along a path is more abstract than taking counters; therefore,
path games are cognitively more difficult than grid games. Path
games provide opportunities for children to discuss their ideas
with others and be confronted with different opinions. When
children defend their beliefs, they may strengthen their know-
ledge base or be forced to rethink how they view a situation. For
example, when one child moves one space for each dot shown
on the dice while the other child moves randomly, or when one
child re-counts the space his mover is on and the other child does
not, one or both of them may be bothered by the results. Over a
period of time these interactions help children move toward
more logical thinking.
What makes a good path game?
A good path game has a clearly defined path and intriguing
movers that encourage children to move in one-to-one correspond-
ence. It involves a topic that is interesting to children and often
coordinates with other aspects of the curriculum. Good path
games are attractive and durable.
What is wrong with commercial path games?
Commercial games generally do not encourage children to con-
struct mathematical relationships or use their own thinking
strategies. They are often too difficult or too easy. Some games,
such as Chutes and Ladders, incorporate a long (100-space) and
confusing path with a relatively simple 1-6 spinner. Games such
as Candyland encourage children to use color matching rather
than quantification strategies. (It is likely that these games were
never intended to be mathematical materials.) Teachers may be
unable to coordinate commercial games with other curriculum
areas. Also, commercial math games do not provide opportunities
for teachers to assess or plan for individual children.
What are the rules for path games?
There are no specific rules for path games. Children are encour-
aged to decide among themselves what the rules will be so that
they can adapt the games to correspond to their own
developmental levels. Children who are not being evaluated pre-
fer more challenging material (see “Your Praise Can Smother
Learning” by David L. Martin in Learning, Feb. 1977, p. 44).
Therefore teachers need not worry that children will consistently
play games below their cognitive level. In fact, children often cre-
ate more difficult problems than teachers would ever think to