Experiencing Mathematics

Experiencing Mathematics PDF
Author: Reuben Hersh
Publisher: American Mathematical Soc.
ISBN: 082189420X
Size: 21.60 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 282
View: 6881

Get Book

The question ``What am I doing?'' haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. --Yuri Manin, Max Planck Institute, Bonn, Germany What happens when mid-career a mathematician unexpectedly becomes philosophical? These lively and eloquent essays address the questions that arise from a crisis of reflectiveness: What is a mathematical proof and why does it come after, not before, mathematical revelation? Can mathematics be both real and a human artifact? Do mathematicians produce eternal truths, or are the judgments of the mathematical community quasi-empirical and historically framed? How can we be sure that an infinite series that seems to converge really does converge? This collection of essays by Reuben Hersh makes an important contribution. His lively and eloquent essays bring the reality of mathematical research to the page. He argues that the search for foundations is misleading, and that philosophers should shift from focusing narrowly on the deductive structure of proof, to tracing the broader forms of quasi-empirical reasoning that star the history of mathematics, as well as examining the nature of mathematical communities and how and why their collective judgments evolve from one generation to the next. If these questions keep you up at night, then you should read this book. And if they don't, then you should read this book anyway, because afterwards, they will! --Emily Grosholz, Department of Philosophy, Penn State, Pennsylvania, USA Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant ``analytic philosophy''. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis. Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science. Hersh is emeritus professor of mathematics at the University of New Mexico.

Experiencing School Mathematics

Experiencing School Mathematics PDF
Author: Jo Boaler
Publisher:
ISBN:
Size: 19.35 MB
Format: PDF, ePub, Docs
Category : Education
Languages : en
Pages : 163
View: 7352

Get Book

This is the first book of its kind to provide direct evidence for the effectiveness of traditional and progressive teaching methods. It reports on careful and extensive case studies of two schools which taught mathematics in totally different ways. Three hundred students were followed over three years and the interviews that are reproduced in the book give compelling insights into what it meant to be a student in the classrooms of the two schools. The different school approaches are compared and analyzed using student interviews, lesson observations, questionnaires given to students and staff and a range of different assessments, including GCSE examinations. Questions are raised about the effectiveness of different teaching methods in preparing students for the demands of the 'real world' and the 21st century, the impact of setted and mixed ability teaching upon student attitude and achievement, and gender and learning styles. New evidence is provided for each of these issues. The book draws some radical new conclusions about the ways that traditional teaching methods lead to limited forms of knowledge that are ineffective in non-school settings. The book will be essential reading for math teachers, parents, and policy makers in education.

Experiencing Mathematics

Experiencing Mathematics PDF
Author: R. James Breunlin
Publisher: R & L Education
ISBN:
Size: 38.16 MB
Format: PDF, Mobi
Category : Education
Languages : en
Pages : 184
View: 5961

Get Book

Experiencing Mathematics: Activities to Engage the High School Student is the result of the collaborative effort of nine Adolescent Young Adult (AYA) National Board Certified Teachers (NBCTs) in mathematics. This student edition is a compilation of successful activities that prompt high school students to explore, conjecture, and reflect on their mathematical adventures--thus "experience" mathematics. The relevant nature of the activities will motivate students to pursue their investigations with vigor and take the intellectual risk necessary to construct knowledge and improve problem-solving competence. This book provides student activities grouped in algebra, geometry, and algebra 2 sections that parallel the traditional sequencing in major texts. Through activity design, students are lead through an inductive inquiry in which they conjecture, formulate, and test ideas and concepts. This inductive student-centered approach to learning will not only excite students but also increase student effort.

Experiencing School Mathematics

Experiencing School Mathematics PDF
Author: Jo Boaler
Publisher: Routledge
ISBN: 0805840044
Size: 40.30 MB
Format: PDF, Mobi
Category : Education
Languages : en
Pages : 202
View: 185

Get Book

First edition published in 1997 by Open University Press as: Experiencing school mathematics: teaching styles, sex and setting.

Learning Directory

Learning Directory PDF
Author:
Publisher:
ISBN:
Size: 17.56 MB
Format: PDF, ePub, Mobi
Category : Teaching
Languages : en
Pages :
View: 7304

Get Book

The Mathematics Of Mathematics

The Mathematics of Mathematics PDF
Author: Wolff-Michael Roth
Publisher: Springer
ISBN: 9463009264
Size: 16.14 MB
Format: PDF, Docs
Category : Education
Languages : en
Pages : 10
View: 3254

Get Book

This book takes up where L. S. Vygotsky has left off during the last few months of his life, when he renounced much of what he had done before. A month before Vygotsky died, he wrote in his notebook that he felt like Moses who had seen the promised land but was never allowed to set foot on it. The vision Vygotsky laid out during his final days had been influenced by his readings of the Dutch philosopher Baruch Spinoza and a book by Karl Marx published for the first time a year before Vygotsky died. In the present book, the author lays out a view of mathematics based on a monist view of knowing, learning, and development. Just as the essence of what is specifically human, the mathematics of mathematics exists in the ensemble of societal relations. For the individual, this means that mathematical thinking and reasoning was a society-typical relation with another person first, often the teacher. Using data from a variety of situations, including school students as well as scientists, the book develops some fundamental concepts and categories for mathematics education research, including the thinking body, sociogenesis, the intra-intersubjective field, pereživanie (experience), obučenie (teaching | learning), and drama.