Basics of Strategy From a Third Grade Class

11 10 2009
Last week my students and I were reviewing the strategy of the game of Nim in my third grade class.

Nim is a very simple game that can introduce big ideas of strategy.

The object of the game is to force your opponent to take the last marker. That is, the loser removes the last marker. Of course, the game could be played that the winner is the one who takes the last marker.

Construct three rows of markers: the top row has three markers, the center row has five markers and the bottom row has seven markers. The number of markers for each row and the number of rows is open to options. But, 3-5-7 Nim provides for a short game and yet complex enough for variety and analysis.

Players take turns removing as many markers as they like in one row only. Each player must remove at least one marker per turn. The word Nim probably comes from the Shakespearean word meaning “to take away” or “steal”.

This game can be played anywhere because one can use toothpicks, little rocks or play animals,marks on a chalkboard, or on a foggy window.

Nim is a game that has been played, in various forms, on at least four continents for at least four centuries. Like tic tac toe, it is a challenging game until one realizes that there is a correct way to play. In the case of tic tac toe, there is a correct way for both players and, if both players make the correct moves, the game must always end in a tie.

In the case of Nim, when one player makes the correct moves, he will always win. (Whether this is the player who goes first or the player who goes second depends on the variation of nim being played.)

Where the perfect strategy for Tic Tac Toe is discoverable by a bright child, discovery of the correct nim strategy takes a mathematical intuition of the highest order for one without mathematical experience.

After two months of playing one of my third grade students studied with his parents for a week to discover a winning strategy. He came to class and confidently won me in a game. He has now become a partner teacher in strategy for the class.

For some websites on Nim try:

This gave a good introduction to the basics of strategy. Here I laid the foundation to three basic ways students approach games:

1. Superstitious Plans
According to the writer Raymond Lamont Brown: “Superstition is a belief, or system of beliefs, by which almost religious veneration is attached to things mostly secular; a parody of religious faith in which there is belief in an occult or magic connection.”

Another way to put it is that superstition is an irrational or nonscientific belief in the existence of certain powers operant in the world, with positive or ill (usually ill) effects. These are rituals or patterns of behavior that are believed to have some power to influence the outcome of the game.
What are some examples you have seen as we played the game?

2. Psychological Ploys
The art or practice of using tactical maneuvers to further one’s aims or better one’s position. The use in a sport or game of aggressive, often dubious tactics, such as psychological intimidation or disruption of concentration, to gain an advantage over one’s opponent. Here the concepts of Gamesmanship versus sportsmanship are introduced. Also mentioned are ways players try to psych-out your opponent. Psychological Ploys are the use of dubious (although not technically illegal) methods to win a game
What are some examples you have seen as we played the game?

3. Strategic Play
Strategy is a careful plan or method. Victory is completely dependent on your reasoning and pattern recognition skills, and completely independent of luck
What are some examples you have seen as we played the game?

But it is amazing how such a simple game can introduce the ways people approach life.

Teaching Concentration Rather than Cheating

11 10 2009
There are many lessons we learn from games. When players cheat we learn about character and the expression of ethics. Perhaps games give us a clue of the true character of an individual. Like the quote from Ovid, “In our play we reveal what kind of people we are.”As a teacher I am trying to teach students to learn from games and not just play to win. Perhaps winning is the only time students have been rewarded and praised. And sadly this could lure students into cheating. As a teacher I must think of the big picture- the long view. Winning is a great feeling but learning from mistakes and building mental strength has more transferable aspects. Of course building self-esteem by winning is a fine goal but unique and honorable is the student who can pick up the pieces of a lost game and seek to learn from it.

At early ages focus and concentration are often difficult habits to learn. Rather than trying to teach winning at all costs and allow for the temptation to cheat, I am attempting to praise characteristics of staying at something and concentrating.

Here are some character defintitions to help in this goal:
Character attributes of concentration:

1. Determination: The mental act of deciding, establishing and adherence to an aim.

2. Persistence: Persevering in an effort for a considerable time regardless of seeing results.

3. Tenacity: Holding firmly to a course or direction.

4. Resoluteness: Sticking to the focus of the goal.

5. Toughness: Sustaining one’s spirit following defeats.

6. Endurance: Staying power and the ability to sustain an increased level of activity without getting distracted or discouraged.

These are honorable characteristics for games as well as for life. Perhaps these are greater lessons than playing just to win.

What We Can Learn From Games

11 10 2009

by Ben Bishop

I came across an interesting article in the Idaho Statesman two days ago. It was a great article on teaching math to students and one of the final points was to play games that emphasized math like Monopoly or Risk. I am glad that any game can be used to teach concepts; however that seems to be an oversimplification of the potential of a game. If that is all a game is (a conceptual teaching tool) then the higher levels of Bloom’s famous taxonomy are not being reached at all. I can see games like Snakes and Ladders being used for this purpose (after all that is basically a counting game) but doing this is a higher grade class like 6th grade would turn me off of math and games in general.Games are expressions of the struggles we face, a miniature version of reality without the painful loss. If they are used like a set of flash cards then the purpose is lost. Yes, I’ll learn about probability when I roll the dice, I’ll learn about trivia when I play a question game, etc… It’s the participation of play that teaches me not just the memorization of facts and figures.Here’s a link to an article that says about the same thing but in a more logical manner:

Till next time,
Ben Bishop

Lessons from Strategy Games

11 10 2009

I was just interviewed for a local newspaper concerning what we can learn from games. I was quoted saying that students may not naturally learn from games. We often say how helpful games are in teaching life lessons, math, strategy or whatever. As a teacher, I have realized that unless a teacher is explicit, students do not transfer their knowledge to other areas. Here are some ideas about drawing life lessons from games.

Here are some guidelines for guidelines:

They must be easily repeatable, quotable, meaningful, and memorable

They must be a generalization to all or a specified group

They are commands or they implies what we should do

They are short and concisely worded

Examples of Life Lessons written by my students….

-When you don’t understand the rules, you cannot play the game of life successfully.

-Be willing to learn new things so you are more equipped to make better choices and decisions.

-Commit to paying attention and reflecting upon the actions and behaviors of those around you.

-Your actions determine your outcomes.

-Your life experience is made up of the choices you make and the outcomes that accompany them each and every day.

-If you hope to have a winning life strategy you have to be honest about where your life is right now.

-Life rewards action.

-You must realize that your plans will alter and sometimes change along the way. Winners adapt to these new developments.

-A strategy requires courage, commitment and energy in order to succeed.

-When you know your goals, you will recognize which choices support them and which do not.

-Study and dissect your mistakes so you can avoid repeating them.

-Study and analyze your successes so you can repeat the behavior that has brought you positive results.

-Losers just make it up as they go along

Here is a quote that sums up my thoughts………

There are one-story intellects,
two-story intellects,
and three-story intellects with skylights.
All fact collectors who have
no aim beyond their facts
are one-story men.
Two-story men compare, reason, generalize, using the labor
of fact collectors as their own.
Three-story men idealize,
imagine, predict-
their best illumination comes
from above the skylight.
–Oliver Wendell Holmes

Performance Pictures of Bob Bishop

4 10 2009

These are pictures of Bob Bishop performing

in Taipei, Taiwan.

Teipei 103

Teipei 053

2008 010

This picture is Bob Bishop performing at the Special Olympics Banquet in Idaho.


Life Lessons from Chess

4 10 2009
 The following is an essay by Benjamin Franklin on chess. 

THE GAME OF CHESS is not merely an idle amusement; several very valuable qualities of the mind, useful in the course of human life, are to be acquired and strengthened by it, so as to become habits ready on all occasions; for life is a kind of Chess, in which we have often points to gain, and competitors or adversaries to contend with, and in which there is a vast variety of good and ill events, that are, in some degree, the effect of prudence, or the want of it. By playing at Chess then, we may learn:


1st, Foresight, which looks a little into futurity, and considers the consequences that may attend an action; for it is continually occurring to the player, “If I move this Piece, what will be the advantage or disadvantage of my new situation? What use can my adversary make of it to annoy me? What other moves can I make to support it, and to defend myself from his attacks?”


2d, Circumspection, which surveys the whole Chess-board, or scene of action: – the relation of the several Pieces, and their situations; the dangers they are repeatedly exposed to; the several possibilities of their aiding each other; the probabilities that the adversary may make this or that move, and attack this or that Piece; and what different means can be used to avoid his stroke, or turn its consequences against him.



3d, Caution, not to make our moves too hastily. This habit is best acquired by observing strictly the laws of the game; such as, if you touch a Piece, you must move it somewhere; if you set it down, you must let it stand.



Therefore, it would be the better way to observe these rules, as the game becomes thereby more the image of human life, and particularly of war; in which if you have incautiously put yourself into a bad and dangerous position, you cannot obtain your enemy’s leave to withdraw your troops, and place them more securely, but you must abide by all the consequences of your rashness.



And lastly, we learn by Chess the habit of not being discouraged by present bad appearances in the state of our affairs; the habit of hoping for a favorable chance, and that of persevering in the search of resources. The game is so full of events, there is such a variety of turns in it, the fortune of it is so subject to vicissitudes, and one so frequently, after contemplation, discovers the means of extricating one’s self from a supposed insurmountable difficulty, that one is encouraged to continue the contest to the last, in hopes of victory from our skill; or, at least, from the negligence of our adversary: and whoever considers, what in Chess he often sees instances of, that success is apt to produce presumption and its consequent inattention, by which more is afterwards lost than was gained by the preceding advantage, while misfortunes produce more care and attention, by which the loss may be recovered, will learn not to be too much discouraged by any present successes of his adversary, nor to despair of final good fortune upon every little check he receives in the pursuit of it.

That we may therefore, be induced more frequently to choose this beneficial amusement in preference to others, which are not attended with the same advantages, every circumstance that may increase the pleasure of it should be regarded; and every action or word that is unfair, disrespectful, or that in any way may give uneasiness, should be avoided, as contrary to the immediate intention of both the parties, which is, to pass the time agreeable.

1st, Therefore, if it is agreed to play according to the strict rules, then those rules are to be strictly observed by both parties; and should not be insisted upon for one side, while deviated from by the other: for this is not equitable.

2d, If it is agreed not to observe the rules exactly, but one party demands indulgences, he should then be as willing to allow them to the other.

3d, No false move should ever be made to extricate yourself out of a difficulty, or to gain an advantage; for there can be no pleasure in playing with a man once detected in such unfair practice.

4th, If your adversary is long in playing, you ought not to hurry him, or express any uneasiness at his delay; not even by looking at your watch, or taking up a book to read: you should not sing, nor whistle, nor make a tapping with your feet on the floor, or with your fingers on the table, nor do anything that may distract his attention: for all these displease, and they do not prove your skill in playing, but your craftiness and your rudeness.

5th, You ought not to endeavor to amuse and deceive your adversary by pretending to have made bad moves; and saying you have now lost the game, in order to make him secure and careless, and inattentive to your schemes; for this is fraud and deceit, not skill in the game of Chess.

6th, You must not, when you have gained a victory, use any triumphing or insulting expressions, nor show too much of the pleasure you feel; but endeavor to console your adversary, and make him less dissatisfied with himself by every kind and civil expression that may be used with truth; such as, you understand the game better than I, but you are a little inattentive, or, you play too fast; or, you had the best of the game, but something happened to divert your thoughts, and that turned it in my favor.

7th, If you are a spectator, while others play, observe the most perfect silence: for if you give advice, you offend both the parties: him against whom you give it, because it may cause him to lose the game: him in whose favor you give it, because, though it be good, and he follow it, he loses the pleasure he might have had, if you had permitted him to think till it occurred to himself. Even after a move or moves, you must not, by replacing the Pieces, show how they might have been placed better; for that displeases, and might occasion disputes or doubts about their true situation.


All talking to the players lessens or diverts their attention; and is, therefore, unpleasing; nor should you give the least hint to either party, by any kind of noise or motion; if you do, you are unworthy to be a spectator.

If you desire to exercise or show your judgment, do it in playing your own game, when you have an opportunity, not in criticizing or meddling with, or counseling the play of others.


Lastly, If the game is not to be played rigorously, according to the rules before mentioned, then moderate your desire of victory over your adversary, and be pleased with one over yourself.



Snatch not eagerly at every advantage offered by his unskilfulness or inattention; but point out to him kindly, that by such a move he places or leaves a Piece en prise unsupported; that by another, he will put his King into a dangerous situation, &c.


By this general civility (so opposite to the unfairness before forbidden) you may happen indeed to lose the game; but you will win what is better, his esteem, his respect, and his affection; together with the silent approbation and the good will of the spectators.

When a vanquished player is guilty of an untruth to cover his disgrace, as “I have not played so long, – his method of opening the game confused me, – the men were of an unusual size,” &c all such apologies, (to call them no worse) must lower him in a wise person’s eyes, both as a man and a Chess-player; and who will not suspect that he who shelters himself under such untruths in trifling matters, is no very sturdy moralist in things of greater consequence, where his fame and honor are at stake? A man of proper pride would scorn to account for his being beaten by one of these excuses, even were it true; because they have all so much the appearance, at the moment, of being untrue.


 Author: Benjamin Franklin

Quotations About Humor

25 09 2009

Almost all new ideas have a certain aspect of foolishness when they are first produced

           -Alfred North Whitehead


People do not quit playing because they grow old.  They grow old because they quit playing

    -Oliver Wendell Holmes


You don’t stop laughing because you grow old, you grow old because you stop laughing.

  -Michael Pritchard


You cannot deal with the most serious things in the world unless you understand  the amusing

  -Winston Churchill


Sometimes you’re the bug, sometimes you’re the windshield.



Comedy is for those who think and a tragedy is for those who feel.

-Horace Walpole


Wrinkles merely indicate where smiles have been.

-Mark Twain


Laughter is the shortest distance between two people.

-Victor Borge


When humor goes, there goes civilization.

-Erma  Bombeck


Mirth is God’s medicine

-Henry Beecher


Among those whom I like, I can find no common denominator: but among those I love, I can: all of them make me laugh.

-W. H. Auden


Laughter is, after speech, the chief thing that holds society together.


-Max Eastman


 He who laughs, lasts.

-Norwegian Proverb


The jester is brother to the sage.

     -Arthur  Koestler


Humor is a means of obtaining pleasure in spite of the distressing affects that interfere with it.



Humor at its best is a kind of heightened truth- a super-truth.

-E. B. White


Dictators fear laughter more than bombs

-Arthur Koestler


The most wasted day of all is that on which we have not laughed.

-Sebastian Chamfort


When I’m happy I fell like crying, but when I’m sad don’t feel like laughing.  I think it’s better to be happy.  Then you get two feelings for the price of one.

-Lily Tomlin


Against the assault of laughter, nothing can stand.

-Mark Twain



A cheerful heart is good medicine

 -Proverbs 17: 22


 Half this game is 90% mental.

Danny Ozark