what does understanding mathematics mean for teachers

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What Does Understanding Mathematics Mean For Teachers

Author : Yuichi Handa
ISBN : 9781136870521
Genre : Education
File Size : 45. 33 MB
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This book opens up alternative ways of thinking and talking about ways in which a person can "know" a subject (in this case, mathematics), leading to a reconsideration of what it may mean to be a teacher of that subject. In a number of European languages, a distinction is made in ways of knowing that in the English language is collapsed into the singular word know. In French, for example, to know in the savoir sense is to know things, facts, names, how and why things work, and so on, whereas to know in the connaître sense is to know a person, a place, or even a thing—namely, an other— in such a way that one is familiar with, or in relationship with this other. Primarily through phenomenological reflection with a touch of empirical input, this book fleshes out an image for what a person’s connaître knowing of mathematics might mean, turning to mathematics teachers and teacher educators to help clarify this image.

Primary Mathematics Teaching For Understanding

Author : Barmby, Patrick
ISBN : 9780335229260
Genre : Education
File Size : 47. 89 MB
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This book addresses the particular areas of mathematics within the primary curriculum that teachers find difficult to teach and in which children struggle to achieve.. .It begins with introductory sections on how children learn mathematics and is then organised on a subject area basis, dealing with the teaching of particular maths topics. Key topics addressed include rounding and measuring, means and medians, fractions, negative numbers, commutative and associative laws in number operations, and shape and space. .Within each chapter, the authors examine the themes of representing, reasoning and communicating, drawing out both the subject knowledge and ways of teaching each topic. A reference section for studies drawn upon is provided at the end of each chapter.....

Forms Of Mathematical Knowledge

Author : Dina Tirosh
ISBN : 9789401715843
Genre : Education
File Size : 51. 84 MB
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What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.

Becoming A Primary Mathematics Specialist Teacher

Author : Gina Donaldson
ISBN : 9780415604345
Genre : EDUCATION
File Size : 23. 69 MB
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"Becoming a Primary Mathematics Specialist Teacher challenges teachers to think about the role and impact of the Mathematics Specialist in changing staff, parents and children's attitudes to the subject in the primary school. It explores what we really mean by deep mathematical subject knowledge, explains key pedagogical approaches to teaching mathematics, and demonstrates how you can effectively mentor less experienced or confident colleagues to improve teaching and learning. Illustrated throughout with classroom-based examples, research findings and theoretical ideas, this book considers a wide range of issues including the use and application of mathematics, the utilisation of practical resources, and the principles of progression. It also considers some common misconceptions in mathematics, and offers scenarios and reflection activities at the end of each chapter. This supportive text is centred around three key themes of deep subject knowledge, pedagogical knowledge and the skills required for mentoring, coaching and supporting colleagues - features which the authors explore first from a theoretical perspective, and secondly through the context of specific mathematical topics taken from the primary curriculum. Becoming a Primary Mathematics Specialist Teacher supports primary mathematics teachers in their development as reflective practitioners, who can confidently challenge practice in their own classroom and move the whole school forward through collaborative professional development"--

Teaching Mathematics In Secondary Schools

Author : Linda Haggarty
ISBN : 0415260698
Genre : Education
File Size : 56. 94 MB
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A companion to Aspects of Teaching Secondary Mathematics, this book introduces and explores the contemporary issues and key ideas entailed in the teaching and learning of this subject. This book is concerned with exploring the bigger picture of mathematics education, and is aimed particularly at those learning to teach mathematics; teachers in the classroom who want to continue thinking and developing as mathematics teachers; and those concerned with education who would like to be better informed about mathematics education. Divided into seven sections to help structure reading, this book offers a completely up-to-date, comprehensive overview, written by the most-known, well-respected experts in the field.

Wie Kleine Kinder Schlau Werden

Author : John Caldwell Holt
ISBN : 3407228554
Genre :
File Size : 47. 80 MB
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Ausgehend von der Beobachtung des kindlichen Spielens erläutert der Autor, wie Kinder denken und lernen.

Tasks In Primary Mathematics Teacher Education

Author : Barbara Clarke
ISBN : 9780387096681
Genre : Education
File Size : 54. 20 MB
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Tasks in Primary Mathematics Teacher Education is intended to advance relevant research and innovative international practices in the preparation and professional development of mathematics teachers. Emerging from discussion at the ICMI study on teacher professional development, this volume, focused on primary and elementary teachers, culls a richness that can only be found by gathering wisdom from varied experiences around the world. The choice of tasks, and the associated pedagogies, is a key aspect of teaching and learning mathematics. Arguing that what students learn is largely defined by the tasks they are given, several major themes are presented. One such major strand, the form, function and focus of tasks, is discussed throughout several chapters, offering analysis, discussion of implementation, and exemplars of a broader category of illustrative techniques for developing critical understanding.

The Mathematics Teacher In The Digital Era

Author : Alison Clark-Wilson
ISBN : 9789400746381
Genre : Education
File Size : 78. 87 MB
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This volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts. In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity. This is followed by three main sections: An overview of current practices in teachers’ use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiner’s zone theory). A set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues. Meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements

Developing Essential Understanding Of Mathematical Reasoning For Teaching Mathematics In Prekindergarten Grade 8

Author : John K. Lannin
ISBN : 0873536665
Genre : Effective teaching
File Size : 71. 10 MB
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How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organised around one big idea, supported by multiple smaller, interconnected ideas - essential understandings.Taking you beyond a simple introduction to mathematical reasoning, 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.

Strategies For Teaching Mathematics

Author :
ISBN : 9781425893224
Genre : Mathematics
File Size : 31. 46 MB
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Enhance mathematics instruction and build students' understanding of mathematical concepts with this exceptional resource notebook. Choose from a wide range of easy-to-implement strategies that enhance mathematical content. Topics include developing students' mathematical vocabulary and problem-solving abilities, assessing students' mathematics thinking, and using manipulatives. Highlights include tips on planning instruction and managing the mathematics classroom, plus differentiation strategies for each lesson. Includes Teacher Resource CD with reproducibles including rubrics and assessment.

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