Paul White

• PhD
• Australian Catholic University

The term 'curriculum' is used to describe the intended curriculum, the implemented curriculum or the attained curriculum. While the intended curriculum refers to the written or prescribed curriculum, the implemented curriculum refers to curriculum as teachers enact it in classrooms. Consequently, it is difficult to separate the enacted curriculum f...

The Teaching and Learning Consortium (TLC) was initiated in 1996 on the Strathfield campus (NSW) at Australian Catholic University in partnership with nine primary schools in the diocese of Parramatta, Sydney. The program continues to the present with an expansion to over 40 primary schools in the Sydney metropolitan and outer metropolitan areas ac...

The experiences of five U. S. elementary teachers who engaged in lesson study to investigate the teaching and learning of mathematics were quite different. Three teachers accepted the challenges highlighted by the lesson study process. They reflected on and changed their mathematics teaching practice in fundamental ways. The other two teachers reje...

This article outlines a theoretical model for teaching elementary mathematical concepts that we have developed over the past 10 years. We begin with general ideas about the abstraction process and differentiate between abstract-general and abstract-apart concepts. A 4-phase model of teaching, called Teaching for Abstraction, is then proposed that i...

Being numerate involves using mathematical ideas efficiently to make sense of the world, which is much more than just being able to calculate. What is needed is the accurate interpretation of mathematical information and the ability to draw sound conclusions based on mathematical reasoning. This skill may be called "critical numeracy", defined as "...

Five practising teachers in regional NSW implemented Teaching for Abstraction for the Year 6 topic "Percentages". The authors constructed materials for a unit in which students explored familiar percentage contexts, searched for similarities in their mathematical structures and then applied their learnings to more abstract situations. Particular em...