The systematic scientific investigation of human perception began over 130 years ago, yet relatively little is known about how we identify complex patterns. A major reason for this is that historically, most perceptual research focused on the more basic processes involved in the detection and discrimination of simple stimuli. This work progressed in a connectionist fashion, attempting to clarify fundamental mechanisms in depth before addressing the more complex problems of pattern recognit...

Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathem...

Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the stre...

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely s...

Factor analysis is a statistical technique widely used in psychology and the social sciences. With the advent of powerful computers, factor analysis and other multivariate methods are now available to many more people. An Easy Guide to Factor Analysis presents and explains factor analysis as clearly and simply as possible. The author, Paul Kline, carefully defines all statistical terms and demonstrates step-by-step how to work out a simple example of principal components analysis ...

'Seeing' happens effortlessly and yet is endlessly complex. One of the most fascinating aspects of visual perception is its stability and constancy. As we shift our gaze or move about the world, the light projected onto the retinas is constantly changing. Yet the surrounding objects appear stable in their properties. Psychologists have long been interested in constancies, exploring questions such as: How good is constancy? Is constancy a fact about how things look, or is it a product of ou...

To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account...

More than 2000 years ago Greek philosophers were pondering the puzzling dichotomy between our physical bodies and our seemingly non-physical minds. Yet even today, it remains puzzling how our mind controls our body, and vice versa, how our body shapes our mind. How is it that we can think highly abstract thoughts, seemingly fully detached from the actual, physical reality? This book offers an interdisciplinary introduction to embodied cognitive science, addressing the question of how the m...

This work argues that cognitive development is experience driven, and processes entailed in acquiring information about the world are analyzed based on recent models of learning and induction. The way information is represented and accessed when performing cognitive tasks is considered paying particular attention to the implications of Parallel Distributed Processing (PDP) models for cognitive development.The first half of the book contains analyses of human reasoning processes (dr...

Knowledge representation is fundamental to the study of mind. All theories of psychological processing are rooted in assumptions about how information is stored. These assumptions, in turn, influence the explanatory power of theories. This book fills a gap in the existing literature by providing an overview of types of knowledge representation techniques and their use in cognitive models.Organized around types of representations, this book begins with a discussion of the foundation...

When most people think of space, they think of physical space. However, visual space concerns space as consciously experienced, and it is studied through subjective measures, such as asking people to use numbers to estimate perceived distances, areas, angles, or volumes. This book explores the mismatch between perception and physical reality, and describes the many factors that influence the perception of space including the meaning assigned to geometric concepts like distance, the judgmen...

In response to No Child Let Behind, states have developed mathematics curriculum frameworks that outline their intended curriculum for grades K–8. While some have indicated that districts or individual schools may use their framework as a model for specific curricular programs, others have taken a more prescriptive or even mandatory stance. Collectively, these frameworks present a sense of the national mathematics program and what we expect students learn.This volume follows The In...