Social Constructivism as a Philosophy of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Social Constructivism as a Philosophy of Mathematics write by Paul Ernest. This book was released on 1998-01-01. Social Constructivism as a Philosophy of Mathematics available in PDF, EPUB and Kindle. Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
The Philosophy of Mathematics Education
The Philosophy of Mathematics Education - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Philosophy of Mathematics Education write by Paul Ernest. This book was released on 2016-07-15. The Philosophy of Mathematics Education available in PDF, EPUB and Kindle. This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.
Constructivism in Mathematics, Vol 1
Constructivism in Mathematics, Vol 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Constructivism in Mathematics, Vol 1 write by A.S. Troelstra. This book was released on 1988-07-15. Constructivism in Mathematics, Vol 1 available in PDF, EPUB and Kindle. These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy
Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy write by David Sepkoski. This book was released on 2013-05-24. Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy available in PDF, EPUB and Kindle. What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the philosophical community in the seventeenth century? In answering this question, this book demonstrates that a significant group of philosophers shared the belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of mathematical and linguistic discourse. The result is a scholarly reliable, but accessible, account of the role of mathematics in the works of (amongst others) Galileo, Kepler, Descartes, Newton, Leibniz, and Berkeley. This impressive volume will benefit scholars interested in the history of philosophy, mathematical philosophy and the history of mathematics.
Radical Constructivism in Mathematics Education
Radical Constructivism in Mathematics Education - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Radical Constructivism in Mathematics Education write by E. Glasersfeld. This book was released on 2006-04-11. Radical Constructivism in Mathematics Education available in PDF, EPUB and Kindle. Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.
