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.

 

 

This book is part of a book series called Studies in Mathematical Thinking And Learning .

There are 244 pages in this book. This book was published in 2005 by Taylor & Francis Inc .

Frank Frame and John Mason are co-authors of the HTP Higher and Standard Grade Computing titles, experienced examiners and Principal Teachers of Computing. Aaron Shepard and Anne L. Watson are a husband and wife writing team. Aaron is the award-winning author of many retellings of folktales and world classics for young readers. His books include The Legend of Lightning Larry and The Sea King's Daughter. Anne is a novelist. They live in Olympia, Washington. Aaron Shepard and Anne L. Watson are a husband and wife writing team. Aaron is the award-winning author of many retellings of folktales and world classics for young readers. His books include The Legend of Lightning Larry and The Sea King's Daughter. Anne is a novelist. They live in Olympia, Washington. When she was younger, Jennifer Tanner loved to draw humorous comics about dogs who went on spectacular adventures through time and space, meeting alien creatures along the way. She's never lost that love for telling stories with pictures. She attended the Savannah College of Srt and Design where she received her degree in Sequential Art. Today she spends her time illustrating many comic books.