1. FLIPPED CLASSROOM ACTIVITY CONSTRUCTOR Dr. Amruta A Bhandari

2. Table of Contents SECTION SLIDE # ABOUT YOU 3 OUT-OF-CLASS SEGMENT 5
IN-CLASS SEGMENT 11
EVALUATION 13
COMMUNITY BUILDING 17

3. About you
I am working as an Assistant Professor in Applied Science Department, R.C.Patel Institute of Technology, Shirpur ,Maharashtra . I teach Engineering Mathematics. I have completed Ph.D. in Mathematics under the guidance of Dr. V.H Pradhan, National Institute of Technology, Surat. I received MSc degree in Mathematics from Department of Mathematics, Pune University, Pune, India in the year I received the B.Sc degree in Mathematics from Fergusson College, Pune, India in the year

4. A.A.Bhandari Computing Eigenvalues and Eigenvectors
Engineering Mathematics
Mathematics
First year UG Students
R.C.Patel Institute of Technology, North Maharashtra University,Jalgaon.

5. Out-of-class Activity Design -1
Learning Objectives of Out-of-Class Activity
At the end of watching the video student should be able to
Recollect the basics required for computing eigenvalues.
Demonstrate the Shortcut method for finding characteristic equation.
Understand the properties of eigenvalues and its applications
Evaluate Eigenvalues of 2 by 2 and 3 by 3 matrices.
Key Concepts to be covered
Determinants and minors.
Properties of eigenvalues.
Shortcut of finding eigenvalues.

6. Out-of-class Activity Design - 2
Main Video Source URL
License of Video
Creative Commons License (Resuse allowed)
Mapping Concept to Video Source
CONCEPT
VIDEO SEGMENT
Properties of Eigenvalues
Applications to real life
Minors
Determinant
TOTAL DURATION
10 min

7. Guideline for Designing Assessments
A video which under creative commons licence is provided before two weeks of lecture which elaborated the key concepts required for computing eigenvalues.
Students are expected to listen to video carefully and answer the compulsory aligning assignment
Students are asked to submit the assignment the day before the classroom.
The assignment carries 5 marks which will be added to the internal assessment of the University Exam.
After submitting the assignment come prepared with the basics required for computing eigenvalues and eigenvectors in the class so we will continue with detailed example of computing Eigenvalues and Eigenvectors.

8. Out-of-class Activity Design - 3
Aligning Assessment with Learning Objective
Learning
Objective
Assessment Strategy
Expected duration
(in min)
Additional Instructions (if any)
Recollect the basics required for computing eigenvalues
Find the determinant and minors of above matrix
10 min
Watch the video in duration 0.39s to 1.38

9. Out-of-class Activity Design - 3
Learning Objective
Assessment Strategy
Expected Duration
(in min)
Additional Instructions (if any)
Understand the properties of eigenvalues
Q. The Eigenvectors are unique
A)true
B)false
C)Cannot be concluded
QThe product of eigenvalues are
A)S1
B)S2
C)|A|
D)Negative
5 minutes
The answer to this is in the video section

10. Out-of-class Activity Design - 3
Aligning Assessment with Learning Objective
Learning Objective
Assessment Strategy
Expected Duration
(in min)
Additional Instructions (if any)
Demonstrate the Shortcut method for finding characteristic equation
State the characteristic equation of
and
matrix.
10 minutes
Watch the video
Total activity duration
25 minutes

11. In-class Activity Design -1
Learning Objectives of In-Class Activity
At the end of the class, students will be able to,
Solve the problems involving eigenvalues for different cases.
Implement the knowledge and evaluate the eigenvectors to corresponding eigenvalues.
Key Concepts to be covered
Computing Eigenvectors
University exam questions related to eigenvalues and eigenvectors.

12. In-class Activity Design -2
Peer Instruction Strategy
What Teacher will do?
Pose the first PI questions at the start of the class and ask the question randomly to any student after some collective answer will discuss the correct answers
Q 1: What will happen if eigenvalues are repeated?
There will be different eigenvectors
There will be two eigenvectors
Cannot say
What Student will do?
Student who is selected at random by teacher will have answer to the question and then student will listen to explain the different cases that is when the Eigenvalues are repeated and non repeated cases for different matrices and give summary about computing eigenvalues and eigenvectors for such cases.

13. In-class Activity Design -2
Peer Instruction Strategy
What Teacher will do?
Pose the second PI question and after getting the response of this question explain the summarize the properties of eigenvalues
Q 2: What are eigenvalues of lower diagonal matrix?
Elements on principle diagonal
Elements of first row
We need to find determinant A
Cannot say
What Student will do?
Student will poll individually and then will recollect the properties elaborated in the video given to out class activity. After answering the student will note down the answers discussed by teacher in their notebook.
Peer Instruction Strategy

14. In-class Activity Design -2
TPS Strategy
Think (~5 minutes)
Teacher will form five teams based on the roll numbers and A sheet is given by teacher where in two problems are half solved and the students have to fill in the steps unsolved in the sheets
Pair (~10 minutes)
Instruction: Now pair up in your respective teams and compare your answers. Agree on one final answer.
While students are pairing and discussing, instructor takes a round in the class

15. In-class Activity Design -2
TPS Strategy
Share (~5 minutes)
Instructor asks one representative from a group to share their answer with class and see whether there are different answers. After sharing is done, instructor gives feedback on the correct solution .
The teacher concludes and encourages the students who comes to share on the stage.

16. In-class Activity Design -2
Justification for active learning strategy
The peer instruction strategy and think pair share strategy done in the in class activity, students are required to go beyond mere listening of the video think beyond compute the eigenvectors for different cases.
The students need to implement their knowledge about the properties of eigenvalues and implement on particular matrix.
The instructor can conclude on various cases of eigenvalues for different types of matrices which will connect the video with this part of instruction .
An assignment of 5 problems can be given to students which they will submit in next week thus the teacher will get an idea at what level the aim is achieved.
There can be a feed back in last five minutes which ensures the satisfaction of understanding of the students in the topic taken. .

17. Community Building
I would like to work collaborate with my colleagues Dr. S. V. Desale and Dr. P. G. Bhadane and Mr. Bhasargao Walchand from Institute of Technology,Solapur who were the top performers of last FDP and now working as associate faculties of IIT in their respective institutes.

18. Summary
A video is given which is under creative commons is given to students beforehand and aligning assignment to evaluate the understanding of the video is given. When students come in class Peer Instruction Strategy and think pair share strategy is done so the students think beyond the video and expand their thinking to level of problem solving for various cases of Eigenvalues and Eigenvectors. Thus flipped classroom activity is beneficial for students which takes more stress on active learning.