Results 1  10
of
16
Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education
 Educational Studies in Mathematics
, 1999
"... ABSTRACT. This paper suggests that from a cognitiveevolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cogniti ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
(Show Context)
ABSTRACT. This paper suggests that from a cognitiveevolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical. This progression was driven by three cognitive advances: the ability to “represent ” events, the development of symbolic reference, and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture: a “virtual ” culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills.
An introduction to the profound potential of connected algebra activities: Issues of representation, engagement and pedagogy. Paper presented at the
 28th Conference of the International Group for the Psychology of Mathematics Education
, 2004
"... ..."
Using Lego construction to develop ratio understanding
 In
, 2004
"... This paper examines Year 7 students use and learning of ratio concepts while engaged in the technology practice of designing, constructing and evaluating simple machines, that used cogs and pulleys. It was found that most students made considerable progress in accounting for ratio concepts in their ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
This paper examines Year 7 students use and learning of ratio concepts while engaged in the technology practice of designing, constructing and evaluating simple machines, that used cogs and pulleys. It was found that most students made considerable progress in accounting for ratio concepts in their constructions and some constructed sophisticated machines and provided explicit and quantitative descriptions involving ratio reasoning. The findings have implications for the study of mathematics in integrated and contextual settings. One of the critical questions facing mathematics education today relates to learning contexts. In particular what kinds of mathematical tools and representations are needed to promote mathematical learning and how these tools should be used (English, 2002). New technologies are giving rise to major changes in mathematics education. There are now numerous opportunities for students and teachers to engage in mathematical experiences that were scarcely contemplated a decade ago. However, the effective use of new technologies neither happens automatically, nor will the use of technology lead to improvements in mathematics learning without changes to the curriculum (Niss, 1999).
Three LargeScale Studies
 Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics
, 2010
"... means, without permission of the author. ..."
(Show Context)
Why all CSL is CL: Distributed mind and the future of computer supported collaborative learning
, 2005
"... In this paper, we argue that this distinction between CSCL and HCI is based on a particular understanding of the relationship between humans and computers—and more generally between humans and their tools in activity systems. We draw on work by Shaffer and Kaput (1999), Clark (2003), and Latour (1 ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we argue that this distinction between CSCL and HCI is based on a particular understanding of the relationship between humans and computers—and more generally between humans and their tools in activity systems. We draw on work by Shaffer and Kaput (1999), Clark (2003), and Latour (1996a; 1996b; 1996c) to conduct a thought experiment, extending the analytical reach of activity theory (Nardi, 1996b), mediated action (Wertsch, 1998) and distributed cognition (Pea, 1993) by adopting a stronger form of the concepts of distribution and mediation in the context of cognitive activity. For rhetorical purposes, we posit this stronger form of the distribution of intelligence across persons and objects as a theory of distributed mind. Our purpose in describing a theory of distributed mind as an extension of (but not replacement for) extant sociocultural theories on this 10 th anniversary of the International Conference on Computer Supported Collaborative Learning is to problematize for the field its current focus on human collaboration as supported by computers. We are concerned that a field focusing on the interactions of humans will overlook the ways in which meaningful cognitive (and therefore pedagogical) activity is distributed among human and nonhuman agents within activity systems. We argue that all computersupported learning is fundamentally collaborative—whether or not the computer is supporting the interaction of persons in the learning process. The consequences of such a move are a call for a tighter integration of the fields of CSCL and HCI, and a more powerful framework to help guide pedagogical choices in an age marked by rapid expansion of powerful cognitive technologies.
1 CHAPTER 32 MOVING FORWARD IN INTERNATIONAL MATHEMATICS EDUCATION RESEARCH
"... The need is as pressing as ever for a shared, scientific, nonideological framework for empirical and theoretical research in mathematical learning and problem solving (Goldin, chapter 9, p. XX). This final chapter revisits some of the key issues addressed by the authors and explores a selection of ..."
Abstract
 Add to MetaCart
(Show Context)
The need is as pressing as ever for a shared, scientific, nonideological framework for empirical and theoretical research in mathematical learning and problem solving (Goldin, chapter 9, p. XX). This final chapter revisits some of the key issues addressed by the authors and explores a selection of the many research issues that need attention in the advancement of our discipline. Specifically, we give consideration to the following questions: 1. What role can research play in illuminating the multidisciplinary debates on the powerful mathematical ideas required for the 21st century? 2. How can research support more equitable curriculum and learning access to powerful mathematical ideas? 3. How can research support the creation of learning environments that give learners better and more equitable access to powerful mathematical ideas? 4. How can research contribute to the kind of teacher education and teacher development programs that will be needed to facilitate student access to powerful mathematical ideas? 2
Part I: The Evolution of Representational Infrastructures in Static Inert Media
"... We examine the long term history of the development of fundamental representational infrastructures such as writing and algebra, and how they were physically implemented via such devices as the printing press and computers, in order to (1) gain insight into what is occurring today both in terms of r ..."
Abstract
 Add to MetaCart
(Show Context)
We examine the long term history of the development of fundamental representational infrastructures such as writing and algebra, and how they were physically implemented via such devices as the printing press and computers, in order to (1) gain insight into what is occurring today both in terms of representational infrastructure change and in physical embodiments, (2) obtain clues regarding what to do next, and (3) determine the kinds of questions that research will need to answer in the coming decade if we are to make optimal use of new diverse and connected classroom technologies.
1 MultiModal Approach of Teaching Mathematics in a Technological Age
, 1999
"... In the past thirty years, theories of teaching and learning school mathematics have undergone major revisions in the Western worlds. The behaviourist models of direct instruction have been complemented or even replaced in some classrooms by models derived from information processing, constructivism, ..."
Abstract
 Add to MetaCart
In the past thirty years, theories of teaching and learning school mathematics have undergone major revisions in the Western worlds. The behaviourist models of direct instruction have been complemented or even replaced in some classrooms by models derived from information processing, constructivism, and metacognition. However, these changes have weak impacts on mathematics education in the Southeast Asian nations, which is still predominantly traditional in nature and practice. An overdependence of the chalkandtalk method has resulted in unsatisfactory performance in and poor attitude towards school mathematics for many students. This paper will examine some of these shortcomings and then discuss a multimodal approach used to address some of these problems. The multimodal approach makes use of six different modes of representation (numbers, words, symbols, diagrams, stories, and real things) of mathematical knowledge to deepen understanding and flexibility in thinking. Its application in a pilot study shows that the students had good performance in school tests. In recent years, advances in information technology have taken root in most Southeast Asian nations, especially in the business, commerce, and entertainment areas. To fruitfully exploit this powerful medium for teaching and learning, educators have to experiment with new strategies of instruction and to develop materials that are suitable for this medium. The multimodal approach provides a framework for using this medium. By linking a new instructional approach with new technology, it is hoped that more students will be able to master the mathematics they need for the next century, and that the teachers will enjoy teaching with a new vision of mathematics education. Acknowledgement: The MMS framework was first developed together with Mr Palanisamy Veloo
GETTING TO SCALE WITH INNOVATIONS THAT RESTRUCTURE DEEPLY HOW STUDENTS LEARN MATHEMATICS
"... Most people enter the field of educational research with good intentions of improving education and the lives of children. However, countless good ideas remain in university halls. Curricular and pedagogical innovations rise and fall in schools because there is insufficient understanding of how the ..."
Abstract
 Add to MetaCart
(Show Context)
Most people enter the field of educational research with good intentions of improving education and the lives of children. However, countless good ideas remain in university halls. Curricular and pedagogical innovations rise and fall in schools because there is insufficient understanding of how the innovation can and will be used. At the same time, technological innovations in schools are becoming more and more politically contentious. People, reasonably, want to know that we are giving their children “proven” curricular materials. To Congress, this means that evaluators should engage in “scientifically based research ” ("No child left behind act", 2001). Not willing to cede the definition of scientific methodology to lawmakers, educational researchers have begun their own vigorous debate. Fundamentally, they ask (and this book asks): “What should count as a scientific warrant that evidence supports a claim?” Partisans of two important educational research perspectives have made strong progress toward defining and defending their answers. Taking the perspective of program evaluation and educational psychology, some researchers ask: “What works? ” (Shavelson & Towne, 2002). The objects of their inquiry are selected from available materials or programs and the measures are related closely to today’s critical tests. Although researchers in this group acknowledge the utility of multiple research methods, they make their strongest case for the virtues of experimentation, preferably with randomized
UNDERSTANDING THE RELATION BETWEEN ACCUMULATION AND ITS RATE OF CHANGE IN A COMPUTATIONAL ENVIRONMENT THROUGH SIMULATION OF DYNAMIC SITUATIONS
"... Some difficulties which are often present when learning calculus using paper and pencil is understanding that the accumulation of a quantity is closely related to its rate of change. To help students overcome these difficulties and understand these relations we designed a program which simulates the ..."
Abstract
 Add to MetaCart
Some difficulties which are often present when learning calculus using paper and pencil is understanding that the accumulation of a quantity is closely related to its rate of change. To help students overcome these difficulties and understand these relations we designed a program which simulates the inflow and outflow of water in a tank. The study documents the behaviors of two students who were exposed to these dynamics situations.