This highly motivational text approaches the study of algebra with imaginative applications and clear problems derived from the real world. Technology tools are used to assist with time-comsuming calculations and to integrate graphing and problem-solving skills.
'The question for me is how can the human mind occur in the physical universe. We now know that the world is governed by physics. We now understand the way biology nestles comfortably within that. The issue is how will the mind do that as well.' --Alan Newell, December 4, 1991, Carnegie Mellon University The argument John Anderson gives in this book was inspired by the passage above, from the last lecture by one of the pioneers of cognitive science. Newell describes what, for him, is the pivotal question of scientific inquiry, and Anderson gives an answer that is emerging from the study of brain and behavior. Humans share the same basic cognitive architecture with all primates, but they have evolved abilities to exercise abstract control over cognition and process more complex relational patterns. The human cognitive architecture consists of a set of largely independent modules associated with different brain regions. In this book, Anderson discusses in detail how these various modules can combine to produce behaviors as varied as driving a car and solving an algebraic equation, but focuses principally on two of the modules: the declarative and procedural. The declarative module involves a memory system that, moment by moment, attempts to give each person the most appropriate possible window into his or her past. The procedural module involves a central system that strives to develop a set of productions that will enable the most adaptive response from any state of the modules. Newell argued that the answer to his question must take the form of a cognitive architecture, and Anderson organizes his answer around the ACT-R architecture, but broadens it by bringing in research from all areas of cognitive science, including how recent work in brain imaging maps onto the cogntive architecture.
Motivating Mathematics demonstrates that pupils can be motivated by being given the Big Picture, including a clearer picture of the nature of maths, and by linking topics to the sciences, rather than teaching each topic in isolation. The author emphasises the many virtues of problem-solving, strongly emphasised in secondary education specifications, especially the role of perception, and the ability of pupils to create their own proofs and to appreciate 'cool' ideas and arguments. David Wells draws on his extensive experience of teaching primary and secondary pupils and his understanding not just of how students think about mathematics, but of how they feel about a subject which so often seems merely a collection of facts and rules to be mastered. This book will be of immediate practical use to teachers and students at all levels. Anyone involved in mathematics education will benefit from reading this inspiring book, whether classroom teacher, trainer, teacher in training or professional development, or even parent. The book will also be of interest to policy makers and others with an investment in the future of mathematics education.