This is a book about an attempt to change the way math was taught in a particular classroom. Its title plays on our everyday usage of the terms theory and practice. In education, these terms are conventionally treated oppositionallywe have theories about what we should do and we have what teachers actually do do. In this way, theory stands prior, logically and chronologically, to practice; practice inevitably becoming theorys imperfect realization. We seek in this volume, however, to develop a different stance with regard to the relationship between the two. Taking the details of instructional practice as our principle object of study, we explore what role theories of learning might play in illuminating such practices. The book is about actual practices by which teaching is done and how contemporary theories of learning might help us understand those practices. It seeks to provide a foundation for future practice-based inquiry in education, by addressing the methodological question: How do we go about studying instructional practice in a principled way?

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