give them. For example, a four-year-old child decided to double
every roll of the dice and consistently did this throughout a game.
Children usually want to roll dice in order to tell how many
spaces to move when playing path games. This seems to be a
By kindergarten most children elect to play games competi-
tively. They enjoy playing to win. This seems to be a natural part
of development and occurs even in classrooms where teachers
de-emphasize competition. As children get older, the excitement
and fun of competition motivates them to play path games again
What concepts emerge when children play path games?
As children interact with each other while playing path games,
they continue to consider one-to-one correspondence, equivalence of
sets, and addition, but at a more complex level.
Path games require children to think about one-to-one corre-
spondence in a new context. Rather than take one counter for
each dot on the dice, they must move one space along the path
for each dot. This is more abstract because children cannot see a
specific quantity of items to correspond to the number of dots on
When children construct equivalent sets in path games, the
sets they must compare (the number of dots on the dice versus
the number of spaces moved) are not as concrete as when they
roll dice and take counters. They have to construct the idea that
they can quantify spaces on the path before they can consider
comparing a set of spaces to a number rolled on a die. This is
why children can successfully play grid games before they are
able to play path games, and why short path games are
introduced before long path games.
Long path games are an ideal format for encouraging the ad-
dition of two dice, since the games have many spaces and
children are eager to get to the end! Kindergarten children enjoy
path games so much that many learn all the addition
combinations just by playing the games.
What kinds of path games can teachers make and what
affects their level of difficulty?
Teachers can make short path, long path, continuous path, and
collection games. The level of difficulty of path games is affected
by whether there are separate paths for each player or just one
path for all players and by the length of the path. The number of
dots on the die (1-3 versus 1-6), the number of dice used, and