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THE MATH TEACHERS KNOW eBOOK PRT453 and in fields such asWhat sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledgethat is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the