Resequencing Calculus Existing Solutions An Early Multivariate - PowerPoint PPT Presentation

Resequencing Calculus Gruenwald and Dwyer The Problem Resequencing Calculus Existing Solutions An Early Multivariate Approach Our Solution Revised Sequence Calculus I Calculus II Calculus III Mark Gruenwald and David Dwyer Strengths University of Evansville Challenges Status Next Steps August 5, 2010 Further Information Supported by NSF Grant 0836676

The Problem Resequencing Calculus Gruenwald and Dwyer The Problem The standard calculus sequence is a bad fit for many Existing Solutions students: Our Solution Multivariate calculus comes too late for biology, Revised Sequence Calculus I economics, and some chemistry majors. Calculus II Calculus III Some students who would benefit from a differential Strengths equations course don’t have room for Calc III. Challenges Many STEM students need matrices. Calculus has Status none; linear algebra requires Calc III. Next Steps Further Information

Existing Solutions Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Our Solution Teach calculus just-in-time within discipline Revised Sequence Calculus I Survey of calculus course or sequence Calculus II Calculus III Discipline-specific calculus course or sequence Strengths Challenges Status Next Steps Further Information

Our Solution Early Multivariate Calculus Resequencing Calculus Gruenwald and Dwyer The Problem Reformulate the 3-semester calculus sequence, primarily Existing Solutions by including some multivariate calculus in Calculus II and Our Solution Revised Sequence moving series to Calculus III, so that Calculus I Calculus II First two semesters form strong sequence for majors Calculus III in the life and social sciences and others. Strengths Challenges Three-course sequence is an even better fit for math, Status physics, and engineering majors. Next Steps Further Information

Calculus I Resequencing Calculus Chapters Gruenwald and Dwyer 1. Functions The Problem 2. Limits Existing Solutions 3. The Derivative Our Solution 4. Applications of the Derivative Revised Sequence Calculus I 5. The Integral Calculus II Calculus III Strengths Challenges Status Next Steps Further Information

Calculus I Resequencing Calculus Chapters Gruenwald and Dwyer 1. Functions The Problem 2. Limits Existing Solutions 3. The Derivative Our Solution 4. Applications of the Derivative Revised Sequence Calculus I 5. The Integral Calculus II Calculus III Strengths Key Changes for Calculus I Challenges Status Incorporation of sequences and their limits Next Steps Further Information

Calculus I Resequencing Calculus Chapters Gruenwald and Dwyer 1. Functions The Problem 2. Limits Existing Solutions 3. The Derivative Our Solution 4. Applications of the Derivative Revised Sequence Calculus I 5. The Integral Calculus II Calculus III Strengths Key Changes for Calculus I Challenges Status Incorporation of sequences and their limits Next Steps Inclusion of polar and parametric functions Further Information

Calculus I Resequencing Calculus Chapters Gruenwald and Dwyer 1. Functions The Problem 2. Limits Existing Solutions 3. The Derivative Our Solution 4. Applications of the Derivative Revised Sequence Calculus I 5. The Integral Calculus II Calculus III Strengths Key Changes for Calculus I Challenges Status Incorporation of sequences and their limits Next Steps Inclusion of polar and parametric functions Further Information Introduction of Taylor polynomials (but not series!)

Calculus I Resequencing Calculus Chapters Gruenwald and Dwyer 1. Functions The Problem 2. Limits Existing Solutions 3. The Derivative Our Solution 4. Applications of the Derivative Revised Sequence Calculus I 5. The Integral Calculus II Calculus III Strengths Key Changes for Calculus I Challenges Status Incorporation of sequences and their limits Next Steps Inclusion of polar and parametric functions Further Information Introduction of Taylor polynomials (but not series!) Reduced emphasis on graphing by hand

Calculus II Resequencing Calculus Chapters Gruenwald and Dwyer 6. Techniques of Integration The Problem 7. Applications of Integration Existing Solutions 8. Differential Equations Our Solution 9. Matrices and Vectors Revised Sequence Calculus I Calculus II 10. Functions of Several Variables Calculus III 11. Double Integrals Strengths Challenges Status Next Steps Further Information

Calculus II Resequencing Calculus Chapters Gruenwald and Dwyer 6. Techniques of Integration The Problem 7. Applications of Integration Existing Solutions 8. Differential Equations Our Solution 9. Matrices and Vectors Revised Sequence Calculus I Calculus II 10. Functions of Several Variables Calculus III 11. Double Integrals Strengths Challenges Key Changes for Calculus II Status Next Steps Inclusion of functions of several variables Further Information

Calculus II Resequencing Calculus Chapters Gruenwald and Dwyer 6. Techniques of Integration The Problem 7. Applications of Integration Existing Solutions 8. Differential Equations Our Solution 9. Matrices and Vectors Revised Sequence Calculus I Calculus II 10. Functions of Several Variables Calculus III 11. Double Integrals Strengths Challenges Key Changes for Calculus II Status Next Steps Inclusion of functions of several variables Further Information Double integrals

Calculus II Resequencing Calculus Chapters Gruenwald and Dwyer 6. Techniques of Integration The Problem 7. Applications of Integration Existing Solutions 8. Differential Equations Our Solution 9. Matrices and Vectors Revised Sequence Calculus I Calculus II 10. Functions of Several Variables Calculus III 11. Double Integrals Strengths Challenges Key Changes for Calculus II Status Next Steps Inclusion of functions of several variables Further Information Double integrals Elimination of infinite series

Calculus III Resequencing Calculus Gruenwald and Dwyer Chapters The Problem 12. Infinite Series Existing Solutions 13. Vector-Valued Functions Our Solution 14. Surfaces, Solids, and Multiple Integrals Revised Sequence Calculus I 15. Vector Analysis Calculus II Calculus III 16. Differential Equations Revisted (Optional) Strengths Challenges Status Next Steps Further Information

Calculus III Resequencing Calculus Gruenwald and Dwyer Chapters The Problem 12. Infinite Series Existing Solutions 13. Vector-Valued Functions Our Solution 14. Surfaces, Solids, and Multiple Integrals Revised Sequence Calculus I 15. Vector Analysis Calculus II Calculus III 16. Differential Equations Revisted (Optional) Strengths Challenges Key Changes for Calculus III Status Next Steps Inclusion of infinite series Further Information

Calculus III Resequencing Calculus Gruenwald and Dwyer Chapters The Problem 12. Infinite Series Existing Solutions 13. Vector-Valued Functions Our Solution 14. Surfaces, Solids, and Multiple Integrals Revised Sequence Calculus I 15. Vector Analysis Calculus II Calculus III 16. Differential Equations Revisted (Optional) Strengths Challenges Key Changes for Calculus III Status Next Steps Inclusion of infinite series Further Information Fewer required sections

Strengths Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Better fit for life sciences, chemistry, and economics Our Solution Natural progression of difficulty through the Revised Sequence Calculus I sequence Calculus II Calculus III Greater chance of completing vector calculus Strengths Facilitates an earlier course in differential equations Challenges Status Allows for calculus-based probability after Calc II Next Steps Further Information

Challenges Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Our Solution Placing transfer students Revised Sequence Placing students with AP (especially BC) credit Calculus I Calculus II Calculus III Overcoming inertia Strengths Pacing Challenges Status Next Steps Further Information

Status Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Our Solution Consulted with (external) math advisory board Revised Sequence Consulted with (internal) STEM+ advisory board Calculus I Calculus II Calculus III Completed Calculus I material Strengths Calculus II development in progress Challenges Status Next Steps Further Information

Next Steps Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Classroom testing of Calculus I at the University of Our Solution Evansville (Fall 2010) Revised Sequence Calculus I Classroom testing of Calculus II at UE (Spring 2010) Calculus II Calculus III Assessment and modification Strengths Challenges Classroom testing at other institutions Status Next Steps Further Information

Further Information Resequencing Calculus Gruenwald and Dwyer The Problem Existing Solutions Our Solution Revised Sequence Mark Gruenwald mg3@evansville.edu Calculus I Calculus II Calculus III David Dwyer dd4@evansville.edu Strengths Website resequencingcalculus.com Challenges Status Next Steps Further Information