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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 road map to guide students on their path to become an independent learner and proficient problem solver. This project was originally 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:

Please note:

Class #

Pre-Class Tasks

In-Class Tasks

Post-Class Tasks

1. MW 1/21 (TT 1/20)

Learning Objective

Familiarity with a flipped classroom and course syllabus

  1. What is The Flipped Classroom (graphical illustration by Knewton)
  2. Why Flipped Classroom (YouTube video by Aaron Sam at Woodland Park High School)
  3. The Flipped Classroom Model (YouTube video by MADDrawProductions)
  4. Preview the course syllabus (use the appropriate link above depending on your class)
  5. Individual Quiz (BB.Quiz.1 ->)

2. MW 1/26 (TT 1/22)

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 (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 ->)
  • HW.2:

    Come by my office and say hi

    (identify my availability with this calendar)

3. MW 1/28 (TT 1/27)

Learning Objective

Basic understanding of systems of linear equations

  • Solving Systems of Linear Equations in Algebra Classes (video)
  • Systems of Linear Equations: Geometric Interpretation and Types (video)
  • Solving a System with Row Operations (video)
  • Reading (Lay pg.2-9)
  • Individual Quiz (BB.Quiz.3 ->)
  • HW.3:

    Group.Quiz.3

    (E.C.) Lay pg.10: 7,11,15,17,23-25

4. MW 2/2 (TT 1/29)

Learning Objective

Linear combination, sets, and span

  • HW.4:

    Group.Quiz.4

    (E.C.) Lay pg.32: 3,7,9,11,17,19,23,25

5. MW 2/4 (TT 2/3)

Learning Objective

Reduced row echelon form and Gaussian elimination

  • Row Reduction, Echelon Forms, and Reduced Echelon Forms (video)
  • Solving Systems of Linear Equations with Gaussian Elimination (GE) or Reduced Row Echelon Form (video)
  • GE Example For More Practice ( Khan Academy video)
  • Reading (Lay pg.12-21)
  • Individual Quiz (BB.Quiz.5 ->)
  • HW.5:

    Group.Quiz.5

    (E.C.) Lay pg.21: 1,3,9,11,13,21,23,29

6. MW 2/9 (TT 2/5)

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 (video)
  • Solution Sets of Linear Systems: Algebraic and Geometric Interpretations (video)
  • Reading (Lay pg.34-37; pg. 43-46)
  • Individual Quiz (BB.Quiz.6 ->)
  • HW.6:

    Group.Quiz.6

    (E.C.) Lay pg.40: 9,11,13,15,17,19,23,31;

    pp.47: 1,11,13,19,23,29,31

7. MW 2/11 (TT 2/10)

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 ->)
  • HW.7:

    Group.Quiz.7

    (E.C.) Lay pg.60: 1,5,7,9,11,15,17,19,21,

    23,25,27,29,33,35,37

8. MW 2/16 (TT 2/12)

Learning Objective

Linear transformation

  1. Matrix Multiplication as Linear Transformation (video)
  2. Examples of Linear Transformations (video)
  3. Reading (Lay pg.62-67)
  4. Individual Quiz (BB.Quiz.8 ->)
  • HW.8:

    Group.Quiz.8

    (E.C.) Lay pg.68: 1,3,7,11,13,17,21,31

9. MW 2/18 (TT 2/17)

Learning Objective

Summative Assessment

  • Review for Exam 1
  • Exam 1: Lay 1.1 - 1.7
  • Self Reflection

10. MW 2/23 (TT 2/19)

Learning Objective

1-1 & onto

  1. Standard Matrix of Linear Transformation (video)
  2. Definition and Examples of One-to-One and Onto Maps (video)
  3. Reading (Lay pg.70-76)
  4. Individual Quiz (BB.Quiz.9 ->)
  • HW.9:

    Group.Quiz.9

    (E.C.) Lay pg.78: 3,5,7,19,21,23,25,27

11. MW 2/25 (TT 2/24)

Learning Objective

Two views of matrix multiplication

  1. Matrix Multiplications and Properties (video)
  2. Reading (Lay pg.92-100)
  3. Individual Quiz (BB.Quiz.10 ->)
  • HW.10:

    Group.Quiz.10

    (E.C.) Lay pg.100: 5,9,13,15,17,21,27

12. MW 3/2 (TT 2/26)

Learning Objective

Matrix inverse and its applications

  1. The Inverse of a Matrix (video)
  2. Cryptography: An Application of Matrix Inverse (Mena's Notes [PDF, 5.72 MB] on pg.46)
  3. Reading (Lay pg.102-108)
  4. Individual Quiz (BB.Quiz.11 ->)
  • HW.11:

    Group.Quiz.11

    (E.C.) Lay pg.109: 5,7,9,11,23,31

13. MW 3/4 (TT 3/3)

Learning Objective

Properties of invertible matrices & determinants

  1. The Invertible Matrix Theorem (Lay pg. 112 - 114)
  2. The Matrix Determinant (video)
  3. Properties of Determinants (video)
  4. Reading (Lay pg.164-167; pg.169-174)
  5. Individual Quiz (BB.Quiz.12 ->)
  • HW.12:

    Group.Quiz.12

    (E.C.) 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. MW 3/9 (TT 3/5)

Learning Objective

Vector spaces and subspaces

  1. Definition and Examples of Vector Spaces (video)
  2. Definition and Examples of Vector Subspaces (video)
  3. Reading (Lay pg.190-195)
  4. Individual Quiz (BB.Quiz.13 ->)
  • HW.13:

    Group.Quiz.13

    (E.C.) Lay pg.195: 1,3,5,7,9,11,13,15,17,23

15. MW 3/11 (TT 3/10)

Learning Objective

Summative Assessment

  1. Review for Exam 2
  • Exam 2: Lay 1.8-1.9; 2.1-2.3;3.1-3.2
  • Self Reflection

16. MW 3/16 (TT 3/12)

Learning Objective

Null spaces and column spaces

  1. Null Spaces of a Matrix & Kernel of a Linear Transformation (video)
  2. Column Spaces of a Matrix & Range of a Linear Transformation (video)
  3. Reading (Lay pg.198-205)
  4. Individual Quiz (BB.Quiz.14 ->)
  • HW.14:

    Group.Quiz.14

    (E.C.) Lay pg.205: 5,11,15,17,21,23,25

17. MW 3/18 (TT 3/17)

Learning Objective

Basis

  1. Basis as a Linearly Independent & Spanning Set (video)
  2. Example of Basis & Non-Basis for Matrices and Polynomials (video)
  3. The Spanning Set Theorem (video)
  4. Reading (Lay pg.208-213)
  5. Individual Quiz (BB.Quiz.15 ->)
  • HW.15

    Group.Quiz.15

    (E.C.) Lay pg.213: 9,11,13,15,21,25

18. MW 3/23 (TT 3/19)

Learning Objective

Coordinate systems

  1. Getting Familiar with a Coordinate System (video)
  2. Coordinates Relative to a Basis (video)
  3. Reading (Lay pg.216-222)
  4. Individual Quiz (BB.Quiz.16 ->)
  • HW.16:

    Group.Quiz.16

    (E.C.) Lay pg.222: 3,7,13,15,16,29,31(a)

19. MW 3/25 (TT 3/24)

Learning Objective

Dimension of vector space vs. Rank of a matrix

  1. Dimension of Vector Spaces (video)
  2. Rank & The Rank Theorem (video)
  3. Reading (Lay pg.225-228;pg.230-236)
  4. Individual Quiz (BB.Quiz.17 ->)
  • HW.17:

    Group.Quiz.17

    (E.C.) Lay pg.229: 5,7,9,11,13,19,20;pg.236: 3,5,7,9,11,13,15,17,18,19,25

20. MW 4/6 (TT 3/26)

Learning Objective

Change of basis

  1. Change of Basis (video)
  2. Reading (Lay pg.239-242)
  3. Individual Quiz (BB.Quiz.18 ->)
  • HW.18:

    Group.Quiz.18

    (E.C.) Lay pg.242: 1,5,7,11,13

21. MW 4/8 (TT 4/7)

Learning Objective

Eigenvectors and eigenvalues

  1. Eigenvalues and Eigenvectors (video)
  2. Geometric vs. Algebraic Multiplicity of Eigenvalues (video)
  3. Reading (Lay pg.266-271;pg.274-279)
  4. Individual Quiz (BB.Quiz.19 ->)
  • HW.19:

    Group.Quiz.19

    (E.C.) Lay pg.272: 7,13,17,21,25; pg.279: 7,11,15,21

22. MW 4/13 (TT 4/14)

Learning Objective

Summative Assessment

  1. Review for Exam 3
  • Exam 3: Lay 4.1 - 4.7
  • Self Reflection

23. MW 4/15 (TT 4/9)

Learning Objective

Develop skills for cooperative learning

  1. Research ideas for poster projects.
  • Discuss with your team members on possible poster project topics. Bring laptops if needed.
  • Meet with your teammates if needed.

24. MW 4/20 (TT 4/16)

Learning Objective

Matrix Diagonalization

  1. Why Do We Diagonalize a Matrix? (video)
  2. Diagonalization as a Similarity Transformation (video)
  3. How Do We Diagonalize a Matrix? (video)
  4. Reading (Lay pg.281-286)
  5. Individual Quiz (BB.Quiz.20 ->)
  • HW.20:

    Group.Quiz.20

    (E.C.) Lay pg.286: 1,7,11,15,21,22,23,31,32

25. MW 4/22 (TT 4/21)

Learning Objective

Approximating Ax = b; quantifying Ax-b

  1. Approximation to Ax = b (video)
  2. Inner Product, Normalization, Lengths, and Distances (video)
  3. Notion of Orthogonality, Pythagorean Theorem, and Orthogonal Complement (video)
  4. Reading (Lay pg.330-336)
  5. Individual Quiz (BB.Quiz.21 ->)
  • HW.21:

    Group.Quiz.21

    (E.C.) Lay pg.336: 1-19 odd,22,25,27,31

26. MW 4/27 (TT 4/23)

Learning Objective

Orthogonal projections

  1. Orthogonal Basis for Linear Combinations (video)
  2. Orthonormal Basis for Linear Combinations & Orthogonal Matrix (video)
  3. Orthogonal Projections in 2D (video)
  4. Orthogonal Projections in R^n (video)
  5. Novelty filter as an application to orthogonal projections [PDF, 38.7 KB]
  6. The Approximation Theorem, Distance Between a Point & a Subspace, Matrix Notation for Orthogonal Projections (video)
  7. Reading (Lay pg.338-344;pg.347-351)
  8. Individual Quiz (BB.Quiz.22 ->)
  • HW.22:

    Group.Quiz.22

    (E.C.) Lay pg.344: 9,13,17,23,24; pg.352: 9,11,15,17,21,22

27. MW 4/29 (TT 4/28)

Learning Objective

Gram-Schmidt Process; The least squares problems

  1. The Gram-Schmidt Process for Producing Orthonormal Basis (video)
  2. The QR-Factorization (video)
  3. Reading (Lay pg.354-358)
  4. The Normal Equation and The Least Squares Problems (video)
  5. Reading (Lay pg.360-365; pg.368-372)
  6. Individual Quiz (BB.Quiz.23 -> & BB.Quiz.24 ->)
  • HW.23:

    Group.Quiz.23

    (E.C.) Lay pg.358: 3,7,11,15; pg.366: 5,11,15,17,18; pg.374: 3

28. MW 5/4 (TT 4/30)

Learning Objective

Culmination of skills

Groups 1-4:
  1. compose, practice, revise, print poster
Groups 5-9:
  1. review the grading rubrics [PDF, 268 KB]
  • Groups 1-4: present
  • Groups 5-9: critique
Groups 1:4:
  • None
Groups 5-9:
  • None

29. MW 5/6 (TT 5/5)

Learning Objective

Culmination of skills

Groups 1-4:
  1. review the grading rubrics [PDF, 268 KB]
Groups 5-9:
  1. compose, practice, revise, print poster
  • Groups 1-4: critique
  • Groups 5-9: present
Groups 1-4:
  • None
Groups 5-9:
  • None

29.5 (TT 5/7 only)

Learning Objective

Summative Assessment

  1. Review for Final Exam
  • Review for Final Exam
  • Study for final exam

30. MW 5/15 (TT 5/12)

Learning Objective

Summative Assessment

  1. Review for Final Exam
  • Cumulative Final Exam: MW 8:00 - 10:00 AM (TT 10:15 AM - 12:15 PM)