Set is a commercial game published by SET Enterprises. It involves
determining if three cards satisfy the conditions that define a
"Set." In the standard
game those conditions are that the three cards be identical, or all different,
in four attributes: colour, number, shading, and shape. So a Set consists of three cards that are:
All the same colour or three different colours
AND
All the same shading or three different
shadings
AND
All the same shape or three different shapes
AND
All the same number of three different
numbers.
In the grade 2 class variations were played that were less complex.
Connect Four is a two player commercial game published by Milton
Bradley. The board consists of
seven vertical slots in which counters are dropped.
Six counters fit in each slot. The
object is to form a row of four counters of ones own colour running vertically
in a single slot, horizontally at the same level in four adjacent slots, or
forming a diagonal across four slots. In the classroom the children sometimes played in pairs, and
sometimes with the teacher as a member of one pair.
The Doorbell Rang, by Pat Hutchins is the story of two children who are about to share twelve cookies between them, when the doorbell rings. Each
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Psychology of Students' Reasoning in School Mathematics
David A Reid
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time the doorbell rings more children arrive and the number of
cookies each person gets decreases.
Mastermind is a two player commercial game published by Pressman.
One player makes a code by placing four pegs (chosen from a set of six
colours) behind a screen. The other player then tries to determine the hidden code by
guessing. After each guess the
first player indicates the number of pegs that are in the correct locations,
and the number of pegs that are a correct colour but not in the correct
location. In the classroom the
teacher made the codes. The games
played in March used previously determined codes and guesses instead of having
the children guess.
Tic Tac Drop is a computer version of Connect Four, which allows
different numbers of slots and different winning conditions.
It can be played against the computer.
The teacher read a book called The 512 Ants on Sullivan Street by
Carol A. Losi. The students made predictions about the number pattern that was
present in the book and later had the chance to create their own number
patterns. The pattern presented in the book was a doubling pattern.
Students were given a chart consisting of three rows and 25 columns. The
rows were used for (1) the number to be made using base ten blocks, (2) a
diagram of the base ten blocks used and (3) the number of blocks used. Once
students modelled numbers from 100 to 124, they were asked if they could see
any patterns. It was hoped that students would eventually discover that the
number of blocks they had to use (if they always traded ten of a smaller unit
for 1 of a larger unit) would be the sum of the digits.
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David A Reid
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After they examined the numbers for patterns, they were asked to make
predictions about the number of blocks that would be needed to make particular
numbers and then told to test their guesses by modelling them with base ten
blocks.
Students were given two sheets to do containing examples of "growing
patterns." The two patterns that they were asked to make and observe
using pattern blocks were the square and the triangle. For both patterns the
first three shapes of each pattern were depicted, labelled as 1, 2 and 3. The
students were then required to come up with the 4th shape in each pattern on
their own and eventually make predictions about the number of pattern blocks
needed to make the 5th shape in each pattern.
The students were given a sheet of paper and a hole punch. They were
asked to make a given number of folds in the paper and a specified number of
holes and then asked to predict what the results would be when the paper was
unfolded.
The students were asked to create squares on geoboards and then asked
questions about area related to the squares. Some students were asked to
figure out the area in diamonds.
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Psychology of Students' Reasoning in School Mathematics
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