Preschool children's understanding of basic addition principles - Pavlin-Bernardić, Nina (Array, 2009)
The aim of this study was to explore age-related differences in preschoolers' additive composition, commutativity and associativity understanding. The participants were preschool children aged 4 (N=41) and 6 years (N=76). Children made judgements about the equivalence of pairs of problems in the context of deciding whether two toys had been given the same number of objects. Female experimenters interviewed children individually, one session lasting 15-20 minutes. There were three practice trials and 15 test trials. Test trials were presented in a random order. In every trial, after the child's judgement, the interviewer also asked him/her to explain why he/she thinks the bears have equal (or unequal) number of candies. Older children had more correct judgements than younger children in all three categories of problems representing different addition principles. There were no differences in the percent of correct answers between different addition principles. Qualitative analysis was performed in order to determine whether there are differences in children's justifications of their judgements. Although six-year old children used more elaborate justifications more frequently than four-year old children, both groups mostly used qualitative rather than quantitative terms in explanations of their answers. The results are in accordance with protoquantitative level of mathematical reasoning proposed by Resnick (1992).