Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes downloadable resources with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.
In 'Making Kids Cleverer: A manifesto for closing the advantage gap', David Didau reignites the nature vs. nurture debate around intelligence and offers research-informed guidance on how teachers can help their students acquire a robust store of knowledge and skills that is both powerful and useful. Foreword by Paul A. Kirschner. Given the choice, who wouldn't want to be cleverer? What teacher wouldn't want this for their students, and what parent wouldn't wish it for their children? When David started researching this book, he thought the answers to the above were obvious. But it turns out that the very idea of measuring and increasing children's intelligence makes many people extremely uncomfortable: If some people were more intelligent, where would that leave those of us who weren't? The question of whether or not we can get cleverer is a crucial one. If you believe that intelligence is hereditary and environmental effects are trivial, you may be sceptical. But environment does matter, and it matters most for children from the most socially disadvantaged backgrounds those who not only have the most to gain, but who are also the ones most likely to gain from our efforts to make all kids cleverer. And one thing we can be fairly sure will raise children's intelligence is sending them to school. In this wide-ranging enquiry into psychology, sociology, philosophy and cognitive science, David argues that with greater access to culturally accumulated information taught explicitly within a knowledge-rich curriculum children are more likely to become cleverer, to think more critically and, subsequently, to live happier, healthier and more secure lives.;Furthermore, by sharing valuable insights into what children truly need to learn during their formative school years, he sets out the numerous practical ways in which policy makers and school leaders can make better choices about organising schools, and how teachers can communicate the knowledge that will make the most difference to young people as effectively and efficiently as possible. David underpins his discussion with an exploration of the evolutionary basis for learning and also untangles the forms of practice teachers should be engaging their students in to ensure that they are acquiring expertise, not just consolidating mistakes and misconceptions.There are so many competing suggestions as to how we should improve education that knowing how to act can seem an impossible challenge. Once you have absorbed the arguments in this book, however, David hopes you will find the simple question that he asks himself whenever he encounters new ideas and initiatives Will this make children cleverer? as useful as he does.;Suitable for teachers, school leaders, policy makers and anyone involved in educations
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