Two versions of the conservation-of-number task and their links to numerical difficulties

Abstract

Piaget’s conservation-of-number task remains the subject of many debates, to the extent that it is not clear whether this task is indicative of numerical competencies. Indeed, achievement in this task is influenced by other factors such as the pragmatic aspects of the situation, verbal skills for justifying answers and the ability to inhibit intuitive perceptual responses (Fayol, 1990; Houdé et al., 2011). Interestingly, this task is included in several batteries of numerical skills in relatively different forms. Within a study on early numerical competencies (Mathplay), a test has been created to measure these skills at three times of kindergarten (N=72, mean age = 5,6 years old at time 1). Two versions of the conservation-of-number task have been incorporated for comparison purposes: an easier version in which tokens presented in line are moved in a circle, as in the TEMA-3 battery (Ginsburg & Baroody, 2003), and a classical version in which the tokens are narrowed and children have to justify their answers. Analyses show that failure at the easier task is associated to difficulties in numerical skills five months later whereas children who do not succeed the “narrowed” task have numerical performance that does not differ from the mean. Furthermore, an inter-rater agreement on the children’s justifications shows that classifying them as empirical or logical, as required in the Tedi-math battery (Van Nieuwenhoven, Grégoire & Noël, 2001), is not very easy. In the middle of the school year, only 34% of the children gave responses that were based on quantity.