Structural understanding in advanced mathematical thinking
Author : Naďa Stehlíková
Publisher : Nada Stehlikova
Page : 251 pages
File Size : 47,12 MB
Release : 2004
Category :
ISBN : 8072901729
Author : Naďa Stehlíková
Publisher : Nada Stehlikova
Page : 251 pages
File Size : 47,12 MB
Release : 2004
Category :
ISBN : 8072901729
Author : David Tall
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 42,68 MB
Release : 2006-04-11
Category : Education
ISBN : 0306472031
This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.
Author : Werner Blum
Publisher : Springer
Page : 215 pages
File Size : 48,10 MB
Release : 2019-02-18
Category : Education
ISBN : 3030055140
This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.
Author : Annie Selden
Publisher : Routledge
Page : 76 pages
File Size : 14,99 MB
Release : 2013-10-15
Category : Education
ISBN : 1135478384
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
Author : YOUSEF METHKAL ABD ALGANI
Publisher : Book Rivers
Page : 180 pages
File Size : 46,64 MB
Release : 2022-03-06
Category : Antiques & Collectibles
ISBN : 9355151632
Author : Dina Tirosh
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 23,25 MB
Release : 2013-03-14
Category : Education
ISBN : 940171584X
What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.
Author : Francis Su
Publisher : Yale University Press
Page : 287 pages
File Size : 48,56 MB
Release : 2020-01-07
Category : Mathematics
ISBN : 0300237138
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.
Author : Yusof, Khairiyah Mohd
Publisher : IGI Global
Page : 442 pages
File Size : 14,24 MB
Release : 2012-06-30
Category : Education
ISBN : 1466618108
"This book provides insights into initiatives that enhance student learning and contribute to improving the quality of undergraduate STEM education"--Provided by publisher.
Author : Keith J. Devlin
Publisher :
Page : 0 pages
File Size : 10,73 MB
Release : 2012
Category : Mathematics
ISBN : 9780615653631
"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
Author : James T. Kinard
Publisher : Cambridge University Press
Page : 210 pages
File Size : 42,41 MB
Release : 2008-06-02
Category : Psychology
ISBN : 1139472399
This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.