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We hear all the time how American children are falling behind their global peers in various basic subjects, but particularly in math. Is it our fear of math that constrains us? Or our inability to understand math’s place in relation to our everyday lives? How can we help our children better understand the basics of arithmetic if we’re not really sure we understand them ourselves? Here, G. Arnell Williams helps parents and teachers explore the world of math that their elementary school children are learning. Taking readers on a tour of the history of arithmetic, and its growth into the subject we know it to be today, Williams explores the beauty and relevance of mathematics by focusing on the great conceptual depth and genius already inherent in the elementary mathematics familiar to us all, and by connecting it to other well-known areas such as language and the conceptual aspects of everyday life. The result is a book that will help you to better explain mathematics to your children. For those already well versed in these areas, the book offers a tour of the great conceptual and historical facts and assumptions that most simply take for granted. If you are someone who has always struggled with mathematics either because you couldn’t do it or because you never really understood why the rules are the way they are, if you were irritated with the way it was taught to you with the emphasis being only on learning the rules and “recipes” by rote as opposed to obtaining a good conceptual understanding, then How Math Works is for you!
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.
This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.
Discover how math applies to science, art, music, daily life, and moreApply what you’re learning outside a textbook, and see God’s handiwork in mathFocus is on multiplication, division, fractions, decimals, ratios, percentages, shapes, basic geometry, and more! Math is a real-life tool that points us to God and helps us explore His creation, yet it often comes across as dry facts and meaningless rules. Here at last is a curriculum that has a biblical worldview integrated throughout the text and problems, not just added as an afterthought. Students don’t just learn how to manipulate numbers on paper, but starting with arithmetic and laying the groundwork for geometry and algebra (covered in year 2), this curriculum both firms up the foundational concepts and prepares students for upper-level math in a logical, step-by-step way that helps students understand concepts, build problem-solving skills, and see how different aspects of math connect.
A co-publication of the AMS and the Mathematical Sciences Research Institute. This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K–8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.--Publisher website.
