How likely is the glass to break, given that it is heated? The present study asks questions such as this with or without the premise "if the glass is heated, it breaks." A reduced problem (question without premise) measures the statistical dependency (conditional probability) of an event to occur, given that another has occurred. Such…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Dual-process theories have been proposed to explain normative and heuristic responses to reasoning and decision-making problems. Standard unitary and dual-process theories predict that normative responses should increase with age. However, research has focused recently on exceptions to this standard pattern, including developmental increases in…

When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…

The present study explores how suppositions which conflict with accepted beliefs are represented and reasoned about. Two studies test the predictions regarding the nature and developmental changes in children's ability to represent and reason about hypothetical or make-believe suppositions which violate their everyday knowledge and beliefs. In…

With the increase in prominence of the investigative approach in Hong Kong science curricula from the primary to the senior secondary level, there is urgency for local science educators including primary school teachers to gain a better understanding of pupils' existing cognitive understanding and reasoning ability for performing science…