Core-Plus Mathematics Project
The Core-Plus Mathematics Project is one of the five NCTM-standards-based high school mathematics curriculum development projects funded by the National Science Foundation. The project has developed, tested, and published (Glencoe/McGraw Hill) a four-year comprehensive high school mathematics textbook series. The first edition is entitled, Contemporary Mathematics in Context: A Unified Approach. The second edition, to be available Fall 2007, is entitled, Core-Plus Mathematics. The first three years of the curriculum are designed for all high school students, with a fourth year course designed to continue the preparation of students for college mathematics. Core-Plus Mathematics is an integrated curriculum, in which algebra and geometry are taught every year in addition to topics in statistics, probability, and discrete mathematics. The series is intended to replace the common U.S. high school course sequence, in which there are separate courses in algebra and geometry.
Core-Plus Mathematics emphasizes "real-world" applications and teaching and learning mathematics through problem solving, such as in elementary targeted curricula such as TERC and Everyday Mathematics. Several studies have suggested that graduates are less prepared for college level math and more likely to require remedial math than traditional approaches. Other studies have questioned the validity of those results and suggest that Core-Plus is an effective pedagogy.
Origin of Core-Plus
Core-Plus is part of a worldwide trend toward an integrated approach to mathematics, including in countries that outperform the U.S. on international tests, though textbooks from nations such as Singapore are traditional, not standards-based approaches. Each course of Core-Plus was developed through a five-year process of research, development, and field testing. The author team for Core-Plus Mathematics includes a recent past president of the Mathematical Association of America, a recent past president of the National Council of Teachers of Mathematics, two writers for the 1989 NCTM Standards, a consultant for the 2000 NCTM Standards, and national experts in algebra, geometry, discrete mathematics, and statistics education. In addition, an advisory board of mathematics educators and a consultant team of mathematicians advised the project. The project is based in the Mathematics Department at Western Michigan University.
Core-Plus Mathematics is one of 13 mathematics curriculum projects funded by the National Science Foundation (NSF), for elementary, middle, and high school. NSF spent about $86 million in the 1990s to fund these projects. It is estimated that several million students currently use the NSF-funded curricula, including at least 500 high schools using Core-Plus.
Awards and research evidence
The U.S. Department of Education gave its top rating of “Exemplary” to the Core-Plus mathematics program in 1999. Only five programs were given this award based on a national search and review of 61 programs. U. S. Assistant Education Secretary Kent McGuire stated that, “The exemplary programs have met the highest standards set by our nation’s leading mathematics experts and educators. These programs work, and we encourage teachers, administrators, and policymakers to learn more about them as potential additions to their curriculum.”
Four of the top 25 high schools on the 2003 Newsweek list of “America’s best high schools” used Core-Plus Mathematics.
Numerous journal articles, book chapters, conference presentations, and Ph.D. dissertations document the content, approach, and effectiveness of Core-Plus Mathematics.
The March 2013 issue of the Journal for Research in Mathematics Education reports on what Western Michigan University's Core Plus Mathematics page describes as a "carefully-controlled study in which Core-Plus Mathematics students performed significantly better on a Test of Common Objectives, on a Problem Solving and Reasoning Test, and on the standardized test, ITED Mathematics: Concepts and Problem Solving than did students from publisher-produced, single-subject texts from Glencoe, McDougal Littel, Holt (Kennedy et al), Holt (Schulz et al), and Prentice Hall." The multi-year study followed as close as possible the recent recommendations on evaluating curricular effectiveness from the National Research Council and found "students who studied from integrated [curricula] were significantly advantaged over students who studied from a subject-specific [curricula] on three end-of-year outcome measures.
Andover High School
One of the first schools to pilot Core-Plus was Andover High School in Bloomfield Hills, Michigan, which is ranked one of America's "100 best" high schools. To boost performance and interest in mathematics, Andover stopped traditional mathematics in 1994 and began using Core-Plus Mathematics. Students studied math in context, for example they investigated running shoes, manufacturing, and air-pollution problems. Students often worked in teams using powerful calculators and computers. They were asked to explain their thinking and reasoning, and sometimes asked to write paragraphs, rather than just find correct numbers as answers.
An article in the Christian Science Monitor reported that Melissa Lynn graduated from Andover in 1997 with a 3.97 grade-point average. But the math placement test at the University of Michigan put her into "remedial math." One of the main purposes of the program is to reduce the number of remedial math placements. The article reports on a survey conducted in 1997 of Andover graduates in which 96 percent of students who returned the survey said they were placed into “remedial math” in college. In a neighboring school, 62 percent of the students who returned the survey took remedial math in college. Activism by a group of parents caused Andover to return to offering a traditional math option. By 2000, half of students at Andover were taking Core-Plus and the other half were taking traditional math.
Gregory F. Bachelis, Professor of Mathematics at Wayne State University surveyed students at Andover and Lahser high schools. Among comments returned by students:
- "Core Plus was a waste of my time. I have very few math skills, and none of them helped me with Algebra I in College"
- Core Plus was probably the most horrible experience I have ever gone through in high school.
- Core Plus has got to be one of the worst math programs. We were never taught any of the basics and most are suffering in college math courses
- My math skills went downhill. It is a terrible program. I wouldn’t recommend it to my worst enemy.
- I am completely unprepared and have no way to understand college math. I have to take Math 115 (High School Math)
- By senior year they could not even factor or do other basic mathematics which I learned in 8th grade!
- It could be a useful method in Mathematics if presented correctly
This unpublished survey study has been criticized for involving a self-selected sample, self-reported data, and biased survey methods. Data provided by the University of Michigan registrar at this same time indicate that in collegiate mathematics courses at the University of Michigan graduates of Core-Plus do as well as or better than graduates of a traditional mathematics curriculum. A later study found that graduates of the Core-Plus curriculum entering Michigan State University have placed into increasingly lower level mathematics courses as the implementation of the curriculum has progressed. This study and the published report have been criticized for design flaws and for drawing conclusions that are not supported by the data. Core-Plus continues to be used, with continued criticism across the nation although there has been increased interest in traditional algebra instruction.
U.S. Department of Education
Mathematician Manuel Berriozabal, who was on the Education Department panel that selected Core-Plus as exemplary said that "the panel was a good idea" but that, to the best of his knowledge, none of the selected programs "had any kind of long-term track record of achievement." Steven Leinwant, a principal Research Analyst at the American Institutes for Research (AIR) and former president of the National Council of Supervisors of Mathematics, commenting on this, stated "These programs were just too new to require long-term impact studies. To require that would have postponed any designation for years...If we had built that criterion in, it would have been an uneven playing field, since many programs just haven't been around long enough to have that kind of impact data." Core-Plus was just one of the Education Department's top 10 list of math programs. A letter signed by more than 200 mathematicians, physicists, and four Nobel laureates appeared in the Washington Post as an Open Letter to U.S. Secretary of Education Richard Riley protesting the list. David Klein, a mathematician at California State University at Northridge who co-authored the Open Letter, said "This expert panel's list includes some of the worst math programs you can find anywhere." The letter was prepared and circulated by six mathematics professors, and the Packard Humanities Institute of Los Altos, California, paid about $70,000 to place the open letter as a paid advertisement in the Washington Post. On the panel's use of the NCTM Standards as a "filter" for which curricula would qualify for the list, panel member Jack Price, a mathematics professor from California State Polytechnic University at Pomona, and former NCTM president, noted that forty-three states had NCTM-based standards, and that "those were the only national standards out there."
U.S. Education Secretary Richard Riley replied to the Open Letter stating that, “We do not agree with your assertion that both the panel and the criteria it used were outside the existing mathematics education mainstream. It is important to note that the Panel concluded that each of the programs had demonstrated a measurable difference in student learning.” Steven Leinwand, a member of the Education Department panel, said that “Every one of the programs designated as exemplary had real, clean data that showed test scores going up.” Hyman Bass, President-Elect of the American Mathematical Society at the time, “disagrees with many of the conclusions in the letter, but his main objection is that the letter has inserted the debate over mathematics curricula ‘into the world of journalism and politics, where … serious and balanced discussion will no longer be possible’.”
A response letter written by research mathematicians that is critical of the Open Letter states that, “We believe that their letter [the Open Letter] does a grave disservice to the cause of improving mathematics education in American schools…. We note first that, distinguished in their disciplines though the signers of that letter may be, virtually none of the signatories has any track record whatsoever in pre-university mathematics education.” Another mathematician, in a public written response to the Open Letter, states that the letter “uncritically cites reports of those who dislike these curricula, without making it clear that many mathematicians -- including distinguished ones -- support the curricula (the physicist who signed it from our institution did so under the impression that the mathematics community was united in its condemnation).” Other mathematicians are likewise concerned that the Open Letter gives the false impression that the mathematical community agrees with the letter’s conclusions. “In fact, there is no such clear-cut consensus on the issues the letter raises.” The criticisms of the curricula are not shared by all the signers of the letter. The Open Letter states that, “While we do not necessarily agree with each of the criticisms of the programs stated above [in the letter] … we believe …” that the exemplary designations are “premature” and that there were not enough “well-respected mathematicians” involved in the process. Kent McGuire, U.S. Assistant Secretary of Education at the time, stated that, “Nearly 100 experts were involved in the review process” on which the panel’s exemplary designation was based. “The programs were designated ‘exemplary’ because they provided convincing evidence of their effectiveness in multiple sites with multiple populations.”
Various experiences in schools
Core-Plus is a text series cited as one of the worst reform mathematics texts by groups such as Mathematically Correct. They cite schools that have dropped Core-Plus after adopting it, and cite studies showing graduates of the curriculum scoring poorly in college math placement exams.
Other groups, such as Mathematically Sane, have applauded the NCTM-Standards-based curricula such as Core-Plus Mathematics. They point to the many schools in which Core-Plus is successfully used, and cite research studies supporting the effectiveness of Core-Plus Mathematics that have appeared in journal articles, book chapters, conference presentations, and Ph.D. dissertations.
The other four NSF funded high school curricula projects:
- Interactive Mathematics Program (IMP)
- MATH Connections
- Mathematics: Modeling Our World
- SIMMS Integrated Mathematics
- "U.S. Dept. of Ed. exemplary math programs". Ed.gov. Retrieved 20 February 2015.
- "Annotated Bibliography of Research and Other Publications about Core-Plus Mathematics". Wmich.edu. Retrieved 20 February 2015.
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- "Christian Science Monitor". Web.archive.org. Archived from the original on 2003-02-19. Retrieved 20 February 2015.
- "Preliminary Report on a Survey of the Graduating Classes of 1997 of Andover High School and Lahser High School, Bloomfield Hills, Michigan, Gregory F. Bachelis, Ph.D. Professor of Mathematics, Wayne State University". Math.wayne.edu. Retrieved 20 February 2015.
- "Frequently Asked Questions About the Core-Plus Mathematics Project". Wmich.edu. Retrieved 20 February 2015.
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- "A Study of Core-Plus Students Attending Michigan State University" (PDF). Mth.msu.edu. Retrieved 20 February 2015.
- "Frequently Asked Questions About the Core-Plus Mathematics Project". Wmich.edu. Retrieved 20 February 2015.
- "Steve Leinwand Principal Researcher, Education Program". Air.org. Retrieved 20 February 2015.
- "Steven Leinwand Heinemann author profile". Heinemann.com. Retrieved 20 February 2015.
- "Mathematically Correct web site". Mathematicallycorrect.com. Retrieved 20 February 2015.
- "For Your Information : New 2000 Mathematics subject ClassifiactionNow in Effect" (PDF). Ams.org. Retrieved 20 February 2015.
- "News | U.S. Department of Education". Ed.gov. Retrieved 2015-02-20.
- "Math Forum Discussions - Open letter to Riley: Further reactions". Mathforum.org. Retrieved 2015-02-20.
- "Math Forum Discussions - =Letter to Riley-Uhl et al". Mathforum.org. Retrieved 2015-02-20.
- "Math Forum Discussions - Mathematician reacts to Open Letter". Mathforum.org. 1999-11-29. Retrieved 2015-02-20.
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- Mathematically Sane Evidence for reform mathematics programs including Core-Plus
- Mathematically Correct Reviews critical of reform mathematics programs including Core-Plus
- WhereIsTheMath Washington State-based group critical of reform/constructivist math curricula and pedagogy.
- Compass Curricular Options in Mathematics Programs for All Secondary Schools
- Annotated Bibliography of Core-Plus Publications