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A post-graduate from Indian Institute of Information Technology and Management, with 4.5 years of experience in teaching, presents a flipped classroom activity for teaching Pigeonhole Principle and Principle of Inclusion/Exclusion in Discrete Mathematics to BE 2nd year Computer Science students.
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FLIPPED CLASSROOM ACTIVITY CONSTRUCTOR – USING EXISTING CONTENT
ABOUT YOU A Post-Graduate from Indian Institute of Information Technology and Management, with 4.5 years of experience in teaching. Presently working as an Assistant Professor in Thakur College of Engineering and Technology, Mumbai and teaching Discrete Mathematics to BE 2nd year Computer Science students. For the flipped classroom activity, I have chosen Pigeonhole Principle and Principle of Inclusion/Exclusion which are two most important counting techniques used in real-world scenarios.
KALPANA GANGWAR PIGEONHOLE PRINCIPLE and PRINCIPLE OF INCLUSION/EXCLUSION DISCRETE MATHEMATICS 2ND YEAR UG IN COMPUTER ENGINEERING COMPUTER SCIENCE TCET, MUMBAI (MUMBAI UNIVERSITY)
OUT-OF-CLASS ACTIVITY Learning Objective(s) of Out-of-Class Activity At the end of watching the videos student should be able to: Define pigeonhole principle, Principle of Inclusion/Exclusion(Recall level) Understand the application of pigeonhole principle, Principle of Inclusion/Exclusion (Understand level) Apply Pigeonhole principle, Principle of Inclusion/Exclusion (Apply level) Key Concept(s) to be covered Pigeonhole Principle Principle of Inclusion/Exclusion Applications of pigeonhole Principle, Principle of Inclusion/Exclusion Solving problems using pigeonhole principle, Principle of Inclusion/Exclusion
OUT-OF-CLASS ACTIVITY - 2 Pigeonhole Principle, Principle of Inclusion/Exclusion, Principle of Inclusion/Exclusion-2 Main Videos Source URL CC-BY-NC-SA (Reuse Allowed) License of Video Mapping Concept to Video Source TOTAL DURATION: 25 min (approx.)
OUT-OF-CLASS ACTIVITY- 4 Total activity duration: 27 minutes
IN-CLASS ACTIVITY Learning Objective(s) of In-Class Activity At the end of the class, students will be able to, • Solve real-life scenario problems involving Pigeonhole Principle(ANALYZE Level) • Solve real-life scenario problems on Principle of Inclusion/Exclusion(ANALYZE Level) • Key Concept(s) to be covered • Use of Pigeonhole Principle in real World Problem Solving. • Use of Principle of Inclusion/Exclusion in real World Problem Solving.
IN-CLASS ACTIVITY-1 Active Learning activity(ies) that you plan to do Real world problem solving using. Think-Pair-Share Concept clarification using. Peer Instruction
IN-CLASS ACTIVITY-1 Peer Instruction Strategy – What Teacher Does Pose the two PI questions at the start of class and states Pigeonhole Principle. Q 1: How many integers should be picked (not necessarily consecutive) such that any two of them will have the same remainder when divided by 4. 3 4 5 10
IN-CLASS ACTIVITY-1 Peer Instruction Strategy – What Teacher Does Pose the two PI questions at the start of class and states Pigeonhole Principle. Q 2:There are exactly three types of students in a school: the geeks, the wannabees, and the athletes. Each student is classified into at least one of these categories. And the total number of students in the school is 1000. Suppose that the following is given:The total number of students who are geeks is 310. The total number of students who are wannabees is 650. The total number of students who are athletes is 440. The total number of students who are both geeks and wannabees is 170. The total number of students who are both geeks and athletes is 150. The total number of students who are both wannabees and athletes is 180.What is the total number of students who fit into all 3 categories? a) 100 b) 1400 c) 500 d) 150
IN-CLASS ACTIVITY -1 Peer Instruction Strategy – What Student Does For each question they will first vote individually. Then they will discuss with peers and come to consensus. Listen to instructors explanation.
IN-CLASS ACTIVITY-1 TPS Strategy – What Instructor does Provides an example application: Consider any five points P1, · · · , P5 in the interior of a square S of side length 1. Show that one can find two of the points at distance at most 2/2 apart.
IN-CLASS ACTIVITY -1 TPS Strategy – What Instructor does Think (~2 minutes) Instruction: Let’s try to make five points as far as we can and identify how much will the maximum distance between them. Think individually and identify the position of points.
IN-CLASS ACTIVITY -1 TPS Strategy – What Instructor does Pair (~5 minutes) Instruction: Now pair up and compare your answers. Agree on one final answer. While students are pairing and discussing, instructor goes to 2~3 sections to see what they are doing. When the points are in this configuration i.e. 4 points are at corners and the other one is at the centre of square then, the distances from the center point to each of the other points is exactly √ 2/2. Intuitively, this is as far as the points can be apart. So are we done?
IN-CLASS ACTIVITY-1 TPS Strategy – What Instructor does Share (~8 minutes) Instructor asks 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. CORRECT SOLUTION: Consider partitioning the square into 4 sub squares as shown. By the pigeonhole principle, 2 of the points must be in one “sub-box.” The distance between those two points must be less than the diameter of the sub-box: √ 2/2 (the length of the sub-box’s diagonal). This proves the desired result.
IN-CLASS ACTIVITY-2 TPS Strategy – What Instructor does Provides an example application: There are 50 students in a class who are given a test with 3 questions on it: Q1, Q2, and Q3. All the students answer at least 1 question. If 12 did not answer Q1, 14 did not answer Q2, 10 did not answer Q3 and 25 answered all the 3 questions, then how many students answered exactly 1 question?
IN-CLASS ACTIVITY-2 TPS Strategy – What Instructor does Think (~2 minutes) Instruction: Think individually and try to draw the scenario using Venn diagram.
IN-CLASS ACTIVITY-2 TPS Strategy – What Instructor does Pair (~5 minutes) Instruction: Now pair up and compare your answers. Agree on one final answer. While students are pairing and discussing, instructor goes to 2~3 sections to see what they are doing.
IN-CLASS ACTIVITY-2 TPS Strategy – What Instructor does Share (~8 minutes) Instructor asks 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. CORRECT SOLUTION: We are given that: a+ b+ c+ x+ y+ z=25 ------ (1) b+ c+ z=12 ------ (2) a+ c+ x=14 ------ (3) a+ b+ y=10 ------ (4) Add (2), (3) and (4) and then subtract (1) from it. a+b+c=11;
IN-CLASS ACTIVITY OUTCOME In both the above strategies, students are required to go beyond mere listening and execution of prescribed steps. They are required to think deeply about the content they were familiarized in out-of-class and do higher order thinking.
