Enhancing Pedagogical Practices in teaching and learning to promote multidisciplinary research and Education in STEM Part II

Transcription

1 Enhancing Pedagogical Practices in teaching and learning to promote multidisciplinary research and Education in STEM Part II Padmanabhan (Padhu) Seshaiyer Program Director, NSF Professor, Mathematical Sciences Director, STEM Accelerator Program Director, COMPLETE Center George Mason University Universidad Nacional de Colombia Bogota, Colombia January 17, 2017

2 Mathematics and Number Sense Think of a 2-digit positive number. Add the digits in this number. Subtract this sum from the original number. Find the result in the table in the next slide.

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4 Let me Check! Padmanabhan Seshaiyer

5 Mathemagic One more time! Think of a 2-digit positive number. Add the digits in this number. Subtract this sum from the original number. Find the result in the table in the next slide.

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7 Let me Check! Padmanabhan Seshaiyer

8 How Many? How many piano tuners are in Chicago? Population = 3,000,000 Number of families in Chicago = 750,000 Number of Pianos in Chicago = 150,000 Number of Pianos serviced = 1000 Number of Piano Tuners = 150

9 How Many? How many kernels of popcorn would it take to fill this room?

10 Can you guess How many? How many piano tuners are there in Chicago? How many people in the world are talking on their cell phones in any given minute? How many kernels of popcorn would it take to fill this room? How many new passenger cars are sold each year in the USA? How many pennies would need to be stacked to reach the height of Mount Everest?

11 Hand Shake Problem Padmanabhan Seshaiyer

12 Good Afternoon! If everyone at your table shakes hands with each other, how many different handshakes happen at your table? Show us how you would prove it to your friend.

13 Show your work! There are twenty-five people in a room, and each person shakes every person s hand exactly one time. How many different handshakes will be there? Explain your thinking.

14 Think Quick! There are twenty-five people in a room, and each person shakes every other person s hand exactly one time. How many handshakes will be there?

15 How do we MODEL this? S = n = n( n 1)

16 Pictorial Approach Handshake with three people = = 3 Handshake with four people = = 6 Handshake with five people = = 10 Padmanabhan Seshaiyer

17 Tabular Approach Number of People Number of Handshakes = = 6

18 Number of Handshakes Graphical Approach Padmanabhan Seshaiyer n H(n) Number of People Series1

19 Finite Differences n H(n) First Difference Second Difference H ( n) an 2 bn c H (1) a(1) 2 H (2) a(2) H (3) a(3) 2 b(1) c 0 2 b(2) c 1 b(3) c a 1 2, b 1 2, c 0

20 Multiple Approaches to Problem Solving Padmanabhan Seshaiyer

21 Modeling a Real-world Problem All the faculty and staff attended the annual department dinner. Everyone that attended the dinner shook the hand of every other person once. If one of them carried a very bad flu and there were a total of 190 handshakes then how many people were at the banquet? Explain your thinking. Any formula that you may use need to be explained as well. n 2 n( n 1) n( n n 2 1) 380 n 380 0

22 Which Switch is it? Padmanabhan Seshaiyer

23 Which Switch? On a wall are 3 standard on/off switches. One (and only one) controls a light bulb inside a light-tight, well-insulated closet. The other two switches do nothing. You can only open the closet door once, and cannot touch/change any switches after the door is open (or re-closed, for that matter). Damaging or disassembling the door, walls, or switches is against the rules. Within these constraints, can you determine with certainty which switch controls the light bulb?

24 Be CREATIVE! Padmanabhan Seshaiyer

25 Which Switch? Turn all switches to their off position for one hour, then turn on switch "A" for a few minutes. Turn it off and turn on switch "B". Quickly open the door and touch the lightbulb if it's off. If the light is on, it is "B" If the light is off and hot, it is "A" If the light is off and cold, it is "C"

26 Marshmallow Tower Challenge

27 Procedure Challenge: Build the tallest tower. Material: Use spaghetti, tape, string One marshmallow on top of tower.

28 Design Challenge: Build the tallest freestanding structure The winning team is the one that has the tallest structure measured from the table top surface to the top of the marshmallow. The structure cannot be suspended from a higher structure, like a chair, ceiling or chandelier. height

29 The Entire Marshmallow Must be on Top The entire marshmallow needs to be on the top of the structure. Padmanabhan Seshaiyer Cutting or eating part of the marshmallow disqualifies the team.

30 Use as Much or as Little of the material Use as many or as few of the 20 spaghetti sticks, as much or as little of the string or tape.

31 Break up the Spaghetti, String or Tape Padmanabhan Seshaiyer Teams are free to break the spaghetti, cut up the tape and string to create new structures.

32 Challenge Lasts 18 minutes Teams cannot hold on to the structure when the time runs out. Those groups touching or supporting the structure at the end of the exercise will be disqualified. HAVE FUN!

33 Let the Games Begin Have FUN Padmanabhan Seshaiyer

34 What did we learn? Padmanabhan Seshaiyer

35 What did we learn? Padmanabhan Seshaiyer

36 What did we learn? Padmanabhan Seshaiyer

37 What did we learn? Padmanabhan Seshaiyer

38 What did we learn? Padmanabhan Seshaiyer

39 What did we learn? Padmanabhan Seshaiyer

40 What did we learn? Padmanabhan Seshaiyer

41 Marshmellow Challenge Padmanabhan Seshaiyer

42 Fail early and often Padmanabhan Seshaiyer

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50 Why a Marshmallow challenge? Shared Experience Common Language 21 st Century Skills Collaboration Creativity Critical Thinking Communication Prototyping and Facilitation

51 What are some of new practices that you learnt today? polleverywhere.com Respond at PollEv.com/pseshaiyer217 Text PSESHAIYER217 to once to join

52 Contact Padmanabhan (Padhu) Seshaiyer Professor, Mathematical Sciences Director, COMPLETE Center Director, STEM Accelerator Program George Mason University Phone: (703) web: