Core-Plus Mathematics Project
Encyclopedia
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
.
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.
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.
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:
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.
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.
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.”
. 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.
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....
-standards-based high school
High school
High school is a term used in parts of the English speaking world to describe institutions which provide all or part of secondary education. The term is often incorporated into the name of such institutions....
mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
curriculum
Curriculum
See also Syllabus.In formal education, a curriculum is the set of courses, and their content, offered at a school or university. As an idea, curriculum stems from the Latin word for race course, referring to the course of deeds and experiences through which children grow to become mature adults...
development projects funded by the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
. 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
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
are taught every year in addition to topics in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, and discrete mathematics
Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
. 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
Problem solving
Problem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Consideredthe most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of...
, 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
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
.
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 SingaporeSingapore
Singapore , officially the Republic of Singapore, is a Southeast Asian city-state off the southern tip of the Malay Peninsula, north of the equator. An island country made up of 63 islands, it is separated from Malaysia by the Straits of Johor to its north and from Indonesia's Riau Islands by the...
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.
Andover High School
One of the first schools to pilot Core-Plus was Andover High SchoolAndover High School (Bloomfield Hills, Michigan)
Andover High School is a public high school in Bloomfield Hills, Michigan, USA and is part of the Bloomfield Hills School District. The school's current principal is Rob Durecka. The school was founded in 1955. The school boasts well-rounded programs in academics, the arts and sports...
in Bloomfield Hills, Michigan
Michigan
Michigan is a U.S. state located in the Great Lakes Region of the United States of America. The name Michigan is the French form of the Ojibwa word mishigamaa, meaning "large water" or "large lake"....
, 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
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of 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 was on the Education Department panel that selected Core-Plus as exemplary, but he said none of the selected programs "had any kind of long-term track record of achievement." 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 RileyRichard Riley
Richard Wilson Riley , American politician, was United States Secretary of Education under President Bill Clinton and the 111th Governor of South Carolina. He is a member of the Democratic Party....
protesting the list. David Klein
David Klein (California State University Northridge)
David Klein is a professor of Mathematics at California State University in Northridge. He is an advocate of increasingly rigorous treatment of mathematics in school curricula and a frequently cited opponent of reforms based on the NCTM standards...
, a mathematician at California State University
California State University
The California State University is a public university system in the state of California. It is one of three public higher education systems in the state, the other two being the University of California system and the California Community College system. It is incorporated as The Trustees of the...
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.
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
Hyman Bass
Hyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959-1998 he was Professor in the Mathematics Department at Columbia University, where he is now professor emeritus...
, President-Elect of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
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 CorrectMathematically Correct
Mathematically Correct is a website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards...
. 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.
See also
The other four NSF funded high school curricula projects:- Interactive Mathematics Program (IMP)Interactive Mathematics Program (IMP)The Interactive Mathematics Program is a four-year, problem-based mathematics curriculum for high schools, designed to meet the needs of both college-bound and non-college-bound students. It was one of several curricula funded by the National Science Foundation and designed around the 1989 ...
- MATH Connections
- Mathematics: Modeling Our World
- SIMMS Integrated Mathematics
External links
- 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