Illustrative Resources for CUPM Guide 2004
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Illustrative Resources
Introduction and Table Of Contents
Part I
1: Understand the student population and evaluate courses and programs
Placement Exams
Mathematical Autobiography
Advising
Redesigning Courses and Programs in Response to Information about Students
Assessing Programs, Courses, and Blocks of Courses
External Support for Assessing Undergraduate Mathematics
Assessment Tools for the Classroom
Gathering Information about Students and Alumni to Improve Programs
2: Develop mathematical thinking and communications skills
Discovery Learning/Inquiry-Based Learning/Problem-Based Learning
Research on Reasoning and Problem Solving
Activities to Help Students Learn to Reason and Work Logically to Conclusions
Strategies for Problem Solving
Motivating Student Reading
Specific Techniques to Improve Students' Ability to Read Mathematical Writing
Use of Mathematical Language in the Classroom
Mathematical Writing Assignments
Assessing Students' Skills in Writing Mathematics
Additional Resources
3: Communicate the breadth and interconnections
Key Ideas and Concepts from Varied Perspectives
Promote Awareness of Connections between Mathematics and Other Subjects
Examples and Applications
Contemporary Topics
Enhance Perception of Vitality and Importance of Mathematics
Additional Resources
4: Promote Interdisciplinary Cooperation
Connecting with other Disciplines within a Mathematics Course
Interdisciplinary Courses
Interdisciplinary-Project-Based Curriculum
Interdisciplinary Programs
Additional Resources
5: Use computer technology to support problem solving and understanding
Tools for Visualization and for Promoting Understanding
Technology Throughout the Curriculum
Additional Resources
6: Provide faculty support for curricular and instructional improvement
Teaching and Learning
Faculty and Professional Development Programs
Practices at Specific Institutions
Additional Resources
Part II. Additional Recommendations Concerning ...
A: Students taking general education or introductory collegiate courses in the mathematical sciences
A.1: Offer suitable courses
General Introductory Courses
Precalculus--New Approaches
Integrating Precalculus and Calculus
Introductory Statistics--New Approaches
College Algebra--New Approaches
Engaging Students in Project Work
Quantitative Literacy
Developing Mathematical and Quantitative Literacy Across the Curriculum
Offering Choices to Satisfy a General Mathematics Requirement
Examples of Introductory Course Syllabi
Support for Faculty Teaching Developmental Mathematics
A.2: Examine the Effectiveness of College Algebra
Refocusing College Algebra
College Algebra – New Approaches
A.3: Ensure the effectiveness of introductory courses
College Algebra --- New Approaches
Pre-Calculus --- New Approaches
Integrating Pre-Calculus and Calculus
B: Students majoring in partner disciplines & prospective teachers
B.1: Promote interdisciplinary collaboration
Strengthening Mathematics Courses to Support Future STEM Study
Learning Communities (See C.5 for Interdisciplinary Majors)
B.2: Develop mathematical thinking and communication
Research on Teaching and Learning
Improving Students' Abilities to Think about and Do Mathematics
Writing in Introductory and Service Courses
Additional Resources
B.3: Critically Examine Course Prerequisites
Prerequisites
Including three-dimensional topics in the first year.
B.4: Pre-service elementary (K-4) and middle-school (5-8)teachers
Guidance to Colleges and Universities
Programs for Elementary Teachers
Programs for Middle School Teachers
Programs for All Grade Levels
Research to Practice – Elementary and Middle School Teachers
Programs for Mathematicians Teaching Future Teachers
Use of Video in Teacher Preparation
Additional Resources
C: Students majoring in themathematical sciences
Examples of Effective Majors
Descriptions of Some Programs at Schools with a Large Number of Mathematics Majors
C.1: Develop mathematical thinking and communication skills
Research on Reasoning and Proof
Inquiry-Guided, Problem-Oriented Learning
Classroom Practice: Writing, Reading and Exploring Proofs
Reasoning with Data: Probability and Statistics
Reading, Writing and Speaking Mathematics
Evaluating Oral Presentations
C.2: Develop skill with a variety of technological tools
Resources for the Use of Technology
Using a Computer Language
C.3: Provide a broad view of the mathematical sciences
A General Resource
Discrete Mathematics and Data Analysis
Geometry and Geometric Thinking
Statistic and Probability and Data Analysis
Linkages – Algebra and Discrete Mathematics
Linkages - Algebra and Geometry
Linkages – Number Theory and Geometry
Linkages - Complex Variables and Geometry
Linkages – Probability and Analysis
Powerful Applications and Contemporary Questions
Breadth of Mathematics and Connectedness to other Disciplines
Broader and More Flexible Major
C.4: Require study in depth
Pairs of Courses
Capstone Courses and Projects
C.5: Create interdisciplinary majors
Joint Majors
Tracks Within the Major
C.6: Encourage and nurture mathematical sciences majors
General References
Designing Introductory Courses to be Effective and Engaging
Encouraging Prospective Majors
Providing Career Information
Mentoring and Advising Mathematics Majors
Co-Curricular Activities for Mathematics Majors
D: Mathematical sciences majors with specific career goals
D.1: Majors preparing to be secondary (9-12) school teachers
Connecting Students’ Learning to their Future Teaching
Geometry
Capstone Courses for Secondary Teachers
Programs for Mathematicians Teaching Future Teachers
Collaboration with Local School Districts
D.2: Majors preparing for the non-academic workforce
Upper-Level Statistics
Skills Needed for Industry
Advising and Mentoring for the Nonacademic Workforce
Internships and Summer Research
Professional Master’s Degree
Additional Resources
D.3: Majors preparing for post-baccalaureate study in the mathematical sciences and allied disciplines
Internships and Summer Research
Special Programs for Graduate School Preparation
Mentoring and Supporting Underrepresented Students
Advising Mathematics Students
Program Examples
Annotated Bibliography
Curriculum Guide
Illustrative Resources
Submit to CUPM-IR
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About CUPM
CRAFTY
MAA
Mathematical Association of America's Committee on the Undergraduate Program in Mathematics (CUPM)
Prepared with support from the National Science Foundation and from the Calculus Consortium for Higher Education
