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science by everybody
Uniquely, in the game of Crypt-0-Graph
everybody, preschoolers to professors, can
graphically make theories, experiments and
discoveries with the millions of things that can
be shown on a grid of numbered lines.
A board with grid of lines numbered -10, 0, 10,to assist players negative lines and numbers are coloured red, positive lines and numbers black, 60 to 70 round pieces about same diameter as distance between lines, say 15 mm.
Three or more players, any age, pieces pooled on middle of top margin of board.
One makes up a secret rule or code that the others can think of as a secret of nature to be discovered by experiments with placing pieces onto the grid.
The code can be very simple, say shape of animal, letter, etc. or it can be a complex mathematical calculation, or an interesting pattern, or some sequence.
However if early success with the experiments is too hard or too easy the code-maker gets a bad score.
Example, Jill, Tom, Dick, Harriet and Pat play.
Jill makes up a code, say “pieces to go where lines with numbers 3, 6, 9, (multiples of 3, 3 times table) cross.” She notes it on some paper, folds it away, it helps consistency and can prove it. Nature is consistent !
Tom takes a piece from pool of pieces which is on top margin of board in reach of all, and puts piece on centre 0,0. of board.
That is quite a good try, many simple ratios go through there, and if the codemaker says 'no',as happens in this case, than those ratios are out.
A 'no' means, researcher takes that piece off and places it in front of self so that each researcher keeps pieces in front of self as tally of own 'no' s.
The next researcher clockwise Dick, has a turn, tries piece where lines with number 1 cross (1,1).
There is logic in trying a steady ascent of numbers, but it gets a 'no' also, and that piece goes in front of Dick.
Harriet tries 2,2, with prob. the same idea, also gets 'no' , puts piece in front of Harriet.
Pat tries 3,3, gets 'yes', jubilation, that piece stays there.
Tom wonders,is 3,3 part of a square, or is it a number pattern, both may be symmetrical, what would be the best way of finding that out, while perhaps at the same time discerning if it is a square or if it is a number pattern or something else, has turn and tries .......?
Experiments continue till there are too few pieces left in pool for another complete round.
Then the score for the codemaker is worked out, it varies with the difference between the 'no' s of the leading(with fewest 'no's) and other researchers, always little if things were too easy or too hard!
If Tom got 5 'no' s, Dick got 8, Harriet 6, Pat 4, total 23, If all went as well as Pat the total would be 4+4+4+4 =16. the difference, 23 -16=7, that is the code maker Jill’s score. i.e. multiply leaders’ tally by number of researchers, subtract that from total 'no' s. to get codemakers’ score.
Now researchers continue by using pieces from their own no piles, re and re-using them till one runs out, at the completion of that round, calculate researchers’ scores, similarly, i.e. each researcher’s tally now left multiplied by how many researchers then subtracted from total no s left. If Tom got 2, Dick 5, Harriet 3, Pat 0. total 10.
Tom gets 10 minus 2x4=2. Dick 10 minus 5x4=-10 ! Harriet 10 minus 3x4=-2. Pat 10 minus 0x4=10.
Notice how researchers scores balance.
Pat won with 10, Jill 2nd with 7, then Tom with 2, Harriet with -2, Dick with -10.
Each player should have a turn at codemaker, a high score means a good game. Knowing the code gives interesting insights into research and solutions.
Sometimes various researchers’ ideas may ‘work’, can experiments sort them out ?
Can grouping possibilities according to characteristics help?
Is a theory better because it is simpler, because trying it yields more information, because it fits all evidence, it is easier to test?
How certain can knowledge be, or is methodology more important?
C.0.G. sets $12. p&post (Aust) $3.
Correspondence about interesting ideas, developments, even orders, gladly welcomed by Fred Groenier. c/-.P.O. Don.7310. Australia.
Groenier@keypoint.com.au
Crypt-o-Graph for education.
Why games in education?
I am sure many an educator seeing students playing chess, wished that students would get as involved in lessons.
Games such as chess have many favourable attributes with rewards and demands and getting player’s interactions mostly self-regulating.
Why crypt-0-graph?
For all of the above reasons, but especially because it is a game of actually seeking and gaining information, any of the limitless information that can be shown on a grid of numbered lines but perhaps more important the method of gaining that information graphically models that of science with the exercise of those abilities that are outstanding in making breakthroughs.
What level of abilities or age is required?
Remarkably any level or age group The game completely self adjusts to the abilities of any group of players, because players set to solve a code made by another player who gets pressured by the scoring system (based on that of Eleusis) to make everything so playable that success is neither too hard or too easy for that group of players. It has been played and enjoyed by players ranging from preschoolers to professors.
In what way are “those breakthrough making abilities” exercised?
There is of course a whole lot of science and philosophy about cognition etc. but in the game players are unlimited in the ideas they can lay out with pieces onto the grid of numbered lines, as the experiments build up more evidence and at the end of the game, it can be seen clearly how effective each idea and experiments was in making a breakthrough.
The person who made the secret code does of course from the beginning check each afford vis a vis the complete code.
How would that fit in with other learning?
As players enhance their reasoning and their knowledge, such exercise must be applicable in life generally, ignorance and irrationality are a bane generally.
The reasoning is mostly inductive logic although deduction also has a place, induction because more information can make a difference so is most apt for when seeking more information, it does not give the certainty of deduction where no extra information can make a difference, mistakes in this can lead to unwarranted certainty.
Surely applicable in all fields of life.
If this game is seen as a means to increase open minded enlightenment, so be it.
Fred groenier. links www.schoolgamemaker.rupert.id.au/links.htm also Eleusis in Martin Gardner 'More Mathematical puzzles and diversions'. Gerrald Abrahams 'The Chess Mind'. Polya "How to solve it.' Jonathan Cohen 'Implications of induction'.
F of Am scientists games
Send E-Mail to: groenier@keypoint.com.au
Copyright © 2007 fred groenier. All Rights Reserved