In this study, the authors investigate the ways in which young students demonstrate their critical mathematical thinking (CMT). Students aged 5-6 who are beginning their first formal year of education participated in the study. Data is presented from individual clinical interviews undertaken with 16 students. These interviews were analysed using…

Piaget's theory of stage structure is synonymous with discussions involving cognitive development. As with any theoretical model, researchers inevitably and rightly seek to affirm and/or contest the elements of the model presented. In this comparative study, students' performance across three hands-on engineering tasks for two distinct student…

Critical thinking when engaged in science problem solving around even simple tasks such as the Piagetian volume conservation task is a complex endeavor. Tasks such as the conservation task often require the interaction of multiple cognitive systems. Parity judgment, retrieval, and lateral thinking are three examples of such systems interacting…

In this article, I examine changes in the field of cognitive development and in my own thinking over the past 40 years. The review focuses on three periods. In the first, Piaget's theory was dominant, and my research and that of many others was aimed at understanding the many fascinating changes in children's thinking that Piaget documented and at…