The Mathematical Experience Book Pdf
The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it.
Author: Philip Davis
Publisher: Springer Science & Business Media
ISBN: 9780817682941
Category: Mathematics
Page: 500
View: 931
Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
Author: Philip J. Davis
Publisher:
ISBN: 0710803648
Category: Mathematics
Page: 440
View: 600
"This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent from the experience of most college and university students (as well as their teachers). This new edition provides an excellent initiation of students into some of the more challenging aspects of mathematics The study edition of The Mathematical Experience will help its readers acquire a real understanding of mathematics." -Notices of the AMS "Two distinguished mathematicians...have written a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." --The New Yorker (1984 American Book Award Edition)
While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms.
Author: Leslie P. Steffe
Publisher: Springer Science & Business Media
ISBN: 9781461231783
Category: Psychology
Page: 312
View: 722
On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.
It is a wealth of experience with ideas that WORK, gained through live classroom interaction by the authors and shared in this book with the reader.
Author: Philip J. Davis
Publisher: Birkhauser
ISBN: 3764338490
Category: Mathematics
Page: 120
View: 188
The Companion Guide to The Mathematical Experience, Study Edition has been created as a teaching tool, not only for the teacher and the student, but also for those students who are potential teachers. Its major purpose is to enhance the value of The Mathematical Experience, Study Edition as a textbook for teachers and to provide content and method for prospective teachers. Thus, unlike instructional guides that are available to the adopting teacher only, this Companion is available to the student or the teacher who wants independently to develop further skills in teaching mathematics. An additional value is that it provides suggested topics to explore that are not in the text but that coordinate beautifully to the text. The inclusion of these topics makes The Companion Guide a flexible teaching tool, adaptable to a variety of courses and useable with many individual selections of other course materials.
Author: Davis
Publisher:
ISBN: OCLC:249227848
Category:
Page:
View: 171
Author: Mary Ann Haubner
Publisher: Houghton Mifflin College Division
ISBN: 0395494109
Category: Juvenile Nonfiction
Page: 556
View: 998
Author:
Publisher: Steck-Vaughn
ISBN: 0395499240
Category: Mathematics
Page:
View: 231
So, mathematics seems to develop when imagined, or hypothetical activity is provoked. ... 4 Gordon (1978) in his paper 'Conflict and Liberation: Personal Aspects of the Mathematical Experience' suggests that the teacher should replace ...
Author: Alan Bishop
Publisher: Springer Science & Business Media
ISBN: 0792312708
Category: Education
Page: 196
View: 422
Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Its reputation is awe-inspiring. Everybody knows how important it is and everybody knows that they have to study it. But few people feel comfortable with it; so much so that it is socially quite acceptable in many countries to confess ignorance about it, to brag about one's incompe tence at doing it, and even to claim that one is mathophobic! So are teachers around the world being apparently legal sadists by inflicting mental pain on their charges? Or is it that their pupils are all masochists, enjoying the thrill of self-inflicted mental torture? More seriously, do we really know what the reasons are for the mathematical activity which goes on in schools? Do we really have confidence in our criteria for judging what's important and what isn't? Do we really know what we should be doing? These basic questions become even more important when considered in the context of two growing problem areas. The first is a concern felt in many countries about the direction which mathematics education should take in the face of the increasing presence of computers and calculator-related technol ogy in society.
Davis , Philip J. and Hersh , Reuben . 1980. The Mathematical Experience . Boston , MA : Birkhauser . Dehaene , Sanislas . 1997. The Number Sense : How the Mind Creates Mathematics . New York , NY : Oxford University Press .
Author:
Publisher:
ISBN: UIUC:30112041261071
Category: Government publications
Page: 78
View: 325
Inverting is the mathematical term for undoing, and you've probably come across it in your past mathematical experience when computing the inverse of a function. The procedure for finding the inverse of a function is often described as ...
Author: Nathan Carter
Publisher: American Mathematical Soc.
ISBN: 9781614441229
Category: Mathematics
Page: 462
View: 780
This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.
In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world.
Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN: 0195113683
Category: Mathematics
Page: 368
View: 113
Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism.Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political ramifications.Written by the co-author of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirty-five years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science.
Furthermore, and because there exists an inexhaustible list of such problems, it was easy to plan such problems into students' mathematical experience. Publications that form part of such a list can easily be found in catalogues ...
Author: Mike Ollerton
Publisher: A&C Black
ISBN: 9781847060112
Category: Education
Page: 176
View: 938
A comprehensive handbook for mathematics teachers with practical advice on all aspects of the maths curriculum including developing an effective classroom culture, assessment and progressing mathematical concept development.
Focusing on the episte- mology of mathematics, I will contrast this feature with two striking aspects of mathematical experience implicit in repeated remarks of Kurt Godel. The first, the conceptional aspect, is connected to the notion ...
Author: Alexander George
Publisher: Oxford University Press on Demand
ISBN: 9780195079296
Category: History
Page: 204
View: 821
The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.
This book is a biography of one of the most famous and influential living mathematicians, Peter Lax.
Author: Reuben Hersh
Publisher: American Mathematical Soc.
ISBN: 9781470417086
Category: Mathematics
Page: 253
View: 722
This book is a biography of one of the most famous and influential living mathematicians, Peter Lax. He is virtually unique as a preeminent leader in both pure and applied mathematics, fields which are often seen as competing and incompatible. Although he has been an academic for all of his adult life, his biography is not without drama and tragedy. Lax and his family barely escaped to the U.S. from Budapest before the Holocaust descended. He was one of the youngest scientists to work on the Manhattan Project. He played a leading role in coping with the infamous "kidnapping" of the NYU mathematics department's computer, in 1970. The list of topics in which Lax made fundamental and long-lasting contributions is remarkable: scattering theory, solitons, shock waves, and even classical analysis, to name a few. His work has been honored many times, including the Abel Prize in 2005. The book concludes with an account of his most important mathematical contributions, made accessible without heavy prerequisites. Reuben Hersh has written extensively on mathematics. 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.
Years of Teaching MKT Score Teacher School Experience Percentage Level of Practice Scott Baltic Elementary 0—5 83% Mid Lily ... While his elementary and middle school mathematics experiences led Scott to believe he was above average, ...
Author:
Publisher: Stanford University
ISBN: STANFORD:ck171qs7892
Category:
Page:
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Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.
This volume provides a necessary, current and extensive analysis of probabilistic thinking from a number of mathematicians, mathematics educators, and psychologists.
Author: Egan J. Chernoff
Publisher: Springer Science & Business Media
ISBN: 9789400771550
Category: Education
Page: 747
View: 333
This volume provides a necessary, current and extensive analysis of probabilistic thinking from a number of mathematicians, mathematics educators, and psychologists. The work of 58 contributing authors, investigating probabilistic thinking across the globe, is encapsulated in 6 prefaces, 29 chapters and 6 commentaries. Ultimately, the four main perspectives presented in this volume (Mathematics and Philosophy, Psychology, Stochastics and Mathematics Education) are designed to represent probabilistic thinking in a greater context.
Author: Mary Ann Haubner
Publisher: Houghton Mifflin
ISBN: 0395494095
Category: Arithmetic
Page: 521
View: 116
If this reflection about your own experiences and aspirations for your future makes you feel that an impossible task lies ahead of you, do not worry as it is not impossible. An increasing awareness of what your mathematical perceptions ...
Author: Elizabeth Jackson
Publisher: SAGE
ISBN: 9781473934054
Category: Education
Page: 224
View: 425
'This original book shows the crucial importance of personal philosophies of mathematics. Using current research it guides us to reflect on our attitudes and beliefs. Essential reading for anybody interested in mathematics and its teaching.' Paul Ernest, Emeritus Professor of Mathematics Education, University of Exeter Teaching mathematics can be challenging, and returning to a mathematics classroom yourself may not inspire you with confidence. This book can help you to become an assured teacher who can give young learners the high quality mathematics education that they deserve, by exploring the philosophy that lies behind good mathematics teaching and its application in the classroom. Throughout the book you are encouraged to put your own thoughts on mathematics learning and teaching under the microscope and examine your perceptions and understanding in order to develop as a critically reflective teacher, aware of potential challenges and what underpins effective mathematics teaching in primary schools. Coverage includes: · developing your own philosophy towards mathematics teaching · understanding links between confidence and learning · the importance of subject knowledge · common beliefs and attitudes among mathematics learners · how to develop your relationship with the subject. This is essential reading for all students studying primary mathematics on initial teacher education courses, including undergraduate (BEd, BA with QTS), postgraduate (PGCE, School Direct, SCITT, Teach First) and NQTs. Elizabeth Jackson has over thirty years' experience of mathematics education through primary and secondary school teaching, lecturing in initial teacher education and supervising mathematics Master's dissertations, as well as conducting research into mathematics and writing.
As Otte remarked , young teachers tend either to forget completely their post - school mathematical studies and try to connect their interpretation and treatment of the subject matter directly to their own school experience , or attempt ...
Author: Basic components of mathematics education for teachers
Publisher: Springer Science & Business Media
ISBN: 9027719292
Category: Education
Page: 371
View: 323
BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.
I8.6 THE TECHNOLOGICAL REVOLUTION AND ITS IMP ON MATHEMATI ATION THE COMPUTER AND MATHEMATICAL EXPERIENCE Andred A. disesso Massachusetts Institute of Technology Boston, Massachusetts "Mathematics arises from human experience.
Author: M. Zweng
Publisher: Springer Science & Business Media
ISBN: 9781468482232
Category: Mathematics
Page: 725
View: 474
Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.
The Mathematical Experience Book Pdf
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