Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015. All rights were returned to the authors in 2024, who have made all textbooks freely available.
Key Features The first edition of Core-Plus Mathematics was designed to meet the curriculum, teaching, and assessment standards from the National Council of Teachers of MathematicsNational Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.National Council of Teachers of Mathematics. (1991). Mathematics professional standards for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. and the broad goals outlined in the National Research Council report, Everybody Counts: A Report to the Nation on the Future of Mathematics Education.National Research Council; Mathematical Sciences Education Board; Board on Mathematical Sciences and Their Applications. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: The National Academies Press. Later editions were designed to also meet the American Statistical Association Guidelines for Assessment and Instruction in Statistics Education (GAISE)Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education. Alexandria, VA: American Statistical Association. and most recently the standards for mathematical content and practice in the Common Core State Standards for Mathematics (CCSSM).Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
The program puts an emphasis on teaching and learning mathematics through mathematical modeling and mathematical inquiry. Each year, students learn mathematics in four interconnected strands: algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematical modeling.Fey, J., & Hirsch, C. (2007). The case of Core-Plus Mathematics. In C. Hirsch (Ed.), Perspectives on the design and development of school mathematics curricula (pp. 129–142). Reston, VA: National Council of Teachers of Mathematics.
First Edition (1994-2003) The program originally comprised three courses, intended to be taught in grades 9 through 11. Later, authors added a fourth course intended for college-bound students.
Unit No. Course 1 Course 2 Course 3 1 Patterns in Data Matrix Models Multiple-Variable Models 2 Patterns of Change Patterns of Location, Shape and Size Modeling Public Opinion 3 Linear Models Patterns of Association Symbol Sense and Algebraic Reasoning 4 Graph Models Power Models Shapes and Geometric Reasoning 5 Patterns in Space and Visualization Network Optimization Patterns in Variation 6 Exponential Models Geometric Form and Its Function Families of Functions 7 Simulation Models Patterns in Chance Discrete Models of Change Capstone Planning a Benefits Carnival Forest, the Environment, and Mathematics Making the Best of It: Optimal Forms and Strategies
Course 4 UnitsCore UnitsAdditional Units for Students Intending to Pursue Programs in: Mathematical, Physical and Biological Sciences or Engineering Social, Management, and Health Sciences or Humanities 1. Rates of Change 6. Polynomial and Rational Functions 5. Binomial Distributions and Statistical Inference 2. Modeling Motion 7. Functions and Symbolic Reasoning 9. Informatics 3. Logarithmic Functions and Data Models 8. Space Geometry 10. Problem Solving, Algorithms, and Spreadsheets 4. Counting Models
Second Edition (2008-2011) The course was re-organized around interwoven strands of algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematics. Lesson structure was updated, and technology tools, including CPMP-Tools software was introduced.
Unit No. Course 1 Course 2 Course 3 Course 4: Preparation for Calculus 1 Patterns of Change Functions, Equations, and Systems Reasoning and Proof Families of Functions 2 Patterns in Data Matrix Methods Inequalities and Linear Programming Vectors and Motion 3 Linear Functions Coordinate Methods Similarity and Congruence Algebraic Functions and Equations 4 Vertex-Edge Graphs Regression and Correlation Samples and Variation Trigonometric Functions and Equations 5 Exponential Functions Nonlinear Functions and Equations Polynomial and Rational Functions Exponential Functions, Logarithms, and Data Modeling 6 Patterns in Shape Network Optimization Circles and Circular Functions Surfaces and Cross Sections 7 Quadratic Functions Trigonometric Methods Recursion and Iteration Concepts of Calculus 8 Patterns in Chance Probability Distributions Inverse Functions Counting Methods and Induction
CCSS Edition (2015) The course was aligned with the Common Core State Standards (CCSS) mathematical practices and content expectations. Expanded and enhanced Teacher's Guides include a CCSS pathway and a CPMP pathway through each unit. Course 4 was split into two versions: one called Preparation for Calculus, for STEM-oriented students, and an alternative course, Transition to College Mathematics and Statistics (TCMS), for college-bound students whose intended program of study does not require calculus.
Unit No. Course 1 Course 2 Course 3 Course 4: Preparation for Calculus TCMS 1 Patterns of Change Functions, Equations, and Systems Reasoning and Proof Families of Functions Interpreting Categorical Data 2 Patterns in Data Matrix Methods Inequalities and Linear Programming Vectors and Motion Functions Modeling Change 3 Linear Functions Coordinate Methods Similarity and Congruence Algebraic Functions and Equations Counting Methods 4 Discrete Mathematical Modeling Regression and Correlation Samples and Variation Trigonometric Functions and Equations Mathematics of Financial Decision-Making 5 Exponential Functions Nonlinear Functions and Equations Polynomial and Rational Functions Exponential Functions, Logarithms, and Data Modeling Binomial Distributions and Statistical Inference 6 Patterns in Shape Modeling and Optimization Circles and Circular Functions Surfaces and Cross Sections Informatics 7 Quadratic Functions Trigonometric Methods Recursion and Iteration Concepts of Calculus Spatial Visualization and Representations 8 Patterns in Chance Probability Distributions Inverse Functions Counting Methods and Induction Mathematics of Democratic Decision-Making
Evaluations, Research, and Reviews Project and independent evaluations and many research studies have been conducted on Core-Plus Mathematics, including content analyses, case studies, surveys, small- and large-scale comparison studies, research reviews, and a longitudinal study.
Positive reviews
There are multiple research studies and evaluations in which students using Core-Plus Mathematics performed significantly better than comparison students on assessments of conceptual understanding, problem solving, and applications, and results were mixed for performance on assessments of by-hand calculation skills.Schoen, H. L., & Hirsch, C. R. (2003). The Core-Plus Mathematics Project: Perspectives and student achievement. In S. Senk & D. Thompson (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? (pp. 311–344). Hillsdale, NJ: Lawrence Erlbaum Associates.Schoen, H. L., Hirsch, C. R., & Ziebarth, S. W. (1998). An emerging profile of the mathematical achievement of students in the Core-Plus Mathematics Project. Paper presented at the 1998 Annual Meeting of the American Educational Research Association. San Diego, CA. Some of these studies were funded by the National Science Foundation, the same organization that funded the development of Core-Plus Mathematics program.
Large-scale comparison studies A three-part study of Core-Plus Mathematics and more conventional curricula were reported by researchers at the University of Missouri. The research was conducted as part of the Comparing Options in Secondary Mathematics: Investigating Curricula project, supported by the National Science Foundation under REC-0532214. The research was reported in the March and July 2013 issues of the Journal for Research in Mathematics Education and in the December 2013 issue of the International Journal of Science and Mathematics Education. The three studies examined student achievement in schools in 5 geographically dispersed states. The first study involved 2,161 students in 10 schools in first-year high school mathematics courses, the second study involved 3,258 students in 11 schools in second-year mathematics courses, and the third study involved 2,242 students in 10 schools in third-year mathematics courses. Results in the first study showed that Core-Plus Mathematics students scored significantly higher on all three end-of-year outcome measures: a test of common objectives, a problem solving and reasoning test, and a standardized achievement test. Results in the second study showed that Core-Plus Mathematics students scored significantly higher on a standardized achievement test, with no differences on the other measures. Results in the third study showed that Core-Plus Mathematics students scored significantly higher on a test of common objectives, with no differences on the other measure.
Other comparison studies A study conducted by Schoen and Hirsch, two authors of Core-Plus Mathematics, reported that students using early versions of Core-Plus Mathematics did as well as or better than those in traditional single-subject curricula on all measures except paper-and-pencil algebra skills.
A study on field-test versions of Core-Plus Mathematics, supported by a grant from the National Science Foundation (Award MDR 9255257) and published in 2000 in the Journal for Research in Mathematics Education, reported that students using the first field-test versions of Core-Plus Mathematics scored significantly better on tests of conceptual understanding and problem solving, while Algebra II students in conventional programs scored significantly better on a test of paper-and-pencil procedures.
Other studies reported that Core-Plus Mathematics students displayed qualities such as engagement, eagerness, communication, flexibility, and curiosity to a much higher degree than did students who studied from more conventional programs. A review of research in 2008 concluded that there were modest effects for Core-Plus Mathematics on mostly standardized tests of mathematics.