This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.

It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.

Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. Whether in the classroom, university or workplace, there is a growing requirement to use and interpret a large variety of external representational forms and tools for knowledge acquisition, problem solving, and to communicate with others.

Use of Representations in Reasoning and Problem Solving brings together contributions from some of the world's leading researchers in educational and instructional psychology, instructional design, and mathematics and science education to document the role which external representations play in our understanding, learning and communication. Traditional research has focused on the distinction between verbal and non-verbal representations, and the way they are processed, encoded and stored by different cognitive systems. The contributions here challenge these research findings and address the ambiguity about how these two cognitive systems interact, arguing that the classical distinction between textual and pictorial representations has become less prominent. The contributions in this book explore:

• how we can theorise the relationship between processing internal and external representations
• what perceptual and cognitive restraints can affect the use of external representations
• how individual differences affect the use of external representations
• how we can combine external representations to maximise their impact
• how we can adapt representational tools for individual differences.

Using empirical research findings to take a fresh look at the processes which take place when learning via external representations, this book is essential reading for all those undertaking postgraduate study and research in the fields of educational and instructional psychology, instructional design and mathematics and science education.

Over the past years a substantial amount of research has been undertaken relating to the development of powerful learning environments for the acquisition in students of worthwhile educational objectives focussing on conceptual understanding, higher-order cognitive and metacognitive skills, and self-regulated learning. This research has been mainly undertaken from three distinct, but related perspectives in the study of learning and instruction, namely instructional psychology, instructional technology, and instructional design. Against this background a "research community" involving 14 European research teams has recently been initiated with the aim of interactively contributing to the advancement of theory and methodology relating to the design, implementation, and evaluation of powerful learning environments.This volume, based on the plenary lectures and working sessions during the community's third workshop, constitutes a collective output of this research community, focussing on the identification and analysis of major components and dimensions of powerful learning environments aimed at the promotion of deep conceptual and strategic learning in major domains of school curricula, like mathematics, physics, history, and social sciences.In Part I of the volume three chapters present general perspectives on the central theme of the third workshop. In Part II six studies are reported wherein novel learning environments for elementary and secondary mathematics education have been designed, implemented and evaluated. In Part III of the volume another set of five investigations is presented relating to the design, implementation and evaluation of powerful learning environments in other subject-matter domains (physics, history, social sciences) and in teacher training.

Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. Whether in the classroom, university or workplace, there is a growing requirement to use and interpret a large variety of external representational forms and tools for knowledge acquisition, problem solving, and to communicate with others.

Use of Representations in Reasoning and Problem Solving brings together contributions from some of the world s leading researchers in educational and instructional psychology, instructional design, and mathematics and science education to document the role which external representations play in our understanding, learning and communication. Traditional research has focused on the distinction between verbal and non-verbal representations, and the way they are processed, encoded and stored by different cognitive systems. The contributions here challenge these research findings and address the ambiguity about how these two cognitive systems interact, arguing that the classical distinction between textual and pictorial representations has become less prominent. The contributions in this book explore:

• how we can theorise the relationship between processing internal and external representations
• what perceptual and cognitive restraints can affect the use of external representations
• how individual differences affect the use of external representations
• how we can combine external representations to maximise their impact
• how we can adapt representational tools for individual differences.

Using empirical research findings to take a fresh look at the processes which take place when learning via external representations, this book is essential reading for all those undertaking postgraduate study and research in the fields of educational and instructional psychology, instructional design and mathematics and science education.

To celebrate Erik De Corte??'s scientific career in the international scientific field of instructional psychology, high profile researchers and scholars were invited by the editors to write an essay on ???the past, present, and future??? of the subdomain of instructional psychology of their personal interest and expertise.
This book addresses the core topics of the learning sciences from a diversity of perspectives. The sixteen chapters are grouped into the following six sections: 1) Learning and Development, 2) Learning, Reasoning, and Problem Solving; 3) Motivational and Emotional Aspects of Learning, 4) Learning and Assessment, 5) Learning and Technology, and 6) Instructional and Organizational Designs for Learning.
These chapters provide overviews of and commentaries on the past decades of research on learning and teaching. Furthermore, the authors look also at the future of research on learning and instruction and its changing role in our fast developing knowledge society.
*16 chapters written by high profile researchers and scholars
*Content provide both a review of existing literature and a discussion of the future of the discipline

This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap - to create a transition. The book concludes with directions for future research on transitions in mathematics education.

Most would agree that the acquisition of problem-solving ability is a primary goal of education. The emergence of the new information technologiesin the last ten years has raised high expectations with respect to the possibilities of the computer as an instructional tool for enhancing students' problem-solving skills. This volume is the first to assemble, review, and discuss the theoretical, methodological, and developmental knowledge relating to this topical issue in a multidisciplinary confrontation of highly recommended experts in cognitive science, computer science, educational technology, and instructional psychology. Contributors describe the most recent results and the most advanced methodological approaches relating to the application of the computer for encouraging knowledge construction, stimulating higher-order thinking and problem solving, and creating powerfullearning environments for pursuing those objectives. The computer applications relate to a variety of content domains and age levels.

Over the past ten to fifteen years the international scene of research on learning and instruction has witnessed the emergence of important and promising developments. New theoretical frameworks, design principles, and research methodologies focusing on the construction, implementation, and evaluation of powerful learning environments have been put forward, coming from three intersecting subdomains within the broader field of research on learning and instruction - namely instructional psychology, instructional technology, and instructional design. Although it is obvious that the developments in those three subdomains are characterized by similarities and convergencies, there are still important differences. Therefore, there is a great need for scientific debate and attempts to integrate, or justify, the contrasting theoretical frameworks, methodological approaches, and empirical outcomes.
A European research network, coordinated by the Center for Instructional Psychology and Technology of the University of Leuven, has been set up to work towards this end. The present volume is the first collective output of this European research network, and focuses on unravelling and identifying basic component and dimensions of powerful learning environments. It is based on the presentations and discussions that constituted the "piece de r??sistance" of a first meeting of the research network.

This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.

It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.