This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school.
The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver.
The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole.
The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.
Автор: Karoline Afamasaga-Fuata`i Название: Concept Mapping in Mathematics ISBN: 1441947051 ISBN-13(EAN): 9781441947055 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This heavily-illustrated collection of research articles is the first comprehensive book on concept mapping in mathematics. It flows from a historical development overview into numerous applications and contains case studies and field-tested resources.
Автор: Haylock D & Cockburn A Название: Understanding Mathematics for Young Children: Fifth Edition ISBN: 1473953510 ISBN-13(EAN): 9781473953512 Издательство: Sage Publications Рейтинг: Цена: 35890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Essential guide for teaching children aged 3-7, developing knowledge of key mathematical ideas and concepts in the nursery and primary classroom.
Автор: Heid Mary Kathleen, Wilson Patricia S., Blume Glendon W. Название: Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations (Hc) ISBN: 168123114X ISBN-13(EAN): 9781681231143 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 104410.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level.The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice.Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.
Автор: Heid M. Kathleen, Wilson Patricia S., Blume Glendon W. Название: Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations ISBN: 1681231131 ISBN-13(EAN): 9781681231136 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 76690.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level.The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice.Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.
Автор: Claire Mooney, Alice Hansen, Lindsey Ferrie, Sue Fox, Reg Wrathmell Название: Primary Mathematics: Knowledge and Understanding ISBN: 1526440512 ISBN-13(EAN): 9781526440518 Издательство: Sage Publications Рейтинг: Цена: 71810.00 T Наличие на складе: Невозможна поставка. Описание: This highly recommended and well established text helps trainee primary teachers develop and consolidate their knowledge of mathematics.
Автор: Nathalie Sinclair, David Pimm, Melanie Skelin Название: Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 ISBN: 0873536924 ISBN-13(EAN): 9780873536929 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 36960.00 T Наличие на складе: Невозможна поставка. Описание: Focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students-and teachers.
Автор: Kristen Bieda, Eric Knuth, Amy Ellis Название: Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 ISBN: 0873536754 ISBN-13(EAN): 9780873536752 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 36960.00 T Наличие на складе: Невозможна поставка. Описание: What is the difference between “proof” in mathematics and “proof” in science or a court of law? In mathematics, how does proof differ from other types of arguments? What forms can proof take besides the traditional two-column style? What activities constitute the process of proving? What roles do examples play in proving? Can examples ever prove a conjecture? Why does a single counterexample refute a conjecture?How much do you know…and how much do you need to know?Helping your students develop a robust understanding of mathematical proof and proving requires that you understand this aspect of mathematics deeply. But what does that mean?This book focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students…and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic.Focus on the ideas that you need to understand thoroughly to teach confidently.
Автор: Nathalie Sinclair, David Pimm, Melanie Skelin Название: Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8 ISBN: 0873536916 ISBN-13(EAN): 9780873536912 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 36960.00 T Наличие на складе: Невозможна поставка. Описание: By exploring the other side of what is prescriptively understood as proper Asian gastronomy, Robert Ji-Song Ku suggests that Asian cultural expressions occurring in places such as Los Angeles, Honolulu, New York, and even Baton Rouge are no less critical to understanding the meaning of Asian food - and, by extension, Asian people - than culinary expressions that took place in Tokyo and Shanghai.
Автор: Mary Fiore, Ryan Tackaberry Название: Making Sense of Number, K-10: Getting to Know Your Students So You Can Support the Development of their Mathematical Understanding ISBN: 1551383322 ISBN-13(EAN): 9781551383323 Издательство: Taylor&Francis Рейтинг: Цена: 32650.00 T Наличие на складе: Невозможна поставка. Описание: Shows you how to get to know the needs and abilities of your students so you can help them make sense of maths concepts. You will discover how to structure learning experiences around key number concepts: quantity, counting, relating, and representing.
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