advertisement

Puzzle Based Learning

50 %
50 %
advertisement
Information about Puzzle Based Learning
Education

Published on October 1, 2009

Author: AustralianComputerSo

Source: authorstream.com

advertisement

slide1: 1 Puzzle-Based Learning Zbigniew (Mike) Michalewicz Slide683: 2 Outline of the talk The need and the motivation Some examples Connection with solving real-world puzzles Current status Slide689: 3 Outline of the talk The need and the motivation Some examples Connection with solving real-world puzzles Current status Slide505: 4 The need What’s missing in most curricula – from elementary schools through to universities – is the development of problem solving skills, creative thinking, thinking 'out-of-the-box,' etc. Slide507: 5 Puzzle-based learning Puzzles represent 'unstructured' problems; they teach how to think 'out of the box.' Puzzles are not attached to any chapter of any text. Puzzles illustrate many general and powerful problem solving techniques. Puzzles illustrate importance of science. Puzzles are fun and easy to remember! Supporting evidence: 6 Supporting evidence Editorial Board of the International Journal Teaching Mathematics and Computer Science. Earlier 'experiments' in USA, Poland, Sweden, Argentine, Netherlands, Germany, China, Singapore, Australia, and Denmark. Recent classes at the University of Adelaide, comments by students and faculty. Recent workshops for industry and government (Holden, ETSA Utilities, Department of Education). Supporting evidence: 7 Supporting evidence 'This book teaches you how to think of a solution for the problem you face…' '…anyone interested in […] human thinking should read and understand this book.' 'I used this book in a Master's class on Heuristics (Systems Engineering, University of Virginia) and received the most positive textbook reviews I have seen in my fifteen years of teaching.' 'Most importantly, it does so in a way that no other book I've seen does – it makes it fun and it makes you think!' Some comments (Amazon.com) on How to Solve It: Modern Heuristics (Springer, 2000): A well-known puzzle: 8 A well-known puzzle A man has to take a wolf, a goat, and some cabbage across a river. His rowboat has enough room for the man plus either the wolf or the goat or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. How should the man carry the wolf, goat, and cabbage across the river? Supporting evidence: 9 Supporting evidence English scholar Alcuin (born around 732) published his main work, Problems to Sharpen the Young (in that book, one of the puzzles was the famous river-crossing puzzle – used 1,200 years later in all Artificial Intelligence courses all over the world!). The first known puzzles are from Neolithic Age (3,000 – 2,500 BC). Statements by famous mathematicians (Polya, Gardner, Steinhauss, Smullyan, etc.). Other quotes: Other quotes 'Puzzle-solving seems to grant us entrance into the knowledge of all existing things and all obscure secrets.' Ahmes, Rhind Papyrus, 1800 B.C. 'The fact is that our lives are largely spent in solving puzzles; for what is a puzzle, but a perplexing question?' Henry Dudeney, 1900s 'Puzzles are small-scale experiments of the larger questions that life poses to us.' D. Perkins, 2000, Archimedes’ Bathtub: The Art and Logic of Breakthrough Thinking. 10 Slide513: 13 The rejection of mathematics and any precision of thought in Six Thinking Hats (1999) by Edward de Bono, expresses itself in author’s statement like: 'In a simple experiment with three hundred senior public servants, the introduction of the Six Hats method increased thinking productivity by 493 percent.' Additional motivation A Perspective: 14 The rejection of mathematics and any precision of thought in Six Thinking Hats (1999) by Edward de Bono, expresses itself in author’s statement like: 'In a simple experiment with three hundred senior public servants, the introduction of the Six Hats method increased thinking productivity by 493 percent.' Additional motivation Understanding the problem: 20 Goals of the proposed course Learning experience for students, Enhancement of problem solving skills, Introduction to mathematics and science, Enhancement of students’ motivation to stay in the program; reduction of drop-out rates. Introduction to real-world problems. What does it mean?: 21 A Perspective Real World Abstract/Model World Dealing with uncertainty and changing conditions Reasoning with domain- specific methods Critical thinking; logical reasoning What does it mean?: 22 Outline of the talk The need and the motivation Some examples Connection with solving real-world 'puzzles' Current status Implications: 23 Understanding the problem A farmer has: 20 pigs, 40 cows, and 60 horses. How many horses does he have, if he calls the cows horses? Slide608: 24 Understanding the problem A farmer has: 20 pigs, 40 cows, and 60 horses. How many horses does he have, if he calls the cows horses? Answer: The farmer has 60 horses… Slide609: 25 A B Understanding the problem You drive a car at a constant speed of 40 km/h from A to B, and on arrival at B you return immediately to A, but at a higher speed of 60 km/h. What was your average speed for the whole trip? Slide610: 26 Understanding the problem Suppose that you go from A to B at a constant speed of 40 km/h. What should your constant speed be for the return trip from B to A if you want to obtain the average speed for the whole trip of 80 km/h? Slide611: 27 Understanding the problem Two groups of students are attending a college. One day, one of the students from group A approached another from group B, and said 'We are taller than you!' Constraints: 28 Does it mean that: Each a is taller than each b? The tallest a is taller than the tallest b? Each a is taller than some b’s? Each b is smaller that some a’s? Each a has a corresponding b (and each of them a different one) whom he surpasses in height? Each b has a corresponding a (and each of them a different one) by whom he is surpassed? The shortest b is shorter than the shortest a? The shortest a exceeds more b's than the tallest b exceeds a's? What does it mean? Slide617: 29 Does it mean that: The sum of heights of a's is greater than the sum of heights of b's? The average height of a's is greater than the average height of b's? There are more a's who exceed some b than there are b's who exceed some a? There are more a's with height greater than the average height of b's, than there are b's with height greater than the average height of a's? The median height of a's is greater than that of b's? What does it mean? Slide618: 30 There are four cards on the table; each card has a letter on one side and a number on the other side: Implications A 7 4 d Which cards you have to turn over in order to test the rule: 'If there is a capital letter on one side of the card, there is an even number on the other side.' Three boxes: 31 Judy is thirty-three, unmarried, and quite assertive. A magna cum laude graduate, she majored in political science in college and was deeply involved in campus social affairs, especially in anti-discrimination and anti-nuclear issues. Which statement is more probable: Judy works as a bank teller. Judy works as a bank teller and is active in the feminist movement? Intuition Three boxes: 32 You won $1,000. Consider 2 scenarios: (A) You get an additional $500 (B) On flip of a coin, you get an additional $1,000 or nothing. Some Psychology Slide697: 33 You won $2,000. Consider 2 scenarios: (A) You immediately lose $500. (B) On flip of a coin, you lose $1,000 or nothing. Some Psychology Slide703: 34 You won $1,000. Consider 2 scenarios: (A) Get additional $500 (B) On flip of a coin, get additional $1,000 or nothing. You won $2,000. Consider 2 scenarios: (A) Lose $500 (B) On flip of a coin, lose $1,000 or nothing. You leave with $1,500 You leave with either $1,000 or $2,000 (50-50 chances) Some Psychology Slide699: 35 Two men meet on the street (they have not seen each other for many years): A: All three of my sons celebrate their birthday today. Can you tell me how old each one is? B: Yes, but you have to tell me something about them… A: The product of their ages is 36. B: I need more info… A: The sum of their ages is equal to the number of windows in the building next to us… B: I need more info… A: My oldest son has blue eyes. B: That is sufficient! Constraints Optimisation: 36 1 1 2 1 3 1 9 4 1 9 2 2 6 6 1 6 3 2 4 3 3 Constraints The product of their ages is 36: x y z Optimisation: 37 + 1 + 1 = 38 + 2 + 1 = 21 + 3 + 1 = 16 9 + 4 + 1 = 14 9 + 2 + 2 = 13 6 + 6 + 1 = 13 6 + 3 + 2 = 11 4 + 3 + 3 = 10 Constraints The sum of their ages is equal to the number of windows in the building next to us… x y z Optimisation: 38 Three boxes There are three boxes; two are empty and the third one contains a great prize (a Ferrari Modena F430; red black interior...) Slide580: 39 Final decision: Should you stay with your original choice, or switch? EMPTY!!! The host of the game asks you to pick a box. The host, knowing where the prize is, opens ONE of the empty boxes to show you that the prize isn’t there. Three boxes Statistics: 40 Russian Roulette Two men play a game of Russian roulette with a gun. The gun has six chambers, where two bullets were placed in two adjacent chambers. After a random spin of the barrel, the first man puts the gun to his head and pulls the trigger. Click. Now it is the turn of the second man. What should he do to increase his chances of staying alive: to spin the barrel first or just pull the trigger? Slide663: 41 Mushrooms A farmer sells 100kg of mushrooms for $1 per kg. The mushrooms contain 99% moisture. A buyer makes an offer to buy these mushrooms a week later for the same price. However, a week later the mushrooms would have dried out a bit to 98% of moisture content. How much will the farmer lose if he accepts the offer? Slide664: 42 A(1), B(2), C(5), D(10) Four travellers approached a bridge… How should the travelers schedule the crossing of the bridge to minimize the total time? Optimisation Slide658: 43 Optimisation all solutions (search space) Slide659: 44 Optimisation quality measure all solutions (search space) Slide660: 45 Optimisation feasible solution infeasible solution quality measure Optimisation task: Find the highest quality feasible solution… Slide661: 46 Saturdays and Sundays Which day of the week, Saturday or Sunday, appears more often as January 1st? Slide652: 47 Statistics Assume there is a (deadly) virus X and the test is 98% accurate. This means that if you contract virus X, the test will be positive in 98% of cases. On the other hand, if someone does not contract this virus, the test will also be negative in 98% of cases. Assume also that 0.5% of the population has contracted virus X. You have taken a test and result is positive! How much should you worry? Homework: 48 We are often presented with statistical material from which it is tempting to formulate some hypothesis. One famous example was reported by Science Times on August 22, 1989, which described the ability of cats to survive large falls. The distance of the fall for 129 of the 132 cats was recorded, which ranged from 2 to 32 stories! All the data were pulled from the Animal Medical Center from June to November 1984. The most amazing part of the article was the following: Presenting statistical information Homework: 49 'Even more surprising, the longer the fall, the greater the chance of survival. Only one of 22 cats that plunged above 7 stories died and there was only one fracture among the 13 that fell more than 9 stories. The cat that fell 32 stories on concrete, Sabrina, suffered [only] a mild lung puncture and a chipped tooth…' Can you explain this phenomenon? Falling cats Homework: 50 Try to memorize the following coding of numbers 1 – 9: 1 2 3 4 5 6 7 8 9 Pattern recognition Slide656: 51 1 2 3 4 5 6 7 8 9 What is the coded version of the number 3875 ? Pattern recognition Slide668: 52 The 'pattern': 1 2 3 4 5 6 7 8 9 Pattern recognition Connection: 53 1 2 3 4 5 6 7 8 9 What is the coded version of the number 3875 ? Pattern recognition Slide669: 54 Homework With a 7-minute hourglass and an 11-minute hourglass, find the easiest way to time the boiling of an egg for 15 minutes. Find the simplest solution… Slide446: 55 Homework A solution: Start with the 7- and 11-minute hourglasses, when the egg is dropped into the boiling water. After 7 minutes, turn the 7-minute hourglass over. After 4 additional minutes (i.e. when sand stops in 11-minute hourglass), turn the 7-minute hourglass over again. When the sand stops in the 7-minute hourglass, 15 minutes will have elapsed. Slide447: 56 Homework Another solution: Start the 7- and 11-minute hourglasses. After 7 minutes, drop the egg into the boiling water. After 4 additional minutes (i.e. when sand stops in 11-minute hourglass), turn the 11-minute hourglass over. When the sand stops in the 11-minute hourglass again, 15 minutes will have elapsed from the time the egg was dropped into the water. Slide468: 57 Homework Question: Which of these two solutions is simpler? First solution was the quickest (took 15 minutes from the start to completion) and required 2 turn-overs… The second solution required 22 minutes, but required just 1 turn-over… Which is simpler? Slide688: 58 effort time For more than one objective, often the best we can do is to explore the tradeoffs between various solutions… Multi-objective optimisation Slide297: 60 Outline of the talk The need and the motivation Some examples Connection with solving real-world puzzles Current status

Add a comment

Related presentations

Related pages

Puzzle-Based Learning – An introduction to critical ...

IPOS’12 PBL Presentation. Puzzle Based Learning is a new teaching and learning methodology that is focused on the development of problem-solving skills.
Read more

Puzzle-based Learning: Introduction to critical thinking ...

Z Michalewicz, M - Puzzle-based Learning: Introduction to critical thinking, mathematics, and problem solving jetzt kaufen. ISBN: 9781876462635 ...
Read more

Puzzle-Based Learning (3rd Edition): An Introduction to ...

Lesen Sie Puzzle-Based Learning (3rd Edition): An Introduction to Critical Thinking, Mathematics, and Problem Solving von Zbigniew Michalewicz mit Kobo.
Read more

Puzzle-Based Learning - University of Adelaide

Michalewicz and Michalewicz, Puzzle Based Learning Proceedings of the 2007 AaeE Conference, ... 2 The puzzle is the “river crossing problem”: ...
Read more

Puzzle-based Learning: An introduction to critical ...

Lesen Sie Puzzle-based Learning: An introduction to critical thinking, mathematics, and problem solving von Zbigniew Michalewicz mit Kobo. What is missing ...
Read more

Puzzle-based Learning: Introduction to critical thinking ...

- Puzzle-based Learning: Introduction to critical thinking, mathematics jetzt kaufen. Kundrezensionen und 0.0 Sterne. …
Read more

Puzzle-Based Learning for Engineering and Computer Science

Raja Sooriamurthi, Nickolas Falkner, Zbigniew Michalewicz, "Puzzle-Based Learning for Engineering and Computer Science", Computer, vol. 43, no. , pp. 20-28 ...
Read more

Puzzle-Based Learning: The first experiences

The puzzle-based learning approach The puzzle-based learning approach aims at encouraging students to thinkabout how to frame ... Puzzle-Based Learning: ...
Read more

Puzzle-Based Learning (3rd Edition): An Introduction to ...

eBook Shop: Puzzle-Based Learning 3rd Edition : An Introduction to Critical Thinking, Mathematics, and Problem Solving als Download. Jetzt eBook ...
Read more

COMP SCI 1010 - Puzzle Based Learning | Course Outlines

Course Code: COMP SCI 1010: Course: Puzzle Based Learning: Coordinating Unit: School of Computer Science: Term: Semester 1: Level: Undergraduate: Location ...
Read more