The minicomputers, produced by CEMREL as part
of its Comprehensive School Mathematics
Program, were developed by a Belgian
mathematician, Georges Papy.  They are 8 1/2" x
11" pieces of cardboard on which are printed
two equal squares each of which is subdivided
into four squares of different colors.  Each of
the smaller squares represents a number;
students places various combinations of
positive or negative markers on these squares
to represent numbers.  In addition, the squares
can be used to represent place value.


Papy's minicomputer - this is used in grades 3
and 4 to teach mathematics concepts. Each digit
in a decimal number is represented by a 2x2
grid. Each grid square corresponds to one of
the numbers 1,2,4, or 8

[1][2]
[4][8]

as shown below, each grid square can hold a
"checker". Placing checkers on grid squares
represents a decimal number.

Here are some examples for single digit
numbers, where * represents a checker:

[*][ ]        = 1
[ ][ ]

[ ][*]        = 2
[ ][ ]      

For larger numbers, each digit is represented by
its own 2x2 grid.

The minicomputer applet could run in one of two
modes: (1) either the student would be given a
number and asked to place the checkers and push
a button when done (the applet would then give
feedback on whether the placement was correct or
incorrect), or (2) the student could place the
checkers and ask what number that placement
represents.

The minicomputer game for the Commodore 64 is a
simple cbm basic representation of Papy's
minicomputers.

In Level 1, the 1,2,4, and 8 boards are
represented on the display screen by colorful
squares in which students can type digits, one
per box.  Level 1 displays a number on the
right side of the screen and students can type
a digit in each of the boards until the value
of the number displayed is reached.

Level 2 uses Weighted Checkers, something the
CEMREL program used to indicate multiple
checkers (i.e., instead of putting 2 checkers
on the board to represent the number 2 on the
1's board, the number 2 is put on the 1's board).