The “How many?” task inadequately assesses the understanding of the cardinality principle

Once children have acquired the cardinality principle, they understand that the last number-word used in counting represents the total number of objects in a set. This principle is often assessed using the “How many?” task, which consists in asking “How many?” objects there are in a set after children have counted them. However, we show in this study that out of 188 kindergarteners (mean age: 4 ½ years), 42 (22,3 %) succeeded in repeating the last count word in the “How many?” task but failed to correctly apply the one-to-one correspondence principle during counting. Even when only the easiest countable sets were considered (i.e., linear and homogeneous collections or sets with a very limited number of objects), still more than 10 % of children from our sample repeated the last count word but failed to apply the one-to-one correspondence principle. Such developmental profile, in which children understand that the last word used in counting represents the total number of objects in a set but fail to grasp that each individual object must be associated with a single number word to determine this total, is not psychologically plausible. We conclude that the “How many?” task leads to an inaccurate assessment of the cardinality principle, in both its basic and more meaningful conception, in a non-negligible number of young children.