Mathematics

Since the publication of the first Handbook of Research of Mathematics Teaching and Learning in 1992 and edited by Doug Grouws, research in mathematics education has continued to flourish: moving into new domains, digging more deeply into many enduring questions, and asking new ones. At the same time, mathematics education has continued to mature as a field of study. As the field has matured, there has been growing recognition of the importance of reflecting on what distinguishes the mathematics education research from other fields and on what influences the nature of its activities. During the past dozen or so years, advances in information technology have accelerated the pace of change in society and diverse individuals and groups have begun to promote a variety of old and new instructional approaches, programs, and policies for mathematics education. general, and widespread reform in mathematics education in particular. Researchers are being exhorted to gather and analyze data in support of specific agendas. A pressing challenge for the mathematics education researchers has been to reach out to its constituents and provide research-based advice about questions that concerned that constituent community, and to do so in an unbiased, rational, and convincing manner.

This is the first comprehensive monograph on the mathematical theory of the solitaire game "The Tower of Hanoi" which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game's predecessors up to recent research in mathematics and applications in computer science and psychology.

How can mathematics education foster the skills that are appropriate for innovative societies? Mathematics education is heavily emphasised worldwide, nevertheless it is still considered to be a stumbling block for many students. While there is almost a consensus that mathematics problems appropriate for the 21st century should be complex, unfamiliar and non-routine (CUN), most of the textbooks still mainly include routine problems based on the application of ready-made algorithms.

The time has come to introduce innovative instructional methods in order to enhance mathematics education and students’ ability to solve CUN tasks. Metacognitive pedagogies can play a key role in this. These pedagogies explicitly train students to “think about their thinking” during learning. They can be used to improve not just academic achievement (content knowledge and understanding, the ability to handle unfamiliar problems etc.) but also affective outcomes such as reduced anxiety or improved motivation. This strong relationship between metacognition and schooling outcomes has implications for the education community and policy makers.

This book is designed to assist practitioners, curriculum developers and policy makers alike in preparing today’s students for tomorrow’s world.