Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

Despite the numerous benefits that stem from a coherent mathematical understanding, it is uncommon for teachers to encourage students to form a developed web of mathematical connections (Mousley, 1999). Additionally, when students explain their thinking, they frequently do not state how their reasoning connects to prior knowledge. This obscures…

This article describes some aspects of Piaget's Theory of Cognitive Development. It highlights the importance of giving young children specific access to explore conservation in measurement, which will give students invaluable experiences in measurement that in years to come will be regarded as their prior knowledge of the concept. This is…

In this article, the author describes an open-ended drawing task that was used to discover young children's experiences with, and understandings of, the concept of mass. Mass is defined as the amount of matter in an object, and, like time, it cannot be seen (NSW Department of Education and Training Professional Support and Curriculum Directorate…

When children start school, they bring with them a variety of background skills and informal knowledge that can enrich their learning of new concepts and ideas. A major tenet of many learning theories is that the more children are able to connect a new concept with their existing knowledge and understandings, the more they feel confident and able…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

In this article, the author presents findings of a project that focused on identifying elements in the learning environment that promote numeracy outcomes. The project--"Numeracy Research and Development Initiative"--was undertaken in eight schools across a range of settings within the three schooling systems in Queensland and was…