Supporting Mathematical Thinking

Author: Anne Watson
Publisher: Routledge
ISBN: 1135395861
Format: PDF, ePub
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To what extent do curriculum subjects, particularly highly abstract ones such as Mathematics, have their own unique special needs? This book celebrates the work done by subject specialists in mainstream classrooms to promote inclusive practice. It describes new and creative ways of developing mathematical thinking among pupils. Each chapter demonstrates reflective minds at work, close observation of learners, willingness to understand the students’ thinking process and patient commitment to students over long periods of time. Features of the book include: how low-attaining students can think mathematically numeracy recovery task refusal in primary mathematics progression in written calculation strategies for division using graphic calculators with low-attaining pupils generalising arithmetic: an alternative to algebra learning support assistants in mathematics lessons inclusion and entitlement, equality of opportunity and quality of curriculum provision.

Key Ideas in Teaching Mathematics

Author: Anne Watson
Publisher: OUP Oxford
ISBN: 0191643416
Format: PDF, ePub, Mobi
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Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers, researchers and mathematics educators, and many teachers and researchers have been involved in the thinking behind this book, funded by the Nuffield Foundation. An associated website, hosted by the Nuffield Foundation, summarises the key messages in the book and connects them to examples of classroom tasks that address important learning issues about particular mathematical ideas.

Raising Achievement In Secondary Mathematics

Author: Watson, Anne
Publisher: McGraw-Hill Education (UK)
ISBN: 0335218601
Format: PDF, ePub, Mobi
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A guide to teaching lower attaining students in secondary mathematics offers an alternative view of attainment and capability, arguing that teaching should be based on a learner's proficiency, rather than on knowledge deficits.

Mathematics as a Constructive Activity

Author: Anne Watson
Publisher: Routledge
ISBN: 1135630011
Format: PDF, ePub, Mobi
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This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers, if the responsibility for making examples is transferred to learners, their knowledge structures can be developed and extended. A multitude of examples to illustrate this is provided, spanning primary, secondary, and college levels. Readers are invited to learn from their own past experience augmented by tasks provided in the book, and are given direct experience of constructing examples through a collection of many tasks at many levels. Classroom stories show the practicalities of introducing such shifts in mathematics education. The authors examine how their approach relates to improving the learning of mathematics and raise future research questions. *Based on the authors' and others' theoretical and practical experience, the book includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding. *The ideas presented are generic in nature and thus applicable across every phase of mathematics teaching and learning. *Although the teaching methods offered are ones that engage learners imaginatively, these are also applied to traditional approaches to mathematics education; all tasks offered in the book are within conventional mathematics curriculum content. Mathematics as a Constructive Activity: Learners Generating Examples is intended for mathematics teacher educators, mathematics teachers, curriculum developers, task and test designers, and classroom researchers, and for use as a text in graduate-level mathematics education courses.

New Directions for Situated Cognition in Mathematics Education

Author: Anne Watson
Publisher: Springer Science & Business Media
ISBN: 0387715770
Format: PDF, ePub, Mobi
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This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. No other books are available which take this view specifically in mathematics education. Thus it provides an up-to-date overview of developments and applications to which other researchers can refer and which will inspire future research.

Task Design In Mathematics Education

Author: Anne Watson
Publisher: Springer
ISBN: 331909629X
Format: PDF, ePub, Docs
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This book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.

Making the Connection

Author: Marilyn Paula Carlson
Publisher: MAA
ISBN: 9780883851838
Format: PDF, ePub, Mobi
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The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.

Thinkers

Author: Chris Bills
Publisher:
ISBN: 9781898611264
Format: PDF
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"Thinkers is a collection of activities to provoke matheatical thinking. ... The book contains sixteen different contexts for exemplifying the general and generalisong the partiucular which are processes at the heart of 'doing mathematics'. There are examples of the way in which teachers can use the techniques for any topic in mathematics."--Back cover.