Children’s Combinatorial Counting Strategies and their Relationship to Conventional Mathematical Counting Principles

Abstract

In this chapter results of a qualitative study are presented, the main goals of which were to identify how children solve combinatorial counting problems and to gain insights into the relationship between their strategies and conventional mathematical counting principles. Counting strategies identified and discussed include multiplicative, additive, and compensation strategies. These strategies are examined with respect to their conceptual and operational differences and simi- larities to combinatorial counting principles, including the multiplication principle, the principle of inclusion/exclusion, and the so-called shepherd’s principle.