Nerida F. Ellerton

Florence Mihaela Singer

Jinfa Cai

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years. ​​

From Research to Effective Practice

Mathematical Problem Posing

M. A. Clements

Prepared for units ECT405, ECT705 offered by the Faculty of Education in Deakin University's Open Campus Program.

Reflections on Problem Solving in School Mathematics

Polya, Krutetskii and the Restaurant Problem

M. A. (Ken) Clements

This book tells one of the greatest stories in the history of school mathematics. Two of the names in the title—Samuel Pepys and Isaac Newton—need no introduction, and this book draws attention to their special contributions to the history of school mathematics. According to Ellerton and Clements, during the last quarter of the seventeenth century Pepys and Newton were key players in defining what school mathematics beyond arithmetic and elementary geometry might look like. The scene at which most of the action occurred was Christ’s Hospital, which was a school, ostensibly for the poor, in central London. The Royal Mathematical School (RMS) was established at Christ’s Hospital in 1673. It was the less well-known James Hodgson, a fine mathematician and RMS master between 1709 and 1755, who demonstrated that topics such as logarithms, plane and spherical trigonometry, and the application of these to navigation, might systematically and successfully be taught to 12- to 16-year-old school children. From a wider history-of-school-education perspective, this book tells how the world’s first secondary-school mathematics program was created and how, slowly but surely, what was being achieved at RMS began to influence school mathematics in other parts of Great Britain, Europe, and America. The book has been written from the perspective of the history of school mathematics. Ellerton and Clements’s analyses of pertinent literature and of archival data, and their interpretations of those analyses, have led them to conclude that RMS was the first major school in the world to teach mathematics-beyond-arithmetic, on a systematic basis, to students aged between 12 and 16. Throughout the book, Ellerton and Clements examine issues through the lens of a lag-time theoretical perspective. From a historiographical perspective, this book emphasizes how the history of RMS can be portrayed in very different ways, depending on the vantage point from which the history is written. The authors write from the vantage point of international developments in school mathematics education and, therefore, their history of RMS differs from all other histories of RMS, most of which were written from the perspective of the history of Christ’s Hospital.

Nerida F. Ellerton

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