## Mathematics Education and the Legacy of Zoltan Paul DienesA Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana The name of Zoltan P. Dienes (1916-) stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the Multi-base blocks (also known as Dienes blocks) which he invented for the teaching of place value. He also is the inventor of Algebraic materials and logic blocks, which sowed the seeds of contemporary uses of manipulative materials in mathematics instruction. Dienes' place is unique in the field of mathematics education because of his theories on how mathematical structures can be taught from the early grades onwards using multiple embodiments through manipulatives, games, stories and dance. Dienes' notion of embodied knowledge presaged other cognitive scientists who eventually came to recognize the importance of embodied knowledge and situated cognition - where knowledge and abilities are organized around experience as much as they are organized around abstractions. Dienes was an early pioneer in what was later to be called sociocultural perspectives and democratization of learning. This monograph compiled and edited by Bharath Sriraman honors the seminal contributions of Dienes to mathematics education and includes several recent unpublished articles written by Dienes himself. These articles exemplify his principles of guided discovery learning and reveal the non-trivial mathematical structures that can be made accessible to any student. The monograph also includes a rare interview with Dienes in which he reflects on his life, his work, the role of context, language and technology in mathematics teaching and learning today. The book finds an important place in any mathematics education library and is vital reading for mathematics education researchers, cognitive scientists, prospective teachers, graduate students and teachers of mathematics. |

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### Contents

1 | |

Some Problems with Logic Blocks | 21 |

Logic Blocks to Other Embodiments | 37 |

Some Reflections on Order and Density A Childs Path to the Bolzano Weierstrass Theorem | 49 |

Games Leading to the Tetrahedron | 67 |

Cognitive Psychology and Mathematics Education Reflections on the Past and the Future | 95 |

The Impact of Zoltan Dienes on Mathematics Teaching in the United States | 107 |

### Other editions - View all

Mathematics Education and the Legacy of Zoltan Paul Dienes Zoltan Paul Dienes,Bharath Sriraman No preview available - 2008 |

### Common terms and phrases

2008 by Information aeeaee apple arrow Bharath big blue bird watching bite blue circle BOLZANO-WEIERSTRASS THEOREM car game chain of moves classroom Cognitive Psychology colour pair complex concepts constructivism daisy field Dick Bill Doerr ematics example factor Figure followed friend's house Gazi University increasing sequence Information Age Publishing interval Jean Piaget Jerome Bruner John seldom Laughing Legacy of Zoltan logic blocks Mary seldom math mathematics education meal means middle Modeling Perspective monotonic sequence multiple embodiments number of moves oak tree Piaget player point of accumulation position previous block problem Publishing All rights red circle red square rules score sentence sleeping Sriraman STAGE strength strong properties structures swap symbols teacher tetrahedron theory thick thin third block tion triangle turn University University of Montana vertex yellow circle Zoltan Dienes Zoltan Paul Dienes