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Some Roles of Puzzles and Games in Education Dave Moursund. p2 Introduction. p6 Computerized and non-computerized: Puzzles Board games Card games Word games But not physical sporting event such as Olympic Games Brief Sharing
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Some Roles of Puzzles and Games in EducationDave Moursund. p2
Introduction. p6 • Computerized and non-computerized: • Puzzles • Board games • Card games • Word games • But not physical sporting event such as Olympic Games
Brief Sharing • In groups of 2 or 3, introduce yourself, name a game you really liked to play as a child, and say what you learned by playing the game. • Have a few people share with the whole audience.
Free Books by Dave Moursund • http://uoregon.edu/~moursund/dave/Free.html#Books • Eight relatively recent books are available, including the Games in Education book being discussed in this presentation.
Four Key Ideas in Using Games in Education. p7 • Learning to learn, and earning one’s strengths and weaknesses as a learner. • Becoming better at solving challenging problems and accomplishing challenging tasks. • Transfer of learning from game-playing environments to other environments. • It can take a lot of time and effort to achieve a high level of expertise.
Expertise:“Be all you can be.” p28 • To achieve one’s potential in any deep, narrow, challenging discipline tends to take: • 10,000 hours or more • Spread out over 10 years or more • Excellent coaches, teachers • Strong motivation • Top chess players have put in 15,000 to 30,000 hour or more.
Chapter 1: Thinking Outside the Box: problem posing • Can you do it with three line segments? Prove your answer is correct. • How about two lines? • How about one line? • How about dots on a sphere?
A dot an a point are not the same thing: Nine bigger dots. p13
Chapter 1: …: problem solving. P14-15 Four-part definition of problem: • Clearly defined given initial situation. • Clearly defined goal. • Clearly defined resources such as your time and brain power, money, computers, etc. • Ownership; desire to solve problem.
Chapter 1: Thinking Outside the Box. p23 • Each chapter ends with: • Activities for teachers. • Activities for use with students. • Appendix summarizes lots of problem-solving strategies. • The book has oodles of references, mostly to websites. • The book has an extensive Index.
Chapter 2: Background Information. p24 • An academic discipline of study. • Expertise in a discipline of study. • Learning to learn. • One’s preferred style: competition, independence,or cooperation. • Transfer of learning. • Precise vocabulary & notation.
Chapter 2: Background Info.: vocabulary and notation. p39 White Black • Pe4 Pe5 • Nf3 Nc6 • Bb5 Pa6 • BxN
Chapter 2: Background Information. p35 • Problem solving is part of every discipline. • Transfer of learning: • Low-road transfer • High-road transfer • General problem-solving strategies that fit the high-road model for transfer of learning.
Chapter 2: Background Information: Strategies. p147 divide and conquer. Divide a large problem into smaller sub-problems that are more manageable. Do this in a manner such that once the sub-problems are solved, it is relatively easy to put the pieces together to solve the original problem. Note the value of having a large repertoire of “sub-problems” that one can readily solve. Often, some of the sub-problems can be solved by a computer or other machine.
Chapter 3: Sudoku: strategy of finding a simpler problem. p45
Chapter 3: Sudoku:(problems in general). p47 In general, a problem might have: • No solution. • Exactly one solution. • More than one, but a finite number of solutions. • An infinite number of solutions. • Unknown which of above applies. What is the situation with a specific Sudoku puzzle?
High road transfer exploration of strategy of elimination Challenge to audience: Think of situations in which you apply the strategy of elimination as an aid to solving a personal, real world problem.
Chapter 3: Sudoku. 53 In “playing with” Sudoku we “discovered” four general-purpose strategies: • Create and study a simpler problem. • Explore solvability. • Guess and check. (Note that in some problems, computers are very good at this.) • Elimination.
Chapter 4: More Puzzles. p55 A puzzle is a problem or enigma. Many puzzles stem from serious mathematical or logical problems, whereas others are devised for the sole purpose of being brain teasers. The history of puzzles goes back many thousand years.
Chapter 4: More Puzzles:some uses or purposes. p55 • Historical, cultural • Logical thinking and problem solving • Persistence and self-sufficiency • Learning about oneself • Peer instruction • Differentiated and/or individualization of instruction • Learning or practicing specific content • Busy work
Chapter 4: More Puzzles: free puzzles. p57 • Do a Google search on the quoted phrase “free puzzle” • Example of results: http://perplexus.info/tree.php. This Website uses the following categorization terms for puzzles: logic, probability, shapes, general (includes tricks, word problems, cryptography), numbers, games, paradoxes, riddles, just math, science, and algorithms.
Chapter 4: More Puzzles:a puzzle a day. 56 • Provide your students with a daily puzzle. • Each day, write brief notes about the results. • Do this for a full school year. • Edit the book you have now written. • This illustrates the power of the divide and conquer strategy.
Chapter 4: More Puzzles: free is not necessarily free. p57 Typically, Web sites that provide free puzzles and games make income to sustain themselves by: • Selling ads. • Selling games and puzzles. • Selling subscriptions & memberships.
Chapter 4: More Puzzles: water-measuring puzzles. p62 • Given a 5-liter jug, a 3-liter jug, and an unlimited supply of water, how do you measure out exactly 4 liters? • The strategy of working backwards (from the goal) is helpful here: • Note that 1 + 3 = 4 • Note that 2 + 2 = 4 • Thus, aim at 1 + 3 or aim at 2 + 2.
Chapter 4: More Puzzles; Howard Gardner. p63 • Linguistic intelligence ("word smart"): • Logical-mathematical intelligence ("number/reasoning smart") • Spatial intelligence ("picture smart") • Etc,
Chapter 4: More Puzzles: spatial puzzles. p64 Drag without rotation to fill square. http://www.vemix.com/GlFlashGm.php
Chapter 4: More Puzzles: Tower of Hanoi. 65 Move one disk at a time. No disk may be placed on top of a smaller disk.
Chapter 4: More Puzzles: Tower of Hanoi. p66 Simpler problems.
Chapter 4: More Puzzles:peg puzzles. p72 Jump horizontal or vertical. Remove jumped peg. Goal: one peg in the middle.
Chapter 5: One-Player Games • Fun, relaxing, take’s mind off of other things. • Flow: Mihaly Csikszentmihalyi(chick-sent-me-high-ee) (p93) • Not competitive? Competing with oneself? (p31)
Chapter 5: One-Player Games:eight off card game. p85 • Good play requires figuring out long sequences of moves. • This exercises and challenges one’s working memory (short term memory). • Illustrates a strategy called mobility. • Don’t box yourself into a corner. • Keep your options open. • Rule of thumb: avoid moves (actions) that decrease your range of future choices.
