What types of math manipulatives are more challenging
for older or more advanced children?
Math activities that utilize two or more dice and larger quantities
of counters or manipulative pieces are more complex. Using two
dice introduces children to the concept of adding two sets of num-
bers. At first, many children count the two dice separately before
selecting their counters, and they do not understand that they
could get the same total by counting all of the dots together. Once
children arrive at this realization, they need many opportunities to
experience the results of adding two sets. Counting errors are com-
mon. Eventually, children solidify their counting skills and begin
to remember addition combinations. At this point, some children
may wish to add a third or fourth die to their games to further
increase the complexity. Special dice, such as ten-sided or spheri-
cal dice, also add interest for more experienced children.
How should teachers guide children in their use of math
Teachers should encourage children to use their own thinking
strategies to solve math problems. Telling children how to get the
correct answer, such as moving the child’s finger while counting,
does not help children learn to think logically. Instead, it imposes
the adult’s thinking on the child and teaches children to look to
adults to solve math problems. Children need many opportunities
to think about mathematical relationships in order to develop their
sense of number.
Teachers can encourage children to discuss mathematical prob-
lems that emerge as they interact and play games together.Discus-
sion and disagreement among peers do not inhibit children’s
autonomy and willingness to think about solutions to problems.
Often, as children try to explain a viewpoint to another child, new
ways of thinking emerge. Children learn from one another because
they think and evaluate as they argue and discuss.
Teachers can subtly guide children by modeling mathematical
reasoning at a stage that is just above the thinking level of the child.
Thus, if a child is at a global level of quantification, the teacher
might model one-to-one correspondence; if a child is at a one-to-
one correspondence level, the teacher might model counting. Mod-
eling is not the same as correcting errors. It simply offers an
alternative means to solve a problem.