Mathematical Knowledge and the Interplay of Practices

Author: José Ferreirós

Publisher: Princeton University Press

ISBN: 1400874009

Category: Science

Page: 360

View: 4872

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

EPSA Philosophical Issues in the Sciences

Launch of the European Philosophy of Science Association

Author: Mauricio Suárez,Mauro Dorato,Miklós Rédei

Publisher: Springer Science & Business Media

ISBN: 9789048132522

Category: Science

Page: 332

View: 8267

This volume collects papers presented at the Founding Conference of the European Philosophy of Science Association meeting, held November 2007. It provides an excellent overview of the state of the art in philosophy of science in different European countries.

Refining the Mathematics Knowledge Base

The Relationship Between Knowledge, Practice, and Student Learning

Author: N.A

Publisher: Stanford University



Page: N.A

View: 1608

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.

Science after the Practice Turn in the Philosophy, History, and Social Studies of Science

Author: Léna Soler,Sjoerd Zwart,Michael Lynch,Vincent Israel-Jost

Publisher: Routledge

ISBN: 1317935365

Category: Philosophy

Page: 346

View: 8919

In the 1980s, philosophical, historical and social studies of science underwent a change which later evolved into a turn to practice. Analysts of science were asked to pay attention to scientific practices in meticulous detail and along multiple dimensions, including the material, social and psychological. Following this turn, the interest in scientific practices continued to increase and had an indelible influence in the various fields of science studies. No doubt, the practice turn changed our conceptions and approaches of science, but what did it really teach us? What does it mean to study scientific practices? What are the general lessons, implications, and new challenges? This volume explores questions about the practice turn using both case studies and theoretical analysis. The case studies examine empirical and mathematical sciences, including the engineering sciences. The volume promotes interactions between acknowledged experts from different, often thought of as conflicting, orientations. It presents contributions in conjunction with critical commentaries that put the theses and assumptions of the former in perspective. Overall, the book offers a unique and diverse range of perspectives on the meanings, methods, lessons, and challenges associated with the practice turn.

Culture and Cognitive Development

Studies in Mathematical Understanding

Author: Geoffrey B. Saxe

Publisher: Psychology Press

ISBN: 1317728084

Category: Psychology

Page: 222

View: 4601

Researchers examining children's mathematics acquisition are now questioning the belief that children learn mathematics principally through formalized, in-school mathematics education. There is increasing evidence that children gain mathematical understanding through their participation in out-of-school cultural practices and that their mathematics only occasionally resembles what they learn in the classroom. Culture and Cognitive Development presents the latest research by Dr. Geoffrey Saxe on this issue. In examinations of the mathematical understandings of child candy sellers in an urban center in northeastern Brazil, Dr. Saxe finds sharp contrasts between mathematics as practiced in school and in real-world settings. In this unique research project he presents a penetrating conceptual treatment of the interplay between culture and cognitive development, filling a void in current research literature. Subjects examined include: the interplay between sociocultural and cognitive developmental processes the differences between math knowledge learned in and out of the classroom the ways math learning in the classroom is modified by children's out-of-school mathematics and, correspondingly, how practical out-of-school mathematics use is modified by formal education

Becoming a Reflective Mathematics Teacher

A Guide for Observations and Self-assessment

Author: Alice F. Artzt,Eleanor Armour-Thomas,Frances R. Curcio

Publisher: Routledge

ISBN: 0805861939

Category: Education

Page: 234

View: 8699

"Supplies detailed observation instruments that preservice teachers can use when they observe other teachers; offers reflective activities that provide a structure through which beginning teachers can think about their teaching in an insightful, thorough, and productive manner; includes guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers"--Publisher description.

Evaluating Theory-Practice and Urban-Rural Interplay in Planning

Author: Dino Borri,Abdul Khakee,Cosimo Lacirignola

Publisher: Springer Science & Business Media

ISBN: 9401154627

Category: Technology & Engineering

Page: 245

View: 1322

This volume contains a selection of papers presented at the second workshop on Evaluation and Planning held at Centre International de Hautes Etudes Agronomiques Mediterraneennes (CIHEAM) in Valenzano (Bari) in November 1993. The workshop was financially and otherwise supported by the School of Engineering, Bari Polytechnic; the School of Agriculture, University of Bari; and CIHEAM. The publication of this book was made possible by to the efforts of the contributing authors. Several other persons have provided invaluable support for the workshop or the preparation of this volume. One of these is Patsy Healey for her fascinating challenge to Andreas Faludi's most recent arguments about rational planning theory. Another is John Friedmann whose lecture at the workshop presented world future scenarios depicting interaction between economic growth, social justice and ecological balance. Angela Barbanente provided marvelous support in organizing the workshop and editorial advice in the preparation of this volume. Jeremy Franks carefully improved the English and the clarity of all the papers. Carmelo Torre made a final editing of texts and images. We owe thanks to Maurizio Raeli for providing all the support services during the workshop and Claudia Baublys for her excellent help with various administrative issues with regard to the workshop and publication of this book. This book is dedicated to the memory of Professor Giovanni Grittani, Professor of Land Economics, University of Bari.

Handbook of Psychology, Educational Psychology

Author: Irving B. Weiner,William M. Reynolds,Gloria E. Miller

Publisher: John Wiley & Sons

ISBN: 1118281934

Category: Psychology

Page: 624

View: 7747

Psychology is of interest to academics from many fields, as well as to the thousands of academic and clinical psychologists and general public who can't help but be interested in learning more about why humans think and behave as they do. This award-winning twelve-volume reference covers every aspect of the ever-fascinating discipline of psychology and represents the most current knowledge in the field. This ten-year revision now covers discoveries based in neuroscience, clinical psychology's new interest in evidence-based practice and mindfulness, and new findings in social, developmental, and forensic psychology.

The Nature of Mathematical Thinking

Author: Robert J. Sternberg,Talia Ben-Zeev

Publisher: Routledge

ISBN: 1136487506

Category: Education

Page: 352

View: 9089

Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Conception and Characteristics of Expert Mathematics Teachers in China

Author: Xinrong Yang

Publisher: Springer Science & Business Media

ISBN: 3658030976

Category: Education

Page: 321

View: 1194

The superior performance of East Asian students in recent international studies of mathematics achievement has attracted the attention of educators and policy makers worldwide. Xinrong Yang focuses on exploring how an expert mathematics teacher is conceptualized by mathematics educators in China and the characteristics that expert mathematics teachers share. The author adopts a sociocultural theory and a prototypical view of conception in this study of teacher expertise and shows that some of the roles expected to be played by expert mathematics teachers in China, such as being at the same time a researcher, a mentor, an expert in examination, and an exemplary model, are quite different from the roles expected of an expert teacher in Western cultures. In addition, some characteristics of expert mathematics teachers the author identifies are different from those reported in previous studies. Examples include the expert mathematics teachers ́ contemporary-constructivist oriented beliefs about mathematics and its learning and teaching, and their ability to teach with flexibility, balance, and coherence.​

Modelling and Applications in Mathematics Education

The 14th ICMI Study

Author: Peter L. Galbraith,Hans-Wolfgang Henn,Mogens Niss

Publisher: Springer Science & Business Media

ISBN: 9780387298221

Category: Education

Page: 523

View: 2411

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

Researching Mathematics Education in South Africa

Perspectives, Practices and Possibilities

Author: Renuka Vithal,Jill Adler,Christine Keitel

Publisher: HSRC Press

ISBN: 9780796920478

Category: Education

Page: 360

View: 1649

Reflecting on the theoretical and ideological work that has contributed to the growth of mathematics education research in South Africa, this study provides a historical analysis of forces that have changed and shaped mathematics curricula over the years. The themes researched and explored include radical pedagogy, progressive classroom practices, ethnomathematics, and South African mathematics education research within both its local and international contexts.

Rethinking the Mathematics Curriculum

Author: Celia Hoyles,Candia Morgan,Geoffrey Woodhouse

Publisher: Routledge

ISBN: 1135701067

Category: Education

Page: 270

View: 2840

At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.

Perspectives on Mathematics Education

Papers Submitted by Members of the Bacomet Group

Author: H. Christiansen,A.G. Howson,M. Otte

Publisher: Springer Science & Business Media

ISBN: 9400945043

Category: Education

Page: 371

View: 2992

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.

Constructivism in Education

Author: Leslie P. Steffe,Jerry Gale

Publisher: Routledge

ISBN: 1136476083

Category: Education

Page: 600

View: 969

Unique in offering a multidisciplinary perspective on key issues of alternative epistemologies in education, this collection includes contributions from scholars in family therapy, epistemology, and mathematics, science, and language education. These respected researchers were brought together to develop the theme of constructivism as it applies to many diversified fields. This book examines key distinctions of various constructivist epistemologies, comparing and contrasting the various paradigms. Each section provides both keynote positions on a particular alternative paradigm as well as critical comments by respondents regarding that position. Several chapters also present a synthesis of the alternative epistemological perspectives.

Computer Aided Assessment of Mathematics

Author: Chris Sangwin

Publisher: OUP Oxford

ISBN: 0191635863

Category: Mathematics

Page: 200

View: 6600

Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.

Teaching Mathematics in the Secondary School

Author: Paul Chambers,Robert Timlin

Publisher: SAGE

ISBN: 1446290956

Category: Education

Page: 296

View: 5125

'Chambers and Timlin write with clarity and purpose. The authors link the theory of teaching mathematics with simple reflective questions and interesting maths tasks. There is practical advice on planning, assessment and differentiations, amongst other pertinent themes' -Jacqueline Oldham, PGCE Secondary Mathematics Course Tutor, St Mary's University College 'This is a very practical guide for learning to teach mathematics for student teachers on all training routes. Chapters are focused and readable but succeed in tackling issues in depth giving the reader strong academic support' -Anne Haworth, PGCE Secondary Mathematics Course Tutor, University of Manchester This book is an essential companion for anyone training to teach mathematics in secondary education. It offers clear and engaging coverage of all major aspects of mathematics teaching that you will need to engage with in order to successfully train for the classroom. This Second Edition includes: a new chapter exploring different teaching approaches including active learning, effective group work and creative mathematics teaching expanded coverage of assessment, using resources in the classroom and metacognition and learning updated coverage of recent developments in education policy and the 2012 Teachers' Standards This is essential reading for anyone training to teach secondary mathematics including postgraduate (PGCE, SCITT) and school-based routes into teaching. Free digital resources for extra support is available in the book's companion website. It includes: Web links and further reading for each chapter A video series of a sample classroom lesson filmed in a real-life setting Visit

A Research Companion to Principles and Standards for School Mathematics

Author: Jeremy Kilpatrick,W. Gary Martin,Deborah Schifter,National Council of Teachers of Mathematics

Publisher: National Council of Teachers of English

ISBN: 9780873535373

Category: Mathematics

Page: 413

View: 4991

Provides the anchoring of research and theory for Principles and Standards for School Mathematics, containing research relevant to topics covered in the publication. Supplies a comprehensive analysis of what research should be expected to do in setting standards for school mathematics. Focuses on research derived from professional development of teachers, mathematics assessment, and literature on curriculum topics, among others.

Windows on Mathematical Meanings

Learning Cultures and Computers

Author: Richard Noss,Celia Hoyles

Publisher: Springer Science & Business Media

ISBN: 9400916965

Category: Education

Page: 278

View: 702

This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.