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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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Introduction p6 l.jpg
Introduction. p6

  • Computerized and non-computerized:

    • Puzzles

    • Board games

    • Card games

    • Word games

  • But not physical sporting event such as Olympic Games


Brief sharing l.jpg
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.


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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.


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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.


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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.





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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?




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Chapter 1: …: problem solving. P14-15 p13

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.


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Chapter 1: Thinking Outside the Box. p23 p13

  • 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.


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Chapter 2: Background Information. p24 p13

  • 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.



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Chapter 2: Background Info.: vocabulary and notation. p39 p13

White Black

  • Pe4 Pe5

  • Nf3 Nc6

  • Bb5 Pa6

  • BxN


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Chapter 2: Background Information. p35 p13

  • 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.


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Chapter 2: Background Information: Strategies. p147 p13

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.


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Chapter 3: Sudoku: p13 9 x 9 board and 3 x 3 regions. p44


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Chapter 3: Sudoku: p13 givens (initially filled in). p44



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Chapter 3: Sudoku: p45(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?


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Chapter 3: Sudoku: p45guess and check strategy. p48


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Chapter 3: Sudoku: p45guess and check strategy. p48


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Chapter 3: Sudoku: p45mental guess and check strategy. p49


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Chapter 3: Sudoku: mental p45guess and check strategy. p50


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Chapter 3: Sudoku: p45elimination strategy. p51


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High road transfer exploration of strategy of elimination p45

Challenge to audience: Think of situations in which you apply the strategy of elimination as an aid to solving a personal, real world problem.


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Chapter 3: Sudoku. 53 p45

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.


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Chapter 4: More Puzzles. p55 p45

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.


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Chapter 4: More Puzzles: p45some 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


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Chapter 4: More Puzzles: free puzzles. p57 p45

  • 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.


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Chapter 4: More Puzzles: p45a 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.


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Chapter 4: More Puzzles: free is not necessarily free. p57 p45

Typically, Web sites that provide free puzzles and games make income to sustain themselves by:

  • Selling ads.

  • Selling games and puzzles.

  • Selling subscriptions & memberships.


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Chapter 4: More Puzzles: water-measuring puzzles. p62 p45

  • 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.


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Chapter 4: More Puzzles; Howard Gardner. p63 p45

  • Linguistic intelligence ("word smart"):

  • Logical-mathematical intelligence ("number/reasoning smart")

  • Spatial intelligence ("picture smart")

  • Etc,


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Chapter 4: More Puzzles: spatial puzzles. p64 p45

Drag without rotation to fill square.

http://www.vemix.com/GlFlashGm.php


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Chapter 4: More Puzzles: Tower of Hanoi. 65 p45

Move one disk at a time.

No disk may be placed on top of a smaller disk.



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Chapter 4: More Puzzles: p45symmetric word box. p68


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Chapter 4: More Puzzles: p45logi-number puzzles. p69


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Chapter 4: More Puzzles: p45peg puzzles. p72

Jump horizontal or vertical.

Remove jumped peg.

Goal: one peg in the middle.


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Chapter 5: One-Player Games: p45solitaire card games. p77


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Chapter 5: One-Player Games p45

  • Fun, relaxing, take’s mind off of other things.

  • Flow: Mihaly Csikszentmihalyi(chick-sent-me-high-ee) (p93)

  • Not competitive? Competing with oneself? (p31)


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Chapter 5: One-Player Games: p45Klondike solitaire game. p80


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Chapter 5: One-Player Games: p45eight off card game. p84


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Chapter 5: One-Player Games: p45eight off card game. p85


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Chapter 5: One-Player Games: p45eight 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.



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Chapter 5: One-Player Games: p45Tetris. p92

  • Requires quick hand/eye reaction time.

  • Requires spatial intelligence.

  • Tetris tends to be a game that girls like better than boys.

  • General issue: Boys seem to like computer games better than girls and spend more time playing such games.


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Chapter 6: Two-Player Games. p95 p45

tic-tic-toe, chess, cribbage, backgammon

  • May be played for communication and companionship.

  • May be played competitively.

  • Often may be played against a computer.

  • Tend to require careful planning (look ahead) to play well.


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Two-Player Games: p45tic-tac-toe. p95


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Two-Player Games: p45random move tic-tac-toe

  • Suppose each player makes his/her moves completely at random.p96

  • What percent of games are a draw, won by X, won by O?

  • Suppose we teach X to make first move in center square, and after that both sides play at random. How much do the statistics change?


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Two-Player Games: p45random move tic-tac-toe

  • Suppose we teach X to play in the center square first, and how to make a winning move if there is a file with two Xs, no Os, and it is Xs turn to move?

  • Note the general idea here: When playing against a player who makes random moves, a little training or education goes a long way!!!

  • Educational implications???


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Two-Player Games: p45a little learning goes a long way


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Two-Player Games: p45games allow one to see use in learning


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Two-Player Games: p45hangman. p105


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Two-Player Games: p45letter frequency. p107


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Two-Player Games: p45Gomoku. p99


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Two-Player Games: p45connection games


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Two-Player Games: p45connection games. p100


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Two-Player Games: p45Othello (Reversi) p106


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Two-Player Games: p45Othello


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Two-Player Games: p45dots and boxes: “A” starts. p108


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Two-Player Games: p45Cribbage. p108



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Two Quotes p45

  • “All I really need to know about how to live and what to do and how to be I learned in kindergarten.” Robert Fulghum

  • “Much of what I really needed to know about how to live and what to do and how to be I learned by playing Monopoly.” David Moursund


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Chapter 7: Games for Small and Large Groups: hearts. p115 p45

  • Uses standard deck of 52 cards.

  • Usually four players.

  • Passing 3 cards to another player

  • Players try to take tricks or avoid taking tricks.

    • Each heart a player takes in a trick is one point; the queen of spades is 13 points.

    • The goal is to score as low as possible, or to score all 26 points possible.


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Chapter 7: Games for Small and Large Groups: card games p45

  • Hearts, Whist, Bridge, Oh Heck, etc. all involve taking tricks. (p118)

  • Some involve playing with a partner.

  • Some involve bidding, a process whereby one says how many tricks they believe they will take.

  • Bridge is played competitively at national and world levels. Somewhat like in chess, there is a ranking system.


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Chapter 7: Games for Small and Large Groups: card sense. p117

  • “Reading” other players

  • Probabilities

  • Strategies

  • Thousands of hours of study and practice (reflective analysis) to achieve a high level of expertise.


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Chapter 7: Games for Small and Large Groups: MMOG. p121 p117

  • Massively Multiplayer Online Games

  • Tens of thousands of simultaneous players.

  • Players may organize themselves into teams that cooperate in accomplishing tasks.


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Chapter 7: Games for Small and Large Groups: MMOG p117

  • MMOGs—long and surprisingly complex gaming environments that normally require over forty hours to get beyond novice levels —represent the latest development in the history of video game technology.

  • Success in a MMOG requires developing new literacies, understanding intricate and intersecting rule sets, thinking creatively within constraints, collaborating with other participants towards shared goals, and perhaps most importantly, taking on new identities as players (via their avatars) inhabit game spaces.


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Chapter 7: Games for Small and Large Groups: Holodeck. p123 p117

  • Star Trek’s Holodeck—the future of virtual reality simulation games.

  • Also, a powerful direct tool for immersing students in interactive learning environments.


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Chapter 8: Lesson Planning. p126 p117

Have clearly defined general learning goals:

  • Students learn about themselves as learners and human beings.

  • Students learn more about problem solving and ways to get better at problem solving.

  • Students learn more about games and their roles in our society.


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Chapter 8: Lesson Planning: p117Students should be able to answer: (p129)

1. What is the purpose of this lesson?

2. Why is this important to learn?

3. How am I challenged to think in this lesson?

4. How will I apply, assess, or communicate what I’ve learned?

5. How will I know how good my work is and how I can improve it?

6. Do I feel respected by students in this class?

7. Do I feel respected by the teacher in this class?


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Chapter 8: Lesson Planning: p117Students will learn (page 132):

1. Declarative knowledge about the game—rules, vocabulary, objectives, history.

2. Procedural knowledge about the game—using procedural thinking in making good moves. Knowledge and understanding of algorithmic and heuristic procedures relevant to making good moves.

3. How to learn a game. How expertise increases through gaining improved declarative and procedural knowledge, through practice, through metacognition, and through reflective analysis.


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Chapter 8: Lesson Planning: p117Students will learn:

4. How to obtain and use feedback from oneself, the computer (if playing in a computer environment), and one’s fellow players (if playing with and/or against others).

5.To practice the high-road transfer of learning heuristics of developing an overall long-range strategy and making use of look ahead.

6. How to appropriately interact with fellow players and opponents. This includes learning the culture and social skills of game playing in general, as well as for the particular game being played.


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Chapter 8: Lesson Planning: p117Students will learn:

7. The thrill of victory, the agony of defeat (if it is a competitive game).

8 How to help others learn to play the game; how to be a teach/mentor in a game learning and game playing environment.

9. Self assessment and peer assessment. Receiving and giving feedback from oneself and others that can be used to improve the level of one’s expertise.


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Chapter 9: Miscellaneous Other Topics. p136 p117

  • Women and gaming.

  • Student creation of games.

  • Games and the aging brain—use it or lose it.

  • Artificial intelligence.

  • Research on games and gaming.


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Appendix: Summary of Problem-solving Strategies. p148 p117

  • Every discipline includes the general ideas of gaining increased expertise in solving problems, accomplishing tasks and doing things within the discipline.

  • It takes a lot of effort to achieve a high level of expertise.

  • Algorithmic and heuristic strategies:

    • Domain specific

    • Domain independent


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Questions p117

Tangram


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