
Last Updated: 27 March
2016 
Research Articles in Journals  

Chávez, Ó., Tarr, J. E., Grouws, D. A., & Soria, V. M. (2015, March). Thirdyear high school mathematics curriculum: Effects of content organization and curriculum implementation. International Journal of Science and Mathematics Education. Volume 13, Supplement 1, 97–120.  
We examined the effect of curriculum organization in US 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) subjectspecific approach. The study involved 2,242 high school students, enrolled in either Course 3 or Algebra 2, in 10 schools in 5 geographically dispersed states. Taking account of curriculum implementation and students' prior mathematics learning, we analyzed two endofyear outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in the integrated curriculum scored significantly higher than those in the subjectspecific curriculum on the common objectives test. In both outcome measures, gender and prior achievement were significant studentlevel predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacherlevel, 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.  
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 CorePlus 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 CorePlus Mathematics. However, the CorePlus Mathematics textbooks include more problems requiring explanations and various representations and problems requiring higherlevel cognitive demand.  
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 secondyear 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, CorePlus Mathematics, or a (traditional) subjectspecific approach (published by Glencoe, Holt, McDougal Littell, or Prentice Hall). The study involved 3,258 high school students, enrolled in either CorePlus Mathematics Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. We constructed threelevel hierarchical linear models of scores on three endofyear 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 CorePlus Mathematics scored significantly higher than those in the subjectspecific curricula on the standardized achievement test. Significant studentlevel 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 subjectspecific 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, CorePlus Mathematics, were significantly advantaged over students who studied from subjectspecific curricula (published by Glencoe, Holt, McDougal Littell, or Prentice Hall) on three endofyear 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 proofrelated 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 multiinstitutional 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 Foundationfunded, 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 coursetaking.  
Harwell, M. R., Medhanie, A. G., Post, T. R., Norman, K. W., & Dupuis, D. N. (2012). Preparation of students completing a CorePlus 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 coursetaking patterns of students at a large public research university who completed a commercially developed or standardsbased (CorePlus Mathematics) high school mathematics curriculum, and who subsequently completed at least two college mathematics courses of difficulty level at or beyond precalculus mathematics. Mathematics coursetaking 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 collegebound 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 NSFfunded 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 highestperforming
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 CorePlus
Mathematics Course 4), and the percentage of students
enrolled in fouryear post secondary institutions (Monson, 2011). The results of this study have been validated by several additional multischool studies in Minnesota. The NSFfunded curricula included in these studies prepare students for college mathematics equally as well as commercially developed, singlesubject approaches. Evidence further suggests there may also be precollege pedagogical and sociological advantages to adopting NSFfunded 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 CorePlus Mathematics or conventional, singlesubject texts. Students completed the Precalculus Concept Assessment (PCA) and two openended 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 threeyear 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 fullyear subjectspecific courses (Algebra 1, Geometry, and Algebra 2) and the CorePlus 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 collegelevel mathematics. The purpose of this study was to investigate the relationship between the type of high school mathematics curricula (integrated or conventional singlesubject) and students' postsecondary 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, postsecondary student placement, and future research in this area.  
Capraro, M. M., Capraro, R. M., Yetkiner, Z. E., RangelChavez, A. F., & Lewis, C. W. (2010). Examining Hispanic student mathematics performance on highstakes 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 CorePlus 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 postsecondary mathematics performance, coursetaking, 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 postsecondary 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 Foundationfunded 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 coursetaking 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 postsecondary expectations: Standardsbased 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 CorePlus Mathematics Project (CPMP) at the secondary level is beginning to accumulate; however, much less is known about how prepared these students are for postsecondary 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 Standardsbased 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). Standardsbased 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 1stedition NSFfunded Standardsbased curricula (CorePlus 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 criterionreferenced 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 AfricanAmerican students in a classroom were associated with a stronger effect of attendance on achievement. No differences on the standardized achievement subtests emerged among the Standardsbased curricula studied once background variables were taken into account. The two suburban districts providing data for the criterionreferenced 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 NSFfunded curriculum projects, the CorePlus 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 standardsbased 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 standardsbased curriculum (CorePlus 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 Standardsbased mathematics education: a study of the CorePlus 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 eighthgrade mathematics achievement, were administered a researcherdeveloped 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 paperandpencil 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 (CorePlus 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, renegotiation of mathematical authority.  
Lloyd, G. M. (1999). Two teachers' conceptions of a reformoriented 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 CorePlus 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 reformoriented curricular materials during a 6week 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 PeerReviewed Journal Articles 

Hart, E. (2008). Vertexedge graphs: An essential topic in high school geometry. Mathematics Teacher, 102(3), 178–185.  
This article provides an overview of vertexedge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroomready activity with full teacher notes is also included.  
Arbaugh, F., Lannin, J., Jones, D. L., & ParkRogers, M. (2006). Examining instructional practices in CorePlus 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 problemsbased mathematics textbook series (CorePlus 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 problemsbased, reform mathematics curriculum. Further, findings indicate that the professional development be designed to meet the diverse nature of teacher needs.  
HerbelEisenmann, B., Lubienski, S., & IdDeen, 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 reformoriented, integrated curriculum (CorePlus Mathematics) and a more conventional singlesubject sequence (the University of Chicago series). Each day, Jackie teaches two very different sections of accelerated eighthgrade 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 CorePlus 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 Standardsbased 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 problemcentered 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 Standardsbased 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 collegeeducated parents to access information about the options but were more likely to rank college preparation as a top factor in their decision. Additionally, although collegeeducated 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 Standardsbased 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 problemsolving skills of students in an NCTMoriented curriculum. The Mathematics Educator, 13(1), 5–14.  
An interesting question concerns how well students from a Standardsbased 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 Standardsbased students have? Would other tests reveal skills and understandings that differentiate students from Standardsbased 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 CorePlus Mathematics. The reported study found that students who studied from the CorePlus 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 subjectspecific 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 problembased 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 CorePlus 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), 540545, 589.  
The authors examine five reform high school mathematics textbook series, including the CorePlus 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), 444453.  
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 CorePlus 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 CorePlus Mathematics curriculum.  
Ziebarth, S. W. (1998). Iowa CorePlus 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 CorePlus 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 CorePlus Mathematics material. The article summarizes results on the implementation of CorePlus Mathematics and student outcomes in MIME classrooms.  
Schoen, H. L., & Ziebarth, S W. (1997). A progress report on student achievement in the CorePlus 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 CorePlus 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 sensemaking ways with the CPMP. Mathematics Teacher, 88(8), 694–700.  
The article gives an overview of the CorePlus Mathematics curriculum, focusing on mathematics as "sensemaking." Included are the organization of the curriculum, the mathematical strands, the fourphase instructional model, the threeyear "core" program accommodating all students, the curriculumembedded 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 threeyear 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 CorePlus 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 fiveyear study of the first edition of the CorePlus 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 NSFfunded Standardsbased
high school mathematics curricula. Most previous evaluations
have studied the impact of fieldtest 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 Standardsbased
curriculum and other classes used a conventional curriculum,
rather than using the Standardsbased curriculum with
all students as curriculum developers intended. The volume reports one of the first studies of the efficacy of Standardsbased mathematics curricula (in this case, CorePlus Mathematics) with all of the following characteristics:


Fey, J., & Hirsch, C. (2007). The case of CorePlus 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 CorePlus Mathematics curriculum. A companion volume (next entry) describes the impact of the fieldtest version of the curriculum on student learning and dispositions. 

Hart, E., Hirsch, C., & Keller, S. (2007). Amplifying student learning in mathematics using curriculumembedded Javabased 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 Javabased, 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 Javabased 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 Standardsbased curriculum to college mathematics.  
Schoen, H. L., & Hirsch, C. R. (2003). The CorePlus Mathematics Project: Perspectives and student achievement. In S. Senk & D. Thompson (Eds.), Standardsbased 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 threeyear CorePlus 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 paperandpencil 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 CorePlus 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. HerbelEisenmann (Eds.), Mathematics teachers at work (pp. 171189). New York, NY: Routledge Taylor and Francis Group.  
This chapter
investigates secondary mathematics teacher's interactions with
authors of the CorePlus 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 CorePlus 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 teachercenter classroom to a studentcentered classroom. His research into his own teaching practices occurred over a threeyear 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 CorePlus Mathematics Project (CPMP) curricula.  
Hedden, C. B., & Lanngbauer, D. (2003). Balancing problemsolving 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 problemsolving skills with symbolic manipulation skills.  
Marcus, R., & Fey, J. T. (2003). Selecting quality tasks for problembased 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 CorePlus 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 CorePlus 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 CorePlus 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 CorePlus 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 CorePlus 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 CorePlus 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 CorePlus 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 curriculumembedded communication from the CorePlus 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 NSFfunded 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., WarmUp, Review, Lesson Preview, Teach, Practice and Apply, Assess) and two textbook types: subjectspecific 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 subjectspecific 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: CorePlus Mathematics as a case study. Paper presented at the Proceedings of the International Conference on Education. Honolulu, HI.  
This report uses the CorePlus Mathematics Project (CPMP) as a casestudy 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 CPMPrelated 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 CorePlus Mathematics currently underway.  
Smith, J., & Burdell, C. (2001). The math is different, but I can deal: Studying students' experiences in a reformbased 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
CorePlus 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 CorePlus Mathematics curricula and teaching. All of our 9 students reported differences between their past and present mathematics programs as they moved into the CorePlus 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 reformbased 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, landgrant research
university with an equally large and researchoriented 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 secondyear 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 Standardsoriented 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 reformoriented 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 CorePlus 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 threeyear CorePlus 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 makeup of classes (heterogeneous, high ability, low ability, etc.), by gender, by English or nonEnglish 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 openended 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 standardsbased 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 threeyear CorePlus Mathematics field test (1994–97). This scale contains 15 Likerttype items and an openended writing prompt. Comparisons are made between CorePlus Mathematics students and students in more traditional college preparatory mathematics curricula in the same fieldtest schools. Students perceive the CorePlus Mathematics curriculum as difficult, at least as challenging as traditional collegeprep mathematics courses, but CorePlus 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 reformoriented mathematics curriculum (CorePlus 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 reformoriented mathematics curriculum (CorePlus 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 problemsolving. 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 CorePlus 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 largescale 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 reformoriented 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 studentcentered 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 studentcentered and explorationbased curriculum materials (CorePlus Mathematics Project). The observations and interviews were conducted over a 6week 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 smallgroup and wholeclass discussions and ultimately decided not to hold wholeclass discussions. A third teacher achieved a more equal balance between teacherdirected and studentcentered activities. All three teachers demonstrated more difficulty than did students in changing their expectations about appropriate mathematical activity.  
CPMP Technical Reports 

CorePlus Mathematics Project. (2002, May). Developing mathematical literacy.  
In 1997,
the CorePlus Mathematics Project began a 5year longitudinal
study of students in three high schools in which the 1st edition
of CorePlus 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 fieldtest 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 endofCourse 3 students in the three longitudinal study schools are reported and compared to the performance of endofhigh school students in the U.S., the Netherlands, and the total international cohort. CorePlus 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. 

CorePlus 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 CorePlus 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 NAEPbased 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.  
CorePlus 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 1stedition Courses 1–3 of the CorePlus 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 CorePlus Mathematics Project fieldtest progress report. Unpublished manuscript, University of Iowa.  
This report focuses on standardized achievement test results aggregated across 33 fieldtest schools who were on a regular twosemester 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 NAEPdeveloped 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 12thgrade students.  
Schoen, H. L., & Ziebarth, S. W. (1998). Mathematical achievement on standardized tests: A CorePlus Mathematics Project field test progress report. Unpublished manuscript, University of Iowa.  
This report focuses on performance assessments of student achievement aggregated across 33 fieldtest schools who were on a regular twosemester schedule. On projectdeveloped openended posttests of mainly algebraic and geometric content, CPMP students in both Course 1 and Course 2 performed significantly better on conceptual, application, and problemsolving 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. Problembased 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 CorePlus Mathematics Project field test. Unpublished manuscript, University of Iowa.  
Achievement results based on standardized tests (ITED) and CPMP tests compare traditionally tracked students and CorePlus 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 JAVAbased, curriculumembedded 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 Javabased, curriculumembedded mathematical software. The software, CPMPTools, was designed as part of the development of the 2nd edition of the CorePlus 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 CPMPTools in small groups. Building on other students' ideas was the second most frequent interaction pattern in that setting. During the wholeclass 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 CPMPTools was the secondhighest 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 curriculumembedded software. The dynamic nature and strategic use of colorful visuals used in CPMPTools 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, reformbased
curriculum, CorePlus Mathematics, on student learning
on statewide EndofCourse exams (EOC–Algebra I and II)
and to contextualize these outcomes in a statefunded professional
development program with the elements of a summer program, followup
workshops, and monthly sitebased support with instructional
coaches. The study was also designed to compare and contrast
major subgroups: teachers using CorePlus 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 subjectspecific curricular materials on student
achievement across students in North Carolina. The sample was
then restricted to students of teachers who participated in the
statefunded 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 CorePlus Mathematics. Findings from this study indicate that North Carolina students enrolled in CorePlus Mathematics outperformed subjectspecific students on the Algebra I EndofCourse exam, which was highly aligned with content in CorePlus Mathematics Course 1, and performed no differently on the Algebra II exam, which was not aligned as well with CorePlus Mathematics Course 3. There were favorable findings on the use of CorePlus Mathematics in highminority, highneeds 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 CorePlus Mathematics. This study documented large variance in teachers' implementation of CorePlus 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 CorePlus Mathematics benefit from professional development designed to strengthen their mathematical content knowledge and reformbased instructional practices. Findings suggest encouraging results for the use of CorePlus 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 CorePlus Mathematics Project and student achievement. Unpublished doctoral dissertation, Wayne State University.  
This study focused on the effectiveness of the CorePlus Mathematics Project (CPMP) curriculum in terms of academic achievement. Students' perceptions on their use of CorePlus 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 subjectspecific textbook and the treatment group used the same textbook along with CorePlus 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 CorePlus 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. CorePlus 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 CorePlus 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 nonnegotiable 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 realworld 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 realworld 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 Standardsbased 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 Standardsbased high school mathematics curriculum that emphasizes rate of change as a central theme, the CorePlus 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 taskbased interview, classroom observations, and followup interviews. The results showed that teachers demonstrated a wellconnected 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 nonconstant rates of change when they were embedded in a contextrich 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 nonconstant 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 Standardsbased 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 CorePlus 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 gatekeeping 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 nonsuccess in school mathematics, in the first part of the first course of CorePlus Mathematics, a reform highschool mathematics curriculum. Through an analysis of classroom observations and indepth interviews conducted at three different moments in time of the course, the author investigates the nature of the students' previous nonsuccesses, their experiences with the CorePlus Mathematics curriculum, and their understandings of algebra and functions as presented in CorePlus Mathematics Course 1A. After developing individual portraits of each student, the author reads across all six participants for common features and patterns of their schoolmathematics histories, their experiences of the CorePlus 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 CorePlus 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 nonstatistical arguments when drawing and evaluating conclusions and tended to focus on the direction of association rather than the strength of association. Betweengroup 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.
Twentyfour CorePlus 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 followup 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 CorePlus Mathematics curriculum. Data included audiotaped pre, mid, and postinterviews, 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 standardsbased curriculum: A oneyear study of six secondary school teachers. Unpublished doctoral dissertation, Michigan State University.  
Curriculum that moves from traditional teachercentered and technical skill proficiency to studentcentered inquiryoriented 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 Standardsbased curriculum. The study explores the major differences between the curriculum materials of a traditional algebra course and the CorePlus 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 Standardsoriented and traditional students' problemsolving ability using multiplechoice and openended questions. Unpublished doctoral dissertation, University of Iowa.  
This study investigated how the measured problemsolving ability differs by students' curriculum, traditional or CorePlus Mathematics Project (CPMP). Four tests were administered to approximately 550 ninthgraders. The ITEDQ was used in multiplechoice 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 multiplechoice and openended 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 paperandpencil measures. In class observations of students solving challenging, openended problems, CPMP students engaged more enthusiastically and tried more solution strategies than traditional students.  
Kahan, J. A. (1999). Relationships among mathematical proof, highschool students, and a reform curriculum. Unpublished doctoral dissertation, University of Maryland.  
This study assessed proof competence and approaches to proof of 315 endofyear juniors in three high school sites. In each site, roughly half of the students were enrolled in CorePlus 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 Standardsbased 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 CorePlus 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 Standardsbased 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 CorePlus 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 CorePlus 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 CorePlus Mathematics curriculum in ninth and tenthgrade classrooms with diverse student populations. Data from teacher interviews, classroom observations, field journals, assessment documents, and teacher journals related to a yearend 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 CorePlus Mathematics Project (CPMP) curriculum materials. Mr. Allen voluntarily implemented the ninthgrade 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 studentcentered, contextualized activities with focus on exploring and connecting multiple representations. Mr. Allen participated in 15 interviews during his two years of implementation. Interviews were audiorecorded and transcribed. In both years, daily observations of the Patterns of Change unit were videorecorded. 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 nongraphical 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 contentrelated 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 multiplechoice 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 CorePlus 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 CorePlus 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 CorePlus Mathematics program
in terms of 1stedition 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 CorePlus
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 2ndedition courses. The article provides links to influential curriculum recommendations (in PDF form) from Achieve, the American Association of TwoYear Colleges, the American Statistical Association, the College Board, and the Mathematical Association of America. 

CorePlus 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. 
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