Preface

This resource is the second edition of Key Ideas for Conceptual Development in Mathematics, which was first published in 2013 by the Catholic Education Office in the Archdiocese of Melbourne.

This second iteration was developed by Melbourne Archdiocese Catholic Schools (MACS) Learning Consultants, Mathematics, in response to a need for leaders and teachers to understand the significance of the important ideas in mathematics.

Key ideas are central to the learning of mathematics. They link numerous mathematical understandings into a coherent whole, which supports learners in associating ideas and strategies, as opposed to seeing them as disconnected concepts, skills and facts.

Highly effective mathematics teachers understand the importance of key ideas in developing students’ conceptual understandings in mathematics. They recognise that key ideas enable students to make deeper connections between the mathematical concepts and ideas that encompass and link them. When teachers plan for and implement key ideas into teaching and learning programs, the students have richer mathematical experiences and develop deeper mathematical understanding.

This second edition is based on a culmination of research and, like the first edition, includes full source information of all the studies cited in a references section. To increase the text’s accessibility and enhance its user-friendliness, the team of mathematics learning consultants at MACS collaborated with Dr Vince Wright.

We would like to express our sincere gratitude to Vince for his tireless work in supporting us to make this second edition become a reality. He has provided invaluable advice and expertise in helping us shape this book to its final publication.

Learning Consultants, Mathematics

Melbourne Archdiocese Catholic Schools

Suggestions for using this resource

This resource aims to support leaders and teachers to think deeply about the ideas that underpin mathematical concepts. To enrich the mathematics being learned, it is recommended that this resource be used in conjunction with the Victorian Curriculum Mathematics, Victorian Curriculum and Assessment Authority Numeracy Learning Progressions and student data.

Mathematics leaders can use this resource when facilitating planning, leading professional learning meetings and promoting high-quality teaching of mathematics.

Some areas they may choose to focus on include:

• building a shared understanding of conceptual development

• creating a culture of professional learning

• developing learning progressions of mathematics concepts

• deepening teachers’ knowledge of mathematical and pedagogical content

• supporting teachers to identify and enact appropriate adjustments to facilitate student understanding in mathematics.

Teachers of mathematics can use this resource to plan for effective mathematics learning for their students. They may choose to use this resource to focus on:

• building a deep understanding of the mathematics curriculum

• identifying the important mathematics ideas embedded in the curriculum

• developing appropriate assessment tools

• selecting ways to determine students’ mathematical skills and understanding.