Some Roles of Puzzles and
Games in Education
Dave Moursund. p2
1
Introduction. p6


Computerized and non-computerized:
– Puzzles
– Board games
– Card games
– Word games
But not physical sporting event such as
Olympic Games
2
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.
3
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.
4
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.
5
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.
6
Chapter 1: Thinking Outside
the Box: 9 dots puzzle. p12
7
Chapter 1: Thinking Outside
the Box: 9 dots puzzle. p12
8
Chapter 1: Thinking Outside
the Box: 9 dots puzzle. p12
9
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?
10
A dot an a point are not the
same thing: Nine bigger dots.
p13
11
Chapter 1: …: problem solving.
p14
A
Given initial
situation.
?
B
Desired
goal
situation.
What can I do to
move from A to B?
12
Chapter 1: …: problem solving.
P14-15
Four-part definition of problem:
1. Clearly defined given initial situation.
2. Clearly defined goal.
3. Clearly defined resources such as
your time and brain power, money,
computers, etc.
4. Ownership; desire to solve problem.
13
Chapter 1: Thinking Outside
the Box. p23

Each chapter ends with:
– Activities for teachers.
– Activities for use with students.



Appendix summarizes lots of problemsolving strategies.
The book has oodles of references,
mostly to websites.
The book has an extensive Index.
14
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.
15
Chapter 2: Background Info.:
vocabulary and notation. p39
16
Chapter 2: Background Info.:
vocabulary and notation. p39
White
1. Pe4
2. Nf3
3. Bb5
4. BxN
Black
Pe5
Nc6
Pa6
17
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.
18
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 subproblems 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 “subproblems” that one can readily solve. Often,
some of the sub-problems can be solved by a
computer or other machine.
19
Chapter 3: Sudoku:
9 x 9 board and 3 x 3 regions.
p44
20
Chapter 3: Sudoku:
givens (initially filled in). p44
21
Chapter 3: Sudoku: strategy of
finding a simpler problem. p45
22
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?
23
Chapter 3: Sudoku:
guess and check strategy. p48
24
Chapter 3: Sudoku:
guess and check strategy. p48
25
Chapter 3: Sudoku: mental
guess and check strategy. p49
26
Chapter 3: Sudoku: mental
guess and check strategy. p50
27
Chapter 3: Sudoku:
elimination strategy. p51
28
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.
29
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.
30
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.
31
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
32
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.
33
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.
34
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.
35
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.
36
Chapter 4: More Puzzles;
Howard Gardner. p63




Linguistic intelligence ("word smart"):
Logical-mathematical intelligence
("number/reasoning smart")
Spatial intelligence ("picture smart")
Etc,
37
Chapter 4: More Puzzles:
spatial puzzles. p64
Drag without rotation to fill square.
http://www.vemix.com/GlFlashGm.php
38
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.
39
Chapter 4: More Puzzles:
Tower of Hanoi. p66
Simpler problems.
40
Chapter 4: More Puzzles:
symmetric word box. p68
41
Chapter 4: More Puzzles:
logi-number puzzles. p69
42
Chapter 4: More Puzzles:
peg puzzles. p72
Jump horizontal or vertical.
Remove jumped peg.
Goal: one peg in the middle.
43
Chapter 5: One-Player Games:
solitaire card games. p77
44
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)
45
Chapter 5: One-Player Games:
Klondike solitaire game. p80
46
Chapter 5: One-Player Games:
eight off card game. p84
a
b
c
d
e
f
g
h
47
Chapter 5: One-Player Games:
eight off card game. p85
a
b
c
d
e
f
g
h
48
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.
49
Chapter 5: One-Player Games:
Tetris. p92
50
Chapter 5: One-Player Games:
Tetris. 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.
51
Chapter 6: Two-Player
Games. p95
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.
52
Two-Player Games:
tic-tac-toe. p95
X
X
O
Before
game
begins
X
X's
first
move
O
X
X
X
O's
second
move
X
O
X's
third
move
X
O's
first
move
X
O
O
X
X
O
X's
second
move
O X
O
X
O
X
O
O
X
O's
third
move
X
O
X wins on
X's fourth
move
53
Two-Player Games:
random 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?
54
Two-Player Games:
random 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???
55
Two-Player Games: a little
learning goes a long way
56
Two-Player Games: games
allow one to see use in learning
57
Two-Player Games:
hangman. p105
58
Two-Player Games:
letter frequency. p107
E
T
A
O
I
N
S
H
R
D
L
U
0.12702
0.09056
0.08167
0.07507
0.06966
0.06749
0.06327
0.06094
0.05987
0.04253
0.04025
0.02758
59
Two-Player Games:
Gomoku. p99
60
Two-Player Games:
connection games
61
Two-Player Games:
connection games. p100
62
Two-Player Games:
Othello (Reversi) p106
8
7
6
5
4
3
2
1
a
b
c d
e f
g
h
63
Two-Player Games:
Othello
8
7
x
6
x
5
4
x
x
3
2
1
a
b
c d
e f
g
h
64
Two-Player Games: dots and
boxes: “A” starts. p108
65
Two-Player Games:
Cribbage. p108
66
Chapter 7: Games for Small
and Large Groups. p114
Monopoly
67
Two Quotes

“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
68
Chapter 7: Games for Small and
Large Groups: hearts. p115




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.
69
Chapter 7: Games for Small
and Large Groups: card games




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.
70
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.
71
Chapter 7: Games for Small and
Large Groups: MMOG. p121



Massively Multiplayer Online Games
Tens of thousands of simultaneous
players.
Players may organize themselves into
teams that cooperate in accomplishing
tasks.
72
Chapter 7: Games for Small
and Large Groups: MMOG


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.
73
Chapter 7: Games for Small and
Large Groups: Holodeck. p123


Star Trek’s Holodeck—the future of
virtual reality simulation games.
Also, a powerful direct tool for
immersing students in interactive
learning environments.
74
Chapter 8: Lesson Planning.
p126
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.
75
Chapter 8: Lesson Planning:
Students 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?
76
Chapter 8: Lesson Planning:
Students 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.
77
Chapter 8: Lesson Planning:
Students 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.
78
Chapter 8: Lesson Planning:
Students 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.
79
Chapter 9: Miscellaneous
Other Topics. p136





Women and gaming.
Student creation of games.
Games and the aging brain—use it or
lose it.
Artificial intelligence.
Research on games and gaming.
80
Appendix: Summary of Problemsolving Strategies. p148
•
•
•
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
81
Questions
Tangram
82