in Core-Plus Mathematics scored significantly higher than those in the subject-specific curricula on the common objectives test. In both outcome measures, gender and prior achievement were significant student-level predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacher-level, in addition to curriculum type, teachers' orientation and free-and-reduced-lunch eligibility were significant moderating factors. Opportunity to learn, implementation fidelity, teacher experience, and professional development were not significant predictors.
Tarr, J. E., Grouws, D. A., Chávez, Ó., & Soria, V. M. (2013). The effects of content organization and curriculum implementation on students' mathematics learning in second-year high school courses. Journal for Research in Mathematics Education, 44(4), 683–729.
  We examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using one of two content organizational structures: an integrated approach, Core-Plus Mathematics, or a (traditional) subject-specific approach (published by Glencoe, Holt, McDougal Littell, or Prentice Hall). The study involved 3,258 high school students, enrolled in either Core-Plus Mathematics Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. We constructed three-level hierarchical linear models of scores on three end-of-year outcome measures: a test of common objectives, an assessment of problem solving and reasoning, and a standardized assessment of conceptual understanding and problem solving. Students in Core-Plus Mathematics scored significantly higher than those in the subject-specific curricula on the standardized achievement test. Significant student-level predictors included prior achievement, gender, and ethnicity. At the teacher level, in addition to curriculum type, the opportunity to learn and classroom learning environment factors demonstrated significant power in predicting student scores, whereas implementation fidelity, teacher experience, and professional development were not significant predictors.
Grouws, D. A., Tarr, J. E., Chávez, Ó., Sears, R., Soria, V. M., & Taylan, R. D. (2013). Curriculum and implementation effects on high school students' mathematics learning from curricula representing subject-specific and integrated content organizations. Journal for Research in Mathematics Education, 44(2), 416–463.
  This study examined the effect of two types of mathematics content organization on high school students' mathematics learning while taking into account curriculum implementation and student prior achievement. Hierarchical linear modeling with three levels showed that students who studied from the integrated curriculum, Core-Plus Mathematics, were significantly advantaged over students who studied from subject-specific curricula (published by Glencoe, Holt, McDougal Littell, or Prentice Hall) on three end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.
Thompson, D. R., Senk, S. L., & Johnson, G. J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253–295.
  The nature and extent of reasoning and proof in the written (i.e., intended) curriculum of 20 contemporary high school mathematics textbooks were explored. Both the narrative and exercise sets in lessons dealing with the topics of exponents, logarithms, and polynomials were examined. The extent of proof-related reasoning varied by topic and textbook. Overall, about 50% of the identified properties in the three topic areas were justified, with about 30% of the addressed properties justified with a general argument and about 20% justified with an argument about a specific case.
Dupuis, D. N., Medhanie, A. G., Harwell, M. R., Lebeau, B., & Monson, D. (2012). A multi-institutional study of the relationship between high school mathematics achievement and performance in introductory college statistics. Statistics Education Research Journal, 11(1), 4–20.
  This study examined the effects of prior mathematics achievement and completion of a commercially developed, National Science Foundation-funded, or University of Chicago School Mathematics Project high school mathematics curriculum on achievement in students' first college statistics course. Specifically, we examined the relationship between students' high school mathematics achievement and high school mathematics curriculum on the difficulty level of students' first college statistics course, and on the grade earned in that course. In general, students with greater prior mathematics achievement took more difficult statistics courses and earned higher grades in those courses. The high school mathematics curriculum a student completed was unrelated to statistics grades and course-taking.
Harwell, M. R., Medhanie, A. G., Post, T. R., Norman, K. W., & Dupuis, D. N. (2012). Preparation of students completing a Core-Plus or commercially developed high school mathematics curriculum for intense college mathematics coursework. Journal of Experimental Education, 80(1), 96–112.
  The purpose of this study was to examine the college mathematics achievement and course-taking patterns of students at a large public research university who completed a commercially developed or standards-based (Core-Plus Mathematics) high school mathematics curriculum, and who subsequently completed at least two college mathematics courses of difficulty level at or beyond precalculus mathematics. Mathematics course-taking and achievement data across eight college semesters were analyzed for a sample of 1,588 students. Findings indicated that students (including science, technology, engineering, and mathematics majors) were equally prepared for intense college mathematics coursework regardless of which high school mathematics curriculum they completed. These findings inform high school mathematics curriculum adoption decisions for college-bound students, and college policies and practices for advising students enrolling in mathematics courses.
Post, T. R., Monson, D. S., Anderson, E., & Harwell, M. R. (2012). Integrated curricula and preparation for college mathematics. The Mathematics Teacher, 106(2), 138–143.
  This study examined the performance of students in one suburban school district that implemented NSF-funded mathematics curricula in grades K–12 for all students. Even though this district was high achieving before the change, it is now one of the top two or three highest-performing districts in the state regarding graduation rates, standardized test scores, the number and percentage of students in AP calculus and AP statistics courses, the percent- age of students who take four full years of college- intending mathematics (through Core-Plus Mathematics Course 4), and the percentage of students enrolled in four-year post- secondary institutions (Monson, 2011).

The results of this study have been validated by several additional multi-school studies in Minnesota. The NSF-funded curricula included in these studies prepare students for college mathematics equally as well as commercially developed, single-subject approaches. Evidence further suggests there may also be precollege pedagogical and sociological advantages to adopting NSF-funded curricula.
Teuscher, D., & Reys, R. E. (2012). Rate of change: AP calculus students' understandings and misconceptions after completing different curricular paths. School Science and Mathematics, 112(6), 359–376.
  This study examined Advanced Placement calculus students' mathematical understanding of rate of change, after studying four years of college preparatory mathematics using Core-Plus Mathematics or conventional, single-subject texts. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior achievement with the Iowa Algebra Aptitude Test, students from these two paths performed comparably (F = 3.54, p = .063) on the PCA. Student errors on the three instruments revealed a lack of understanding of the interpretation or meaning of rate of change regardless of the curricular path.
Chávez, Ó., Papick, I., Ross, D. J., & Grouws, D. A. (2011). Developing fair tests for mathematics curriculum comparison studies: The role of content analyses. Mathematics Education Research Journal, 23(4), 397–416.
  This paper describes the process of development of assessment instruments for a three-year longitudinal comparative study that focused on evaluating U.S. high school students' mathematics learning from two distinct approaches to content organization: curricula built around a sequence of three full-year subject-specific courses (Algebra 1, Geometry, and Algebra 2) and the Core-Plus Mathematics sequence of integrated mathematics courses (algebra and geometry content, together with functions, data analysis, probability, and discrete mathematics integrated in each year). The study was conducted in six school districts in five states involving over 4,000 students from schools that were using both curricular approaches but with different groups of students. In order to develop assessment instruments that were not biased toward either of the two curriculum approaches (Fair Tests), an iterative process of content analyses, identification of common topics, internal and external reviews, pilot tests, and revisions was followed, resulting in five tests that were used in the three years of the study. Results indicate that these tests have solid discrimination properties and address adequately mathematics content common to both secondary curriculum programs. The corresponding scoring rubrics are highly reliable, with interrater reliability above 94% for all tests. Mathematics education researchers involved in curriculum comparison studies need to conduct content analyses of the curriculum materials under study in order to identify salient relationships between curriculum programs and student outcomes.
Norman, K. W., Medhanie, A. G., Harwell, M. R., Anderson, E., & Post, T. R. (2011). High school mathematics curricula, university mathematics placement recommendations, and student university mathematics performance. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21(5), 434 455.
  Recent "math wars" have drawn attention to how well various high school mathematics curricula prepare students for college-level mathematics. The purpose of this study was to investigate the relationship between the type of high school mathematics curricula (integrated or conventional single-subject) and students' post-secondary mathematics placement recommendation, specifically how students responded to the mathematics placement recommendations and the students' performance in their first college mathematics class. The results showed no relationship between students' participation in a particular high school mathematics curriculum and mathematics placement recommendation, or between student high school mathematics curriculum and students' responses to a university mathematics placement recommendation. However, students who took a more/less difficult class than what was recommended achieved significantly lower/higher grades than those who followed the recommendation. The findings have implications for high school mathematics curricula selection, post-secondary student placement, and future research in this area.
Capraro, M. M., Capraro, R. M., Yetkiner, Z. E., Rangel-Chavez, A. F., & Lewis, C. W. (2010). Examining Hispanic student mathematics performance on high-stakes tests: An examination of one urban school district in Colorado. Urban Review: Issues and Ideas in Public Education, 42(3), 193–209.
  Mathematics achievement scores from the Colorado Student Assessment Program and Measurement of Academic Progress for Hispanic 9th and 10th grade students (n = 1,318) who used the Core-Plus Mathematics program were compared to the performance of students with other demographic backgrounds (n = 2,003) who used the same curriculum. The results of this study indicated that Hispanic students showed modest gains. However, their relative position compared to other ethnic groups remained low.
Post, T. R., Medhanie, A., Harwell, M., Norman, K. W., Dupuise, D. N., Muchlinski, T., Anderson, E., & Monson, D. (2010). The impact of prior mathematics achievement on the relationship between high school mathematics curricula and post-secondary mathematics performance, course-taking, and persistence, Journal for Research in Mathematics Education, 41(3), 274–308.
  This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student post-secondary mathematics performance. The sample (N = 4,144 from 266 high schools) was partitioned into three strata by ACT mathematics scores. Students completing three or more years of a commercially developed, University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curricula comprised the sample. Of interest were comparisons of the difficult level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over eight semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed.
Davis, J., & Shih, J. (2007). Secondary options and post-secondary expectations: Standards-based mathematics programs and student achievement on college mathematics placement exams. School Science and Mathematics, 107, 336–346.
  Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core-Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate; however, much less is known about how prepared these students are for post-secondary education. Therefore, this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards-based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three or four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.
Harwell, M., Post, T. R., Maeda, Y., Davis, J., Cutler, A., Anderson, E., & Kahan, J. A. (2007). Standards-based mathematics curricula and secondary students' performance on standardized achievement tests. Journal for Research in Mathematics Education, 38(1), 71–101.
  The current study examined the mathematical achievement of high school students enrolled for three years in one of the three 1st-edition NSF-funded Standards-based curricula (Core-Plus Mathematics, Interactive Mathematics Program, Mathematics Modeling Our World). The focus was on traditional topics in mathematics as measured by subtests of a standardized achievement test and a criterion-referenced test of mathematics achievement. Students generally scored at or above the national mean on the achievement subtests. Hierarchical linear modeling results showed that prior mathematics knowledge was a significant but modest predictor of achievement, student SES had a moderate effect, and increasing concentrations of African-American students in a classroom were associated with a stronger effect of attendance on achievement. No differences on the standardized achievement subtests emerged among the Standards-based curricula studied once background variables were taken into account. The two suburban districts providing data for the criterion-referenced test achieved well above the national norm.
Schoen, H. L., & Hirsch, C. R. (2003, February). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, 110(2), 109–123.
  This paper 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 Midwest 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.

Group calculus readiness test items means differed significantly on 12 of the twenty calculus readiness items, 11 in favor of the CPMP students and one in favor of the other direction.
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 paper 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 Mathematics) 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 1st edition Course 3 classes and those in more conventional 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 manipulation of algebraic expressions when those expressions were presented free of application context. 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(2), 146–169.
  This article explores the experiences of three mathematics teachers as they implemented a nontraditional high school curriculum (Core-Plus Mathematics). 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 illustrates 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
Hart, E. (2008). Vertex-edge graphs: An essential topic in high school geometry. Mathematics Teacher, 102(3), 178–185.
  This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included.
Arbaugh, F., Lannin, J., Jones, D. L., & Park-Rogers, M. (2006). Examining instructional practices in Core-Plus lessons: Implications for professional development. Journal of Mathematics Teacher Education, 9(6), 517–550.
  In the research reported in this article, we sought to understand the instructional practices of 26 secondary teachers from one district who use a problems-based mathematics textbook series (Core-Plus Mathematics). Further, we wanted to examine beliefs that may be associated with their instructional practices. After analyzing data from classroom observations, our findings indicated that the teachers' instructional practices fell along a wide continuum of lesson implementation. Analysis of interview data suggested that teachers' beliefs with regard to students' ability to do mathematics were associated with their level of lesson implementation. Teachers also differed, by level of instructional practices, in their beliefs about appropriateness of the textbook series for all students. Results strongly support the need for professional development for teachers implementing a problems-based, reform mathematics curriculum. Further, findings indicate that the professional development be designed to meet the diverse nature of teacher needs.
Herbel-Eisenmann, B., Lubienski, S., & Id-Deen, L. (2006). Reconsidering the study of mathematics instructional practices: The importance of curricular context in understanding local and global teacher change. Journal of Mathematics Teacher Education, 9, 313–345.
  This paper discusses the case of one teacher, Jackie, whose instructional practices illuminate the importance of textbooks and student/parent expectations in shaping pedagogy. Jackie teaches in the Plainview district, which offers parents and students a choice between a reform-oriented, integrated curriculum (Core-Plus Mathematics) and a more conventional single-subject sequence (the University of Chicago series). Each day, Jackie teaches two very different sections of accelerated eighth-grade mathematics using each of these curricular materials. Drawing from students' survey responses, classroom observations, and teacher interview data, we show ways in which Jackie's pedagogy differs considerably between the two courses and we shed light on reasons underlying this variation. By examining one teacher who enacts different practices in each of the two curricular contexts, this paper highlights factors that contribute to teachers' enacted curricula factors that have been understated in previous mathematics education research on teacher development. The study establishes the importance of distinguishing between global and local teacher change and suggests implications for future studies of teaching and reform.
Maurer, S., & McCallum, W. (2006). Advising a precollege curriculum project. Notices of the American Mathematical Society, 53, 1018–1020.
  The authors explain their participation in and the learning experiences they have received working with the Core-Plus Mathematics Project. The authors suggest that professional mathematicians and other readers seek similar opportunities in projects that may intrigue and involve them in precollegiate mathematics.
Lubienski, S. T. (2004). Traditional or Standards-based mathematics? The choices of students and parents in one district. Journal of Curriculum and Supervision, 19(4), 338–365.
  This study examines students' and parents' choices in one district that recently began offering a new problem-centered high school mathematics program aligned with the National Council of Teachers of Mathematics Standards, in addition to its traditional mathematics sequence. Despite the district's previous implementation of Standards-based instruction in grades K through 8, the vast majority of students and parents have chosen the traditional high school sequence. Survey data from more than 300 students and parents were analyzed with attention to parent education level and option chosen. Parents with limited formal education were less likely than college-educated parents to access information about the options but were more likely to rank college preparation as a top factor in their decision. Additionally, although college-educated parents were more likely than other parents to discuss the options with teachers, they were less likely to be influenced by teachers' comments. Parents who chose the traditional sequence expressed more concern about college preparation, whereas parents who chose the Standards-based sequence placed a higher priority on student understanding and enjoyment of mathematics. Overall, many parents and students in the district held strong, persistent antireform beliefs. This study highlights the difficulties and dilemmas of introducing change into the firmly entrenched mathematics curriculum, particularly at the high school level.
Latterell, C. M. (2003). Testing the problem-solving skills of students in an NCTM-oriented curriculum. The Mathematics Educator, 13(1), 5–14.
  An interesting question concerns how well students from a Standards-based curriculum do on standardized mathematics tests. (This has been addressed by many of the evaluation and research studies summarized in this bibliography.) Another important question that has received less attention is: Are standardized tests truly measuring the skills and understanding that Standards-based students have? Would other tests reveal skills and understandings that differentiate students from Standards-based curricula from those who studied a more traditional program? Moreover, what are these skills? This paper contributes tentative answers to some of these questions, in the case of Core-Plus Mathematics. The reported study found that students who studied from the Core-Plus Mathematics program displayed qualities such as engagement, eagerness, communication, flexibility, and curiosity to a much higher degree than did students who studied from more conventional subject-specific programs.
Lloyd, G. M. (2002). Mathematics teachers' beliefs and experiences with innovative curriculum materials. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 149–159). Utrecht, The Netherlands: Kluwer Academic Publishers.
  This chapter draws attention to the educative potential of teachers' experiences with the curriculum materials that have been developed in the context of recent efforts to improve K–12 mathematics education in the United States. Examples from two different professional development settings illustrate how teachers' beliefs can change on the basis of experiences with these innovative curriculum materials. Discussion of these examples suggests the need for greater attention to teachers' beliefs about mathematics curriculum.
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.
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.
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.
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.

Books and Book Chapters Reporting Research
Tarr, J. E., McNaught, M. D., & Grouws, D. A. (2012). The development of multiple measures of curriculum implementation in secondary mathematics classrooms: Insights from a three-year curriculum evaluation study. In D. Heck, K. Chval, I. Weiss, & S. W. Ziebarth (Eds.), Approaches to studying the enacted mathematics curriculum (pp. 89–116). Greenwich, CT: Information Age.
  The authors examine curriculum implementation and methods used by the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project to gather information related to student mathematical learning associated with secondary mathematics curriculum programs such as Core-Plus Mathematics. The authors discuss their conceptual approach to instrument development, outline their instrument development process, describe the instruments developed, and provide reliability and validity data.
Schoen, H. L., Ziebarth, S. W., Hirsch, C. R., & BrckaLorenz, A. (2010). A five-year study of the first edition of the Core-Plus Mathematics curriculum. Charlotte, NC: Information Age.
  The study reported in this volume adds to the growing body of evaluation studies that focus on the use of NSF-funded Standards-based high school mathematics curricula. Most previous evaluations have studied the impact of field-test versions of a curriculum. Since these innovative curricula were so new at the time of many of these studies, students and teachers were relative novices in their use. These earlier studies were mainly one year or less in duration. Students in the comparison groups were typically from schools in which some classes used a Standards-based curriculum and other classes used a conventional curriculum, rather than using the Standards-based curriculum with all students as curriculum developers intended.

The volume reports one of the first studies of the efficacy of Standards-based mathematics curricula (in this case, Core-Plus Mathematics) with all of the following characteristics:
  • The study focused on fairly stable implementations of a first-edition Standards-based high school mathematics curriculum that was used by all students in each of three schools.

  • It involved students who experienced up to seven years of Standards-based mathematics curricula and instruction in middle school and high school.

  • It monitored students' mathematical achievement, beliefs, and attitudes for four years of high school and one year after graduation.

  • Prior to the study, many of the teachers had one or more years of experience teaching the Standards-based curriculum and/or professional development focusing on how to implement the curriculum well.

  • In the study, variations in levels of implementation of the curriculum are described and related to student outcomes and teacher behavior variables.

  Item data and all unpublished testing instruments from this study are available at www.wmich.edu/cpmp/evaluation.html for use as a baseline of instruments and data for future curriculum evaluators or Core-Plus Mathematics users who may wish to compare results of new groups of students to those in the present study on common tests or surveys. Taken together, this volume, the supplement at the CPMP Web site, and the first edition Core-Plus Mathematics curriculum materials (samples of which are also available at the Web site) serve as a fairly complete description of the nature and impact of an exemplar of first edition NSF-funded Standards-based high school mathematics curricula as it existed and was implemented with all students in three schools around the turn of the 21st century.
Fey, J., & Hirsch, C. (2007). The case of Core-Plus Mathematics. In C. Hirsch (Ed.), Perspectives on the design and development of school mathematics curricula (pp. 129–142). Reston, VA: National Council of Teachers of Mathematics.
  This book presents a historical perspective on what is perhaps a unique effort in curriculum development in this country. The directors or associates for 15 comprehensive curriculum development projects, 14 of which were funded by the National Science Foundation, offer perspectives on the design principles that guided their work as well as insights into the challenges they faced and the barriers to their success. The book furnishes useful guidance to future curriculum developers and documents an important historical record of school mathematics.

Chapter 10 of this book discusses the design principles and development process for the Core-Plus Mathematics curriculum. A companion volume (next entry) describes the impact of the field-test version of the curriculum on student learning and dispositions.
Hart, E., Hirsch, C., & Keller, S. (2007). Amplifying student learning in mathematics using curriculum-embedded Java-based software. In W. G. Martin and M. E. Strutchens (Eds.), The learning of mathematics, 69th yearbook of the National Council of Teachers of Mathematics (pp. 175–202). Reston, VA: National Council of Teachers of Mathematics.
  The authors look at the potential impact of technology on students' learning, a promise that has all too rarely been realized over the years. They discuss how technology can be used to amplify learning through Java-based, interactive environments that allow students to investigate and solve problems that might be beyond their reach without such tools. Furthermore, they argue that these tools must be embedded in a curricular context in order to realize their potential. Finally, they assert that the wide availability of Java-based resources over the Internet enhances their potential to become an integral part of learning.
Walker, R. K. (2006). Student voices and the transition from reform high school mathematics to college mathematics. In N. B. Hastings (Ed.), A fresh start for collegiate mathematics: Rethinking the courses below calculus. Washington, DC: Mathematical Association of America.
  This paper reports research that examined students' conceptions about learning, knowing, and doing mathematics after studying four years of Contemporary Mathematics in Context (©1998) 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. The Conceptions of Mathematics Inventory developed by Grouws, Howald, and Colangelo was used in the research. 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 this Standards-based curriculum to college mathematics.
Schoen, H. L., & Hirsch, C. R. (2003). The Core-Plus Mathematics Project: Perspectives and student achievement. In S. Senk & D. Thompson (Eds.), Standards-based 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 theoretical framework and a profile of student outcomes. Achievement results are reported from the three-year Core-Plus Mathematics field test (1994–97) for each subtest of the standardized Ability to Do Quantitative Thinking (ATDQT) test and for students who 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 conventional curricula. On all measures except paper-and-pencil algebra skills, students in CPMP do as well as or better than those in more conventional 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.
  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
Ziebarth, S. W., Hart, E., Marcus, R., Ritsema, B., Schoen, H. L., & Walker, R. (2008). High school teachers as negotiators between curriculum intentions and enactment. In J. Remillard, G. Lloyd & B. Herbel-Eisenmann (Eds.), Mathematics teachers at work (pp. 171-189). New York, NY: Routledge Taylor and Francis Group.
  This chapter investigates secondary mathematics teacher's interactions with authors of the Core-Plus Mathematics curriculum as the materials are being developed. Attention is focused on the ways in which the intended curriculum is negotiated by highlighting how teachers participate in the curriculum development process from early drafts to a final published commercial product.

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.
Ritsema, B., & Verkaik, M. (2006). Professional development as a catalyst for classroom change. In L. VanZoest (Ed.), In Teachers engaged in research: Inquiry into mathematics practice (pp. 253–271). Reston, VA: National Council of Teachers of Mathematics.
  This chapter describes one teacher's journey as he changed from a teacher-center classroom to a student-centered classroom. His research into his own teaching practices occurred over a three-year time period and involved videotaping his class and discussing instructional practices and student thinking with colleagues. The chapter focuses on effective lesson launches, helping students with the problem context, effective teacher questioning, and student struggle.
Coxford, A. (2003). Mathematics curriculum reform: A personal view. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 599–622), Reston, VA: National Council of Teachers of Mathematics.
  This chapter describes the curriculum improvement activities in which the author was involved as well as the ideas, forces, and realities that supported or hindered these attempts at curriculum improvement. The chapter describes the intellectual and professional environment that influenced the author's professional preparation for mathematics education, which at the time involved primarily the SMSG materials and the controversies around the "new math" movement. The author's contributions by way of school geometry materials are discussed. Discussion about the period after "new math" and at the time of An Agenda for Action is followed by the author's subsequent curriculum experiences, particularly the University of Chicago School Mathematics Program (UCSMP) and Core-Plus Mathematics Project (CPMP) curricula.
Hedden, C. B., & Lanngbauer, D. (2003). Balancing problem-solving skills with symbolic skills. In H. L. Schoen & R. I. Charles (Eds.), Teaching mathematics through problem solving: Grades 6–12 (pp. 155–159). Reston, VA: National Council of Teachers of Mathematics.
  The authors are secondary school teachers who teach mathematics through problem solving. Serving as a teacher story, the authors discuss their classroom experiences to capture stories of mathematical activity in real classrooms, accompanied by their own thoughts. In particular, these authors discuss balancing problem-solving skills with symbolic manipulation skills.
Marcus, R., & Fey, J. T. (2003). Selecting quality tasks for problem-based teaching. In H. L. Schoen and R. I. Charles (Eds.), Teaching mathematics through problem solving: Grades 6–12 (pp. 55–67). Reston, VA: National Council of Teachers of Mathematics.
  The authors provide perspective on how to select and use appropriate tasks and learning tools so that the intended mathematical understanding will result, an important dimension of the system of teaching through problem solving. The authors begin by posing four questions to consider when selecting quality tasks. These questions bring out that the important mathematical ideas and methods must be embedded in the tasks; the tasks need to be engaging and problematic, yet accessible to the target students; and work on the tasks needs to help students develop their mathematical thinking and habits of mind. Through several examples, the authors also make the very important point that the collection of tasks in a curriculum must build coherent understanding and connections among important mathematical topics.
Ziebarth, S. W. (2003). Classroom assessment issues related to teaching mathematics through problem solving. In H. L. Schoen and R. I. Charles (Eds.), Teaching mathematics through problem solving: Grades 6–12 (pp. 177–189). Reston, VA: National Council of Teachers of Mathematics.
  This author discusses classroom assessment as an important part of a system of instruction based on teaching mathematics through problem solving. The author illustrates some ways to align classroom assessment with teaching through problem solving, mainly focusing on assessing students' understanding. The author draws on comments about assessment, both from secondary school teachers who teach through problem solving and from their students, in a discussion of several recurring assessment issues, including how to assign grades.
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: National Council of Teachers of Mathematics.
  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: National Council of Teachers of Mathematics.
  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
Grouws, D. A., Tarr, J. E., Sears, R., & Ross, D. J. (2010). Mathematics teachers' use of instructional time and relationships to textbook content organizations and class period format. Paper presented at the Hawaii International Conference on Education, Honolulu, HI.
  In this paper we report findings and implications related to secondary school mathematics teachers' use of instructional time and how patterns of classroom time utilization relate to the type of textbook used (content organization) and the class period format in place. The findings reported are based on data collected from 325 classroom observations of 109 teachers in 5 states during the first two years of the NSF-funded project, Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC), a longitudinal comparative study of the impact of high school mathematics curricula on students' learning. Class time data were classified and analyzed based on Activity Codes (e.g., Warm-Up, Review, Lesson Preview, Teach, Practice and Apply, Assess) and two textbook types: subject-specific content organization (Algebra, Geometry, and Algebra II), in which the content each year is centered around a core mathematics area; and integrated content organization (Course 1, Course 2, Course 3), where the content is presented in an integrated manner with attention to algebra, geometry, statistics, and discrete mathematics each year. Three class period formats (regular, block, modified block) were taken into account. Teachers of the integrated curriculum spent significantly more time developing new mathematical ideas than did teachers of the subject-specific curriculum, but this came at the expense of students practicing and applying what they had learned during class time. This paper provides summary descriptions of time utilization, identifies activity codes where there is substantial variation across curriculum types, and suggests factors that may account for variation in time utilization.
McNaught, M. D., Tarr, J. E., & Grouws, D. A. (2008). Assessing curriculum implementation: Insights from the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project. Paper presented at the annual meeting of the American Education Research Association, New York, NY. (See: http://cosmic.missouri.edu)
  This paper reports and discusses preliminary findings related to curriculum implementation in mathematics classrooms. The primary focus is on the extent and manner in which teachers use textbooks in their daily teaching. Specific attention is given to implementation differences related to two types of mathematics textbooks where the mathematical content is organized differently.
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.
Smith, J., & Burdell, C. (2001). The math is different, but I can deal: Studying students' experiences in a reform-based mathematics curriculum. Paper presented at the Annual Meeting of the American Educational Research Association.
  The research reported in this paper describes the mathematical experiences of 9 students who moved from a traditional mathematics program in junior high school to a high school mathematics program structured by current reforms in curriculum and teaching. We will refer to the high school site of this work as Logan High (though the name is fictitious). Logan has for some years implemented the Core-Plus Mathematics Project materials for most of its grade 9–12 students, including some (but not all) students who come out of the "advanced" mathematics track in the junior high school. We recruited 24 Logan student volunteers starting in January 2000 and have tracked these students in their mathematics work for 2.5 semesters.

We report on the experiences of 9 of these students, drawing on a maximum of 3 semesters of mathematics coursework (Spring 2000, Fall 200, and Spring 2001). We have analyzed their mathematical experiences along 4 dimensions: (1) performance in mathematics, (2) disposition towards the subject, (3) approach to learning the subject, and (4) differences students see between traditional and Core-Plus Mathematics curricula and teaching. All of our 9 students reported differences between their past and present mathematics programs as they moved into the Core-Plus Mathematics program, but in only 2 cases was there any significant change in performance across the curricular shift.
Lewis, G., Lazarovici, V., & Smith, J. (2001). Meeting the demands of calculus and college life: The mathematical experiences of graduates of some reform-based high school programs. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA.
  The research reported in this paper reviews the mathematical experiences of 8 students who moved out of a high school mathematics experience that was structured by current reforms in curriculum and teaching and into a more traditional collegiate mathematics experience. The university site for this work was Michigan State University in East Lansing, Michigan, a very large, land-grant research university with an equally large and research-oriented Department of Mathematics. All 8 were freshmen in Fall 1999 and since then have taken multiple semesters of collegiate mathematics. Our analysis describes and documents the challenges that many of these students have faced at MSU, mainly in Calculus I, and how they dealt with these challenges.

Our paper unfolds as follows. First, we place our work at the MSU site within the work of the Mathematical Transitions Project as a whole, before describing MSU's Mathematics Department's course offerings for first- and second-year students. Then we present our research questions, say a bit about the character of the data we have collected, and describe our efforts to recruit student volunteers and the group of students who agreed to work with us. Then we present the results of our analyses: (1) how these students have performed in their mathematics courses, (2) what sorts of differences they reported to contrast their high school with their collegiate mathematics experience, and (3) whether we feel they have experienced a mathematical transition. (See also Smith & Berk, 2001 for a more detailed discussion), we conceptualize mathematical transitions as involving changes in students' disposition toward mathematics and in their approach to learning mathematics, as well as changes in performance and reported differences.
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.
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 421351)
  Achievement results are reported for the three-year Core-Plus Mathematics 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, etc.), 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 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 420518)
  This paper presents the results from an attitude scale called Attitude Toward Your Mathematics Course during the three-year Core-Plus Mathematics field test (1994–97). This scale contains 15 Likert-type items and an open-ended writing prompt. Comparisons are made between Core-Plus Mathematics students and students in more traditional college preparatory mathematics curricula in the same field-test schools. Students perceive the Core-Plus Mathematics curriculum as difficult, at least as challenging as traditional college-prep mathematics courses, but Core-Plus Mathematics 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, SC.
  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, 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 Mathematics curriculum for 2 years, and this paper focuses primarily on Year 2 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 10 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 6-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 Technical Reports
Core-Plus Mathematics Project. (2002, May). Developing mathematical literacy.
  In 1997, the Core-Plus Mathematics Project began a 5-year longitudinal study of students in three high schools in which the 1st edition of Core-Plus Mathematics was used with all students. Of special interest was the impact of the curriculum on students' mathematical literacy. This interim report begins by reviewing the literature that makes the case for the importance of mathematical (or quantitative) literacy for all adults in contemporary society and outlines the attributes of mathematical literacy.

Next, a short summary is provided of the performance of Course 1, Course 2, and Course 3 field-test students on different versions of the Ability to Do Quantitative Thinking subtest of the nationally normed Iowa Tests of Educational Development.

Finally, development of a test of released items from the TIMSS assessment of general mathematical knowledge and its scoring are described. The test results of end-of-Course 3 students in the three longitudinal study schools are reported and compared to the performance of end-of-high school students in the U.S., the Netherlands, and the total international cohort. Core-Plus Mathematics students outperformed both the U.S. and international samples. Their performance was closest to that of the Netherlands, the top scoring country on the TIMSS general mathematical knowledge assessment.
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 1st edition 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 1st-edition 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 12th-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
Fonkert, K. L. (2012). Patterns of interaction and mathematical thinking of high school students in classroom environments that include use of JAVA-based, curriculum-embedded software. Unpublished doctoral dissertation, Western Michigan University.
  This study analyzes the nature of student interaction and discourse in an environment that includes the use of Java-based, curriculum-embedded mathematical software. The software, CPMP-Tools, was designed as part of the development of the 2nd edition of the Core-Plus Mathematics curriculum. The use of the software on laptop computers used by students working in small groups or as a whole class in interactive lessons with a single computer at the front of the classroom was explored. Data were collected through observations, interviews, and selected items from the students' regular assessments. During the observations, classroom discussion was audiotaped and videotaped, and field notes were taken. The interviews of students and teachers were audio- and/or videotaped. The analysis of these data revealed that the students engaged in inquiry the majority of the time while they were using CPMP-Tools in small groups. Building on other students' ideas was the second most frequent interaction pattern in that setting. During the whole-class interactive lessons with a single computer, the two most frequently found interaction patterns were teacher explaining and giving new ideas. The most frequently occurring level of mathematical thinking found in both types of classroom environments using CPMP-Tools was the second-highest level in the framework—constructing and synthesizing. The students were habitually engaged in productive interaction patterns and high levels of mathematical thinking while using the curriculum-embedded software. The dynamic nature and strategic use of colorful visuals used in CPMP-Tools facilitated students' interactions and high levels of mathematical thinking.
Krupa, E. E. (2011). Evaluating the impact of professional development and curricular implementation on student mathematics achievement: A mixed methods study. Unpublished doctoral dissertation, North Carolina State University, Raleigh.
  This study was designed to investigate the effects of an integrated, reform-based curriculum, Core-Plus Mathematics, on student learning on statewide End-of-Course exams (EOC–Algebra I and II) and to contextualize these outcomes in a state-funded professional development program with the elements of a summer program, follow-up workshops, and monthly site-based support with instructional coaches. The study was also designed to compare and contrast major subgroups: teachers using Core-Plus Mathematics who did or did not participate in different elements of the professional development. In addition, the study was designed to gather evidence on the variations among these groups on key implementation indices, and to use hierarchical linear modeling to investigate the role of these factors in predicting student outcomes. Hierarchical linear modeling was used to account for the nesting of students within teachers within schools to investigate the impact of integrated mathematics and subject-specific curricular materials on student achievement across students in North Carolina. The sample was then restricted to students of teachers who participated in the state-funded professional development to relate teacher characteristics to student outcomes. The sample was further restricted to teachers who participated in different components of the professional development to analyze how curricular implementation affects student achievement and to examine factors that influenced decisions teachers made when implementing Core-Plus Mathematics.

Findings from this study indicate that North Carolina students enrolled in Core-Plus Mathematics outperformed subject-specific students on the Algebra I End-of-Course exam, which was highly aligned with content in Core-Plus Mathematics Course 1, and performed no differently on the Algebra II exam, which was not aligned as well with Core-Plus Mathematics Course 3. There were favorable findings on the use of Core-Plus Mathematics in high-minority, high-needs schools. Consistently prior achievement, student grade level and race, and classroom attendance were related to student achievement, as well as teacher content knowledge, most notably for teachers of Core-Plus Mathematics. This study documented large variance in teachers' implementation of Core-Plus Mathematics based upon the professional development they received and their experiences using the materials with students. Factors that related to their implementation of the curriculum and related instructional practices included their beliefs about how students best learn mathematics; their trust of the curriculum; and systemic factors including mandatory state assessments, access to materials and technology resources, scheduling, and student transition to reform mathematics. Teachers enrolled in the summer workshops more faithfully implemented content from the textbooks, but instructional coaches were an important component to facilitating change in teachers' instructional practices. Results from this study demonstrate that teachers using Core-Plus Mathematics benefit from professional development designed to strengthen their mathematical content knowledge and reform-based instructional practices. Findings suggest encouraging results for the use of Core-Plus Mathematics with typically underserved student populations and among teachers who were provided with sustainable support following an authentic workshop experience.
Harvel, K. R. T. (2010). The relationship between Core-Plus Mathematics Project and student achievement. Unpublished doctoral dissertation, Wayne State University.
  This study focused on the effectiveness of the Core-Plus Mathematics Project (CPMP) curriculum in terms of academic achievement. Students' perceptions on their use of Core-Plus Mathematics were also a focus of the study. Finally, differences in procedural and conceptual knowledge between genders were examined. The control group used a traditional subject-specific textbook and the treatment group used the same textbook along with Core-Plus Mathematics. The results of the study found no significant difference between the two groups in procedural knowledge. However, the treatment group using the CPMP curriculum performed significantly better on the state assessment than the control group. The study also showed that although the students in the treatment group had negative perceptions about using Core-Plus Mathematics, they performed better than students in the control group. Results of the study showed that although the females did better procedurally and conceptually than males, the differences were not statistically significant. Core-Plus Mathematics provided students with a rigorous, conceptually rich instruction that was based on the High School Content Expectations that were derived from national standards.
Perry, Dennis S. (2005). Stratification of expected learning outcomes: The dissection of a spiral mathematics curriculum. Unpublished doctoral dissertation, University of Pennsylvania.
  Summative standardized assessments have become a way of life for students and their teachers since the enactment of the No Child Left Behind Act. Because these assessments are administered yearly, they offer little information to educators to improve instruction. Many schools have implemented reform mathematics programs in an effort to provide students with the critical thinking skills that are aligned with these assessments, as well as providing educators opportunities to learn more about students' development of deep understanding of mathematical concepts. This study examines the decisions that a committee of secondary mathematics educators make as they attempt to develop formative assessment practices to accompany their implementation of the spiral curriculum of the reform mathematics program Core-Plus Mathematics. Using stratified learning goals that sought to determine students' beginning, developing, and secure conceptual understandings at predetermined locations in the curriculum, this committee collaborated to reform their assessment practices and to develop methods for providing more informative feedback to students and their families. This study follows an Action Research design. The researcher provides an emic, or insider, perspective regarding the work of the committee in his role as a participant observer. This research helps us to understand the divide between the content standards as constructed in policy and the performance standards that are the reality for teachers and students. Additionally, this research provides insight into the knowledge that is generated when teachers collaborate to explore their practice. Finally, this research adds to the existing literature regarding reform mathematics and the assessment practices that measure their effectiveness. The major findings from this study are: practitioners benefit from organizational context and supports that promote collaboration; teacher anxiety can be reduced when implementing new material if mechanisms are installed to allow for validation of their efforts; teacher beliefs impact the practices that they are willing to consider changing and also those practices that are non-negotiable for changing; assessment for learning requires a change in the relationship between the teacher and the student; and teachers desire to be viewed as professionals.
Davis, Jon Dewayne. (2004). Supplementation, justification and student understanding: A tale of two "Contemporary Mathematics in Context" classrooms. Unpublished doctoral dissertation, University of Minnesota.
  This study examined how two experienced teachers (Teacher A and B) supplemented their daily instruction of Contemporary Mathematics in Context (CMIC) during two units of Course 1, their justifications for that supplementation, and its effect upon students' conceptual and procedural understanding of function representations. Data were gathered through classroom observations, teacher interviews, student interviews, and classroom artifacts. Both teachers supplemented the curriculum using symbolic manipulation procedures for solving equations and simplifying expressions involving like and unlike terms. Teacher B also supplemented the curriculum with activities that were closely aligned with CMIC. Teacher A's additions to the curriculum focused on procedures with fewer connections to real-world situations. Teacher A also supplemented the curriculum with computation practice activities and labs that contained conceptual translation questions. Teacher B's implementation of the curriculum was closer to the developers' intentions, while Teacher A often abridged CMIC investigations thereby limiting students' exploration opportunities. Teacher A's justifications for supplementation included student mastery, standardized testing, block scheduling, and a dislike of CMIC activities. Teacher B's decisions were heavily influenced by three interrelated communities of teachers at her high school. These communities were a source of supplementation for Teacher B and, at the same time, they helped her to maintain a high fidelity of implementation. Teacher A's students performed much better on conceptual translation tasks than Teacher B's students, except on table to real-world translations. Teacher B's class, on the other hand, outperformed Teacher A's class on solving equations through symbolic manipulation and simplification of expressions, and they showed greater flexibility in solving these problems using technology. These differences were at least partially explained by Teacher B's decision to place supplementation in a unit where these skills were taught and her greater use of the curriculum. Issues of equity arose as the majority of successful responses in both classrooms came from students who were identified as being of high ability. Although technology has been discussed as a means by which students of lower ability can gain access to problems, students of low ability in both classrooms struggled with the steps needed to use technology effectively.
Noh, Jihwa. (2004). An investigation of secondary teachers' knowledge of rate of change in the context of teaching a Standards-based curriculum. Unpublished doctoral dissertation, Western Michigan University.
  This study investigated teachers' mathematical content knowledge and pedagogical content knowledge with respect to rate of change in the context of teaching a Standards-based high school mathematics curriculum that emphasizes rate of change as a central theme, the Core-Plus Mathematics Project (CPMP) materials. A framework was designed to provide a comprehensive guide for analyzing different aspects of rate of change knowledge incorporating existing frameworks relative to rate of change, NCTM recommendations described in Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) and Principles and Standards for School Mathematics (NCTM, 2000), and research related to pedagogical understanding of rate of change. Data for this study were collected from 13 teachers with a wide variety of experience teaching CPMP using a survey, a mathematical task-based interview, classroom observations, and follow-up interviews. The results showed that teachers demonstrated a well-connected understanding and flexible use of different representations in situations involving constant rate of change. Context played an important role with regard to teachers' ability to explore rate of change as more teachers were able to interpret situations involving non-constant rates of change when they were embedded in a context-rich setting. Teachers were generally less able to use graphical representations compared to numerical and symbolic representations. Understanding connections between finding the slope of a line and methods for estimating the rate of change for nonlinear functions proved to be challenging for most teachers, although more experienced teachers demonstrated a better understanding of these connections. Teachers who had more experience with the CPMP curriculum were generally more successful in dealing with non-constant rates of change and recognizing similar and contrasting characteristics of different types of representations across contexts. Teachers' conception of rate of change also differed based on experience with the CPMP curriculum. The findings of this study suggest that Standards-based curriculum materials may support teachers as they learn ideas involving rate of change, but that a more thorough understanding of the concept may require additional resources.
Macomber, Angia E. Sperfslage. (2003). Understanding algebra and functions: An exploration of the learning experiences of previously unsuccessful students in Core-Plus Course 1A. Unpublished doctoral dissertation, Michigan State University.
  A major focus of mathematics reform at the secondary level has been directed at the teaching and learning of algebra, driven by the belief that mathematics instruction, and algebra instruction in particular, must effectively reach all students. It is widely agreed upon in mathematics reform literature that algebra is a gate-keeping course whereby students who do not succeed are denied access to equal participation in a technologically oriented society; moreover, algebra is accessible to all students only when it can be understood conceptually, explored within contexts that are meaningful to students. In this study, the author explores the learning experiences focusing on the algebra and functions content strand of six students, each of whom had previously experienced non-success in school mathematics, in the first part of the first course of Core-Plus Mathematics, a reform high-school mathematics curriculum. Through an analysis of classroom observations and in-depth interviews conducted at three different moments in time of the course, the author investigates the nature of the students' previous non-successes, their experiences with the Core-Plus Mathematics curriculum, and their understandings of algebra and functions as presented in Core-Plus Mathematics Course 1A. After developing individual portraits of each student, the author reads across all six participants for common features and patterns of their school-mathematics histories, their experiences of the Core-Plus Mathematics curriculum, and their understandings of algebra and functions. The findings coalesce around issues attendant to representations of mathematical mathematics, and a construct called "mathematics community membership" that captures a number of qualities that the author claims to be closely associated with navigating a reform curriculum successfully. The implications call for both high school mathematics teachers and mathematics teacher educators to devote serious attention to students' alienation from the subject and to explicitly socialize them into expressly mathematical modes of thinking, speaking, and behaving.
Cebulla, K. 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 Core-Plus Mathematics Project [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 Core-Plus Mathematics Project (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, 16 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 16 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.
Hetherington, Ruth Anne. (2000). Taking collegial responsibility for implementation of standards-based curriculum: A one-year study of six secondary school teachers. Unpublished doctoral dissertation, Michigan State University.
  Curriculum that moves from traditional teacher-centered and technical skill proficiency to student-centered inquiry-oriented instruction is a primary component in the reform of mathematics education. While curriculum developers design materials that conform to the standards set out by the National Council of Teachers of Mathematics, we need to know more about the classroom implementation of such radically different materials. This study examines what happens when experienced high school mathematics teachers take collegial responsibility for sincere and earnest implementation of a new Standards-based curriculum. The study explores the major differences between the curriculum materials of a traditional algebra course and the Core-Plus Mathematics Project. It investigates the challenges teachers faced with the instructional model, and issues that affected timing and pace of instruction.
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 Core-Plus Mathematics Project (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 Core-Plus Mathematics 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 the Core-Plus Mathematics Project (CPMP) curriculum and how those conceptions influenced their 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, in terms of their 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 Mathematics 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 Mathematics 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.
Lloyd, Gwendolyn Monica. (1996). Transforming instruction about functions: One veteran teachers' experience with innovative secondary mathematics curriculum. Unpublished doctoral dissertation, University of Michigan.
  The purpose of this study was to understand how reform recommendations are incorporated into secondary mathematics teachers' instruction when implementing innovative curricula. The constructs of mathematical and pedagogical content conceptions guided the investigation of one high school teacher's experience implementing Core-Plus Mathematics Project (CPMP) curriculum materials. Mr. Allen voluntarily implemented the ninth-grade materials during the 1994–95 and 1995–96 school years. Primary attention was on his conceptions and instruction about mathematical functions. CPMP's Patterns of Change unit treats functions as dependence relationships using student-centered, contextualized activities with focus on exploring and connecting multiple representations. Mr. Allen participated in 15 interviews during his two years of implementation. Interviews were audio-recorded and transcribed. In both years, daily observations of the Patterns of Change unit were video-recorded. In Year 2, lessons from additional CPMP units and several of Mr. Allen's traditional courses were observed. Major analytic categories were developed using Spradley's taxonomic and thematic strategies. Mr. Allen's dialogues with students consistently enacted the robust and integrated understandings of function that he communicated prior to teaching the unit for the first time. In particular, his graphical proficiency and personal focus on patterns of covariation empowered him to effectively utilize the CPMP materials. During Year 2, he even more explicitly and frequently emphasized the importance of recognizing and describing the nature of covariation relationships, and understanding that relationships can be represented in multiple ways. He also displayed evidence in Year 2 of having developed new pedagogical content conceptions (e.g., more equal treatment of non-graphical representations). When concerns about familiarity with new activities were alleviated by a year's experience, Mr. Allen was able to contemplate and experiment more directly with pedagogical struggles (e.g., how to organize small groups). This study illustrates how flexible, connected, and comprehensive content conceptions can support the implementation of novel approaches to subject matter. Moreover, Mr. Allen's experiences demonstrate how strong content conceptions contribute in pivotal ways to facilitating the gradual development of new pedagogical content conceptions. The subtle content-related differences displayed by Mr. Allen in Year 2 contribute meaningful information about how instruction with a novel curriculum changes over time.
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
Fey, J., Hirsch, C., & Schoen, H. (2007). The future of high school mathematics: New priorities and promising innovations. Michigan Section MAA Newsletter, 34(1), 10–14.
  This brief article provides an overview of the Core-Plus Mathematics program in terms of 1st-edition evaluation results, recent major changes in the outcome expectations and background conditions for mathematics education at the high school and undergraduate levels, and how those forces influenced improvements in the 2nd edition of Core-Plus Mathematics. Of particular note is the active involvement of mathematicians and a statistician in the design and review of revised units for each of the four 2nd-edition courses.

The article provides links to influential curriculum recommendations (in PDF form) from Achieve, the American Association of Two-Year Colleges, the American Statistical Association, the College Board, and the Mathematical Association of America.
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.

[ Home ][ Announcements ][ Program Overview ][ Evaluation ][ Implementation ][ Parent Resource ][ Publications ][ Site Map ][ Contact Us ]

Copyright 2014 Core-Plus Mathematics Project. All rights reserved.