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Mathematics as a Constructive Activity

Mathematics as a Constructive Activity
Author: Anne Watson
Publisher: Routledge
Total Pages: 407
Release: 2006-04-21
Genre: Education
ISBN: 1135630011
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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.

Mathematics as a Constructive Activity

Mathematics as a Constructive Activity
Author: Anne Watson
Publisher: Routledge
Total Pages: 221
Release: 2006-04-21
Genre: Education
ISBN: 113563002X
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Explains and demonstrates the role of examples in the teaching and learning of mathematics, and their place in mathematics generally at all levels. Includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding.

Constructing Knowledge for Teaching Secondary Mathematics

Constructing Knowledge for Teaching Secondary Mathematics
Author: Orit Zaslavsky
Publisher: Springer Science & Business Media
Total Pages: 321
Release: 2011-04-11
Genre: Education
ISBN: 0387098127
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Teacher education seeks to transform prospective and/or practicing teachers from neophyte possibly uncritical perspectives on teaching and learning to more knowledgeable, adaptable, analytic, insightful, observant, resourceful, reflective and confident professionals ready to address whatever challenges teaching secondary mathematics presents. This transformation occurs optimally through constructive engagement in tasks that foster knowledge for teaching secondary mathematics. Ideally such tasks provide a bridge between theory and practice, and challenge, surprise, disturb, confront, extend, or provoke examination of alternatives, drawn from the context of teaching. We define tasks as the problems or activities that, having been developed, evaluated and refined over time, are posed to teacher education participants. Such participants are expected to engage in these tasks collaboratively, energetically, and intellectually with an open mind and an orientation to future practice. The tasks might be similar to those used by classroom teachers (e.g., the analysis of a graphing problem) or idiosyncratic to teacher education (e.g., critique of videotaped practice). This edited volume includes chapters based around unifying themes of tasks used in secondary mathematics teacher education. These themes reflect goals for mathematics teacher education, and are closely related to various aspects of knowledge required for teaching secondary mathematics. They are not based on the conventional content topics of teacher education (e.g., decimals, grouping practices), but on broad goals such as adaptability, identifying similarities, productive disposition, overcoming barriers, micro simulations, choosing tools, and study of practice. This approach is innovative and appeals both to prominent authors and to our target audiences.

Designing and Using Mathematical Tasks

Designing and Using Mathematical Tasks
Author: John Mason
Publisher:
Total Pages: 164
Release: 2006
Genre: Education
ISBN:
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Does being able to "do" mathematics mean being competent at techniques and understanding how ideas and techniques fit together? By being given appropriate tasks, learners develop their powers to think mathematically and learn to appreciate how ideas fit together. (Education/Teaching)

Mathematical Knowledge in Teaching

Mathematical Knowledge in Teaching
Author: Tim Rowland
Publisher: Springer Science & Business Media
Total Pages: 300
Release: 2011-01-06
Genre: Education
ISBN: 904819766X
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The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.

Language in Mathematics

Language in Mathematics
Author: Jennie Bickmore-Brand
Publisher:
Total Pages: 136
Release: 1990
Genre: Language experience approach in education
ISBN:
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There is a movement across Australia to pay a closer look at how mathematics can be integrated with the language arts philosophy and curriculum. Teachers are using literature to teach mathematical concepts, and modelling mathematical processing on process writing techniques. However, some fear that these activities could have the effect of trivialising mathematics. This book collates the writings of the major voices in the field of language and mathematics teaching. These writers warn of the dangers of both the traditional approach to teaching mathematics, and of current trends, and seek to offer constructive ways to maximise the contribution that language can make in generating, comprehending and expressing mathematical ideas and mathematical knowledge.

Constructing Mathematical Knowledge

Constructing Mathematical Knowledge
Author: Paul Ernest
Publisher: Routledge
Total Pages: 296
Release: 2012-10-12
Genre: Education
ISBN: 113636479X
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First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.

Transforming Primary Mathematics

Transforming Primary Mathematics
Author: Mike Askew
Publisher: Routledge
Total Pages: 243
Release: 2015-11-19
Genre: Education
ISBN: 1317357558
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Fully updated to reflect the new curriculum, the revised edition of Transforming Primary Mathematics sets out key theories and cutting-edge research in the field to enable teachers to take a fresh look at how they teach mathematics. The book encourages teachers to reflect on their own beliefs and values about mathematics, and asks them to question whether their current methods meet the needs of all learners, and the challenge of having high expectations for all. It provides clear, practical approaches to help implement fundamental change in classroom environments, and offers motivational teaching styles to ensure meaningful mathematics learning. Chapters take an inspiring, sometimes controversial, and often unconventional look at the subject of mathematics, by: endorsing the use of a ‘new mathematics’ – one based on problem solving, modelling, inquiry and reasoning, not on abstract rules, memorising, and regurgitation arguing that there is more to maths teaching than ‘death by a thousand worksheets’ challenging norms, such as the practice of sorting children into sets based on their perceived mathematical ability asking whether mathematical ability is innate or a result of social practices examining what a ‘mastery’ approach might entail highlighting the role of variation in supporting learning advocating an environment where teachers are encouraged to take risks. Transforming Primary Mathematics is for all primary school teachers who want to make mathematics welcoming, engaging, inclusive and successful.