More than 75 motivational problem-solving activities explore geometry in the natural and human worlds: counting, area, construction, congruence, visualization, symmetry, tiling, and dissection. These versatile problems introduce new topics, reinforce and review ideas, or simply serve as a change of pace. Blackline masters and answer key.
Mission Statement: The book series, entitled Research in Curriculum and Instruction, will focus on a) considerations of curriculum practices at school, district, state, and federal levels, b) relationship of curriculum practices to curriculum theories and societal issues, c) concerns derived from curriculum policy analyses and from analyses of various curriculum advocacies, and d) insights derived from investigations into curriculum history. Although the series will emphasize the American curriculum scene, aspects of curriculum practice and theory embedded in non-US countries will not be overlooked. Furthermore, this series will not restrict its concern to general curriculum matters, but it will draw explicit attention to curriculum issues relating to the several curriculum subjects. The series' primary concern will be to illuminate practice and issues toward informed and improved curriculum practice. This volume will contain selected papers presented at meetings of the Society for the Study of curriculum History across the past decade plus several specially commissioned papers from senior scholars in the field. Professor Field was the Society's President for some time during that period. Papers will treat dimensions of the development of the American school curriculum, both elementary and secondary.
'What one takes away from this book is the notion that there’s a lot of potential to do more with these students, and the book stands as a resource for anyone who shares that opinion … Books like Abramovich’s are a welcome addition to our options as we try to do our best by these students, and by extension, their future students.'MAA ReviewsThe book is written to enhance the preparation of elementary teacher candidates by offering teaching ideas conducive to the development of deep understanding of concepts fundamental to the mathematics curriculum they are to teach. It intends to show how the diversity of teaching methods stems from the knowledge of mathematics content and how the appreciation of this diversity opens a window to the teaching of extended content.The book includes material that the author would have shared with teacher candidates should there have been more instructional time than a 3 credit hour master's level course, 'Elementary Mathematics: Content and Methods', provides. Thus the book can supplement a basic textbook for such a course by extending content and diversifying methods.Also, the book can support graduate level mathematics education programs which have problem-solving seminars/courses in their curriculum. The book is well-informed with (available in English) the mathematical standards and recommendations for teachers from Australia, Canada, Chile, England, Japan, Korea, Singapore, and the United States.
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
Elementary School Mathematics: Teaching Developmentally, Second Edition, provides detailed, comprehensive coverage of the teaching of mathematics in grades K-8. Firmly grounded in the NCTM Standards, the text develops a constructivist/developmental approach to learning mathematics that focuses on the nature of mathematical concepts and the manner in which children construct mathematical ideas. It aims to help teachers reconceptualize mathematics as a problem-solving endeavor not as a mastery of rules and procedures. An accessible synthesis of viewpoints and current research, this highly praised text includes topics ranging from the development of basic fact mastery to the important development of "number sense"--All the while encouraging teachers to consider the construction of mathematics from the child's perspective. In-depth treatment of curriculum content teaching, combined with hundreds of teaching activities aimed at conceptual development, makes Elementary School Mathematics a practical teacher's resource as well as a college text. Elementary School Mathematics: Teaching Developmentally, Second Edition, features: greater emphasis on the NCTM Curriculum Standards and the Professional Teaching Standards as the leading forces in mathematics education; a new chapter on mathematics as a "science of pattern and order"; a completely rewritten chapter on alternative assessment; expanded and improved problem-solving examples; enhanced coverage of grades 7 and 8; even more black-line masters with directions for making other useful materials; and an Instructor's Manual with instructional suggestions, activities for group homework, practicum ideas, and essay questions.
The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.
