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A Flipped Experience for Learning Linear Algebra
In this flipped classroom, students are responsible for learning and creating knowledge with the facilitation of the instructor. This webstie provides the roadmap to guide students on their path to become an independent learner and proficient problem solver. This project is supported by the 2013 Enhancing Educational Effectiveness Through Technology Awards Program: Flipping the Classroom at California State University, Long Beach. Any question or comment should be directed to Professor Jen-Mei Chang (jen-mei.chang@csulb.edu).
Course Materials:
- Course Syllabus [PDF, 115 KB]
- Calendar of topics [Excel, 40.5 KB]
- Before first day announcement [PDF, 131 KB]
- For the late comers [PDF, 156 KB]
- Professor Robert Mena's Notes [PDF, 5.72 MB] on Matrix Theory
- Panopto videos should be accessed through Beachboard
Class #
Pre-Class Tasks
In-Class Tasks
Post-Class Tasks
1. 8/26/13
Learning Objective
Familiarity with a flipped classroom and course syllabus
- What is The Flipped Classroom (graphical illustration by Knewton)
- Why Flipped Classroom (YouTube video by Aaron Sam at Woodland Park High School)
- The Flipped Classroom Model (YouTube video by MADDrawProductions)
- Course Syllabus [PDF, 115 KB]
- Individual Quiz (BB.Quiz.1 ->)
- Q & A
- Group.Quiz.1
- HW.1: Academic Preparation Survey.
- HW.1 : Mathematics Attitude Survey. Complete both by 8/29/13.
2. 8/28/13
Learning Objective
Familiarity with teacher expectations and course learning outcomes
- Expected Student Learning Outcomes (YouTube video by Jen-Mei Chang at CSULB)
- Study Strategies for Effective Learning in Mathematics Classes (Panopto video ->)
- Writing Guide & Rubrics For Grading [PDF, 4.22 MB]
- Basic Concepts and Applications of Matrices (Mena's Notes [PDF, 5.72 MB] on pg.1-6)
- Individual Quiz (BB.Quiz.2 ->)
- Q & A
- Group.Quiz.2
- HW.2:
Schedule a 5-minute appointment
with me via email by 8/29/13
(identify my availability with this calendar)
3. 9/4/13
Learning Objective
Basic understanding of systems of linear equations
- Solving Systems of Linear Equations in Algebra Classes (Panopto video ->)
- Systems of Linear Equations: Geometric Interpretation and Types (Panopto video ->)
- Solving a System with Row Operations (Panopto video ->)
- Reading (Lay pg.2-9)
- Individual Quiz (BB.Quiz.3 ->)
- Q & A
- Form Groups & Assign Roles
- Group.Quiz.3
- HW.3: Lay pg.10: 7,11,15,17,23-25
- Understanding group roles [PDF, 496 KB]
4. 9/9/13
Learning Objective
Linear combination, sets, and span
- Vectors: Set Notations (Khan Academy video)
- Vectors: Geometric and Algebraic Interpretations (Khan Academy video)
- Mathematical Sets and Operators (video lecture (1m57s ~ 7m41s) by Bill Shillito)
- Linear Combination & Span (Khan Academy video)
- Reading (Lay pg.24-31)
- Individual Quiz (BB.Quiz.4 ->)
- Q & A
- Group.Quiz.4
- HW.4: Lay pg.32: 3,7,9,11,17,19,23,25
5. 9/11/13
Learning Objective
Reduced row echelon form and Gaussian elimination
- Row Reduction, Echelon Forms, and Reduced Echelon Forms (Panopto video ->)
- Solving Systems of Linear Equations with Gaussian Elimination (GE) or Reduced Row Echelon Form (Panopto video ->)
- GE Example For More Practice ( Khan Academy video)
- Reading (Lay pg.12-21)
- Individual Quiz (BB.Quiz.5 ->)
- Q & A
- rref by Technology
- Group.Quiz.5
- HW.5: Lay pg.21: 1,3,9,11,13,21,23,29
6. 9/16/13
Learning Objective
Technique to prove or disprove if-then statements for true/false problems
- How to Prove or Disprove a Statement (video lecture by GVSUmath)
- Ax = b (Panopto video ->)
- Solution Sets of Linear Systems: Algebraic and Geometric Interpretations (Panopto video ->)
- Reading (Lay pg.34-37; pg. 43-46)
- Individual Quiz (BB.Quiz.6 ->)
- Q & A
- Group.Quiz.6
- HW.6:
Lay pg.40: 9,11,13,15,17,19,23,31;
pp.47: 1,11,13,19,23,29,31
7. 9/18/13
Learning Objective
Linear dependence/independence
- Linear Independence/Dependence: Geometric Interpretation (Khan Academy video)
- Linear Independence/Dependence: Formal Definition (Khan Academy video)
- The logic of if and only if (YouTube video by Kevin deLaplante)
- Reading (Lay pg.55-60)
- Individual Quiz (BB.Quiz.7 ->)
- Q & A
- Group.Quiz.7
- HW.7: Lay pg.60:
1,5,7,9,11,15,17,19,21,
23,25,27,29,33,35,37
8. 9/23/13
Learning Objective
Summative Assessment
- Review for Exam 1
- Exam 1: Lay 1.1 - 1.7
- Self Reflection
9. 9/25/13
Learning Objective
Linear transformation
- Matrix Multiplication as Linear Transformation (Panopto video ->)
- Examples of Linear Transformations (Panopto video ->)
- Reading (Lay pg.62-67)
- Individual Quiz (BB.Quiz.8 ->)
- Q & A
- Group.Quiz.8
- HW.8: Lay pg.68: 1,3,7,11,13,17,21,31
10. 9/30/13
Learning Objective
1-1 & onto
- Standard Matrix of Linear Transformation (Panopto video ->)
- Definition and Examples of One-to-One and Onto Maps (Panopto video ->)
- Reading (Lay pg.70-76)
- Individual Quiz (BB.Quiz.9 ->)
- Q & A
- Group.Quiz.9
- HW.9: Lay pg.78: 3,5,7,19,21,23,25,27
11. 10/2/13
Learning Objective
Two views of matrix multiplication
- Matrix Multiplications and Properties (Panopto video ->)
- Reading (Lay pg.92-100)
- Individual Quiz (BB.Quiz.10 ->)
- Q & A
- Group.Quiz.10
- HW.10: Lay pg.100: 5,9,13,15,17,21,27
12. 10/7/13
Learning Objective
Matrix inverse and its applications
- The Inverse of a Matrix (Panopto video ->)
- Cryptography: An Application of Matrix Inverse (Mena's Notes [PDF, 5.72 MB] on pg.46)
- Reading (Lay pg.102-108)
- Individual Quiz (BB.Quiz.11 ->)
- Q & A
- Group.Quiz.11
- HW.11: Lay pg.109: 5,7,9,11,23,31
13. 10/9/13
Learning Objective
Properties of invertible matrices & determinants
- The Invertible Matrix Theorem (Lay pg. 112 - 114)
- The Matrix Determinant (Panopto video ->)
- Properties of Determinants (Panopto video ->)
- Reading (Lay pg.164-167; pg.169-174)
- Individual Quiz (BB.Quiz.12 ->)
- Q & A
- Group.Quiz.12
- HW.12: Lay pg.115: 7,11,13,21,23,33; pg.167: 9,17,39; pg.175: 9,11,15,17,19,23,27,31
14. 10/14/13
Learning Objective
Vector spaces and subspaces
- Definition and Examples of Vector Spaces (Panopto video ->)
- Definition and Examples of Vector Subspaces (Panopto video ->)
- Reading (Lay pg.190-195)
- Individual Quiz (BB.Quiz.13 ->)
- Q & A
- Group.Quiz.13
- HW.13: Lay pg.195: 1,3,5,7,9,11,13,15,17,23
15. 10/16/13
Learning Objective
Summative Assessment
- Review for Exam 2
- Exam 2: Lay 1.8-1.9; 2.1-2.3;3.1-3.2
- Self Reflection
16. 10/21/13
Learning Objective
Null spaces and column spaces
- Null Spaces of a Matrix & Kernel of a Linear Transformation (Panopto video ->)
- Column Spaces of a Matrix & Range of a Linear Transformation (Panopto video ->)
- Reading (Lay pg.198-205)
- Individual Quiz (BB.Quiz.14 ->)
- Q & A
- Group.Quiz.14
- HW.14: Lay pg.205: 5,11,15,17,21,23,25
17. 10/23/13
Learning Objective
Basis
- Basis as a Linearly Independent & Spanning Set (Panopto video ->)
- Example of Basis & Non-Basis for Matrices and Polynomials (Panopto video ->)
- The Spanning Set Theorem (Panopto video ->)
- Reading (Lay pg.208-213)
- Individual Quiz (BB.Quiz.15 ->)
- Q & A
- Group.Quiz.15
- HW.15: Lay pg.213: 9,11,13,15,21,25
18. 10/28/13
Learning Objective
Coordinate systems
- Getting Familiar with a Coordinate System (Panopto video ->)
- Coordinates Relative to a Basis (Panopto video ->)
- Reading (Lay pg.216-222)
- Individual Quiz (BB.Quiz.16 ->)
- Q & A
- Group.Quiz.16
- HW.16: Lay pg.222: 3,7,13,15,16,29,31(a)
19. 10/30/13
Learning Objective
Dimension of vector space vs. Rank of a matrix
- Dimension of Vector Spaces (Panopto video ->)
- Rank & The Rank Theorem (Panopto video ->)
- Reading (Lay pg.225-228;pg.230-236)
- Individual Quiz (BB.Quiz.17 ->)
- Q & A
- Group.Quiz.17
- HW.17: Lay pg.229: 5,7,9,11,13,19,20;pg.236: 3,5,7,9,11,13,15,17,18,19,25
20. 11/4/13
Learning Objective
Change of basis
- Change of Basis (Panopto video ->)
- Reading (Lay pg.239-242)
- Individual Quiz (BB.Quiz.18 ->)
- Q & A
- Group.Quiz.18
- Discussion of poster projects
- HW.18: Lay pg.242: 1,5,7,11,13
21. 11/6/13
Learning Objective
Eigenvectors and eigenvalues
- Eigenvalues and Eigenvectors (Panopto video ->)
- Geometric vs. Algebraic Multiplicity of Eigenvalues (Panopto video ->)
- Reading (Lay pg.266-271;pg.274-279)
- Individual Quiz (BB.Quiz.19 ->)
- Q & A
- Group.Quiz.19
- HW.19: Lay pg.272: 7,13,17,21,25; pg.279: 7,11,15,21; See Pre-Task for 11/12, come prepared
22. 11/12/13
Learning Objective
Develop skills for independent learning
- Work with your team members to come up with a 5-question practice exam 3 with answers (to be exchanged with other groups during class)
- Individual & group work on mock exams
- Study for Exam 3
23. 11/13/13
Learning Objective
Summative Assessment
- Review for Exam 3
- Exam 3: Lay 4.1 - 4.7
- Self Reflection
24. 11/18/13
Learning Objective
Matrix Diagonalization
- Why Do We Diagonalize a Matrix? (Panopto video ->)
- Diagonalization as a Similarity Transformation (Panopto video ->)
- How Do We Diagonalize a Matrix? (Panopto video ->)
- Reading (Lay pg.281-286)
- Individual Quiz (BB.Quiz.20 ->)
- Q & A
- Group.Quiz.20
- Discussion of poster projects
- HW.20: Lay pg.286: 1,7,11,15,21,22,23,31,32
25. 11/20/13
Learning Objective
Approximating Ax = b; quantifying Ax-b
- Approximation to Ax = b (Panopto video ->)
- Inner Product, Normalization, Lengths, and Distances (Panopto video ->)
- Notion of Orthogonality, Pythagorean Theorem, and Orthogonal Complement (Panopto video ->)
- Reading (Lay pg.330-336)
- Individual Quiz (BB.Quiz.21 ->)
- Q & A
- Group.Quiz.21
- HW.21: Lay pg.336: 1-19 odd,22,25,27,31
26. 11/25/13
Learning Objective
Orthogonal projections
- Orthogonal Basis for Linear Combinations (Panopto video ->)
- Orthonormal Basis for Linear Combinations & Orthogonal Matrix (Panopto video ->)
- Orthogonal Projections in 2D (Panopto video ->)
- Orthogonal Projections in R^n (Panopto video ->)
- Novelty filter as an application to orthogonal projections [PDF, 38.7 KB]
- The Approximation Theorem, Distance Between a Point & a Subspace, Matrix Notation for Orthogonal Projections (Panopto video ->)
- Reading (Lay pg.338-344;pg.347-351)
- Individual Quiz (BB.Quiz.22 ->)
- Q & A
- Group.Quiz.22
- HW.22: Lay pg.344: 9,13,17,23,24; pg.352: 9,11,15,17,21,22
27. 12/2/13
Learning Objective
Culmination of skills
- compose, practice, revise, print poster
- review the grading rubrics [PDF, 268 KB]
- The Gram-Schmidt Process for Producing Orthonormal Basis (Panopto video ->)
- The QR-Factorization (Panopto video ->)
- Reading (Lay pg.354-358)
- Individual Quiz (BB.Quiz.23 ->)
- Groups 1-4: present
- Groups 5-8: critique
- None
- HW.23: Lay pg.358: 3,7,11,15
28. 12/4/13
Learning Objective
Culmination of skills
- review the grading rubrics [PDF, 268 KB]
- The Gram-Schmidt Process for Producing Orthonormal Basis (Panopto video ->)
- The QR-Factorization (Panopto video ->)
- Reading (Lay pg.354-358)
- Individual Quiz (BB.Quiz.23 ->)
- compose, practice, revise, print poster
- Groups 1-4: critique
- Groups 5-8: present
- HW.23: Lay pg.358: 3,7,11,15
- None
29. 12/9/13
Learning Objective
Gram-Schmidt Process; The least squares problems
- The Normal Equation and The Least Squares Problems (Panopto video ->)
- Reading (Lay pg.360-365; pg.368-372)
- Individual Quiz (BB.Quiz.24 ->)
- Q & A
- Group.Quiz.23
- HW.24: Lay pg.366: 5,11,15,17,18; pg.374: 3
30. 12/13/13
Learning Objective
Summative Assessment
- Review for Final Exam
- Cumulative Final Exam: 8:00 - 10:00 AM
-
Extra Credit (10 points towards Final Exam).
Please complete both between 12/10 and 12/15/13.
- Perceptions of Student Learning in a Flipped Linear Algebra Class
- Mathematics Attitude Survey