Core-Plus Mathematics. Curriculum, Instruction, Assessment. The focus of school mathematics is shifting from a dualistic mission—minimal mathematics for the majority, advanced mathematics for a few—to a singular focus on a common core . . . For all students. Everybody Counts
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Curriculum, Instruction, Assessment
The focus of school mathematics is shifting from a dualistic mission—minimal mathematics for the majority, advanced mathematics for a few—to a singular focus on a common core . . . For all students.
National Research Council
“All students must have access to the highest quality mathematics instructional programs. A society in which only a few have the mathematical knowledge needed to fill crucial economic, political, and scientific roles is not consistent with the values of a just democratic system or its economic needs.” (p. 5)
“Expectations must be raised.” (p. 13)
“All students are expected to study mathematics each of the four years that they are enrolled in high school, whether they plan to pursue the further study of mathematics, to enter the workforce, or to pursue other postsecondary education.” (p. 288)
“Whatever the approach taken, all students learn the same core material while some, if they wish, can study additional mathematics consistent with their interests and career directions.” (p. 289)
Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.
Three years of mathematical study revolving around a core curriculum should be required of all secondary school students. This curriculum should be differentiated by depth and breadth of treatment of common topics and by the nature of applications. All students should study a fourth-year of appropriate mathematics (NCTM, 1989).
Each part of the curriculum should be justified on its own merits (MSEB, 1990).
Mathematics is a vibrant and broadly useful subject to be explored and understood as an active science of patterns (Steen, 1990).
Problems provide a rich context for developing student understanding of mathematics (Schoenfeld, 1988; Schoenfeld, 1992; Heibert, Carpenter, Fennema, Fuson, Human, Murray, Olivier & Wearne, 1996).
Deep understanding of mathematical ideas includes connections among related concepts and procedures, both within mathematics and to the real world (Skemp, 1987).
Computers and calculators have changed not only what mathematics is important, but also how mathematics should be taught (Zorn, 1987; Hembree & Dessart, 1992; Dunham & Dick, 1994).
Classroom cultures of sense-making shape students understanding of the nature of mathematics as well as the ways in which they can use the mathematics they have learned (Resnick, 1987; Resnick, 1988; Lave, Smith, & Butler, 1988).
Social interaction (Cobb, 1995) and communication (Silver, 1996) play vital roles in the construction of mathematical ideas.
Algebra and Functions
Develop student ability to recognize, represent, and solve problems involving relations among quantitative variables.
Develop student ability to analyze data intelligently, recognize and measure variation, and understand the patterns that underlie probabilistic situations.
Develop visual thinking and student ability to construct, reason with, interpret, and apply mathematical models of patterns in visual and physical contexts.
Develop student ability to model and solve problems involving enumeration, sequential change, decision-making in finite settings, and relationships among a finite number of elements.
Course 1 Units
Unit 1: Patterns of Change
Unit 2: Patterns in Data
Unit 3: Linear Functions
Unit 4: Vertex-Edge Graphs
Unit 5: Exponential Functions
Unit 6: Patterns in Shape
Unit 7: Quadratic Functions
Unit 8: Patterns in Chance
Course 2 Units
Unit 1: Functions, Equations, and Systems
Unit 2: Matrix Methods
Unit 3: Coordinate Methods
Unit 4: Regression and Correlation
Unit 5: Nonlinear Functions and Equations
Unit 6: Network Optimization
Unit 7: Trigonometric Methods
Unit 8: Probability Distributions
Course 3 Units
Unit 1: Reasoning and Proof
Unit 2: Inequalities and Linear Programming
Unit 3: Similarity and Congruence
Unit 4: Samples and Variation
Unit 5: Polynomial and Rational Functions
Unit 6: Circles and Circular Functions
Unit 7: Recursion and Iteration
Unit 8: Inverses of Functions and Logarithms
The mathematical content and sequence of units in Course 4 allows considerable flexibility in tailoring a course to best prepare students for various undergraduate programs.
Course 4 Units
Unit 1: Families of Functions
Unit 2: Vectors and Motion
Unit 3: Algebraic Functions and Equations
Unit 4: Trigonometric Functions and Equations
Unit 5: Exponential Functions, Logarithms, and Equations
Unit 6: Surfaces and Cross Sections
Unit 7: Rates of Change
Unit 8: Counting Methods and Induction
Unit 9: Binomial Distributions and Statistical Inference
Unit 10: Mathematics of Information Processing and the Internet
Launch Full class discussion of a problem situation and related questions to think about.
Explore Small group cooperative investigations of focused problem(s)/question(s) related to the launching situation.
Share/Summarize Full class discussion of concepts and methods developed by different groups leads to class constructed summary of important ideas.
Apply A task for students to complete individually to assess their understanding.
On Your Own
Applications Tasks in this section provide students with opportunities to use the ideas they developed in the investigations to model and solve problems in other situations.
Connections Tasks in this section help students organize the mathematics they developed in the investigations and connect it with other mathematics they have studied.
Reflections Tasks in this section help students think about what the mathematics they developed means to them and their classmates and to help them evaluate their own understanding.
Extensions Tasks in this section provide opportunities for students to explore the mathematics they are learning further or more deeply.
Review Tasks in this section provide opportunities for students to review previously learned mathematics and to refine their skills in using that mathematics.
Supplementary Assessment Materials
Conceptions and Beliefs of Teachers
Learning is encouraged through students exchanging ideas, conjecturing, and explaining their reasoning.
Core-Plus Mathematics students outperform comparison students on the mathematics subtest of the nationally standardized Iowa Tests of Educational Development ITED-Q.
Core-Plus Mathematics students demonstrate better conceptual understanding than students in more traditional curricula.
Problem Solving Ability
Core-Plus Mathematics students demonstrate better problem solving ability than comparison students.
Applications and Mathematical Modeling
Core-Plus Mathematics students are better able to apply mathematics than students in more traditional curricula.
Core-Plus Mathematics students perform better on tasks of algebraic reasoning than comparison students. On some evaluation tests, Core-Plus Mathematics student do as well or better; on others they do less well than comparison students.
Important Mathematics in Addition to Algebra
Core-Plus Mathematics students perform well on mathematical tasks involving geometry, probability, statistics, and discrete mathematics.
National Assessment of Educational Progress (NAEP)
Core-Plus Mathematics students scored well above national norms on a test comprised of released items from the National Assessment of Educational Progress.
Student Perceptions and Attitudes
Core-Plus Mathematics students have better attitudes and perceptions about mathematics than students in more traditional curricula.
Performance on State Assessments
The pass rate on the 2004-05 Tenth-Grade Washington Assessment of Student Learning Mathematics test for 22 sate of Washington high schools that were in at least their second year using the Core-Plus Mathematics curriculum was significantly higher than that of a sample of 22 schools carefully matched on prior mathematics achievement, percent of students from low-income families, percent of underrepresented minorities, and student enrollment.
Core-Plus Mathematics students do as well as, or better than, comparable students in more traditional curricula on the SAT and ACT college entrance exams.
College Mathematics Placement Exam
On a mathematics department placement test used at a major Midwestern university, Core-Plus Mathematics students performed as well as students in traditional precalculus courses on basic algebra and advanced algebra subtests, and they performed better on the calculus readiness subtest.
Performance in College Mathematics Courses
Core-Plus Mathematics students completing the four-year curriculum perform as well as, or better than, comparable students in a more traditional curriculum in college mathematics courses at the calculus level and above.