The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take…

This is a conceptual paper based on existing literature aiming to provide practical information on designing and implementing activities to promote children's computational thinking. Computational thinking is a relatively new term in early childhood education that refers to a specific problem-solving thinking process involving various logical and…

While the author can see many ways that artificial intelligence can be used as an adult, a professional, and a business owner, she also realized what it was going to do for children who are learning their basic skills, such as how to write, how to work with numbers, how to think for themselves, and how to make considered choices. What would this…

Does modeling matter? We address this question by providing a broad survey of the computational models of cognitive development that have been proposed and studied over the last three decades. We begin by noting the advantages and limitations of computational models. We then describe four key dimensions across which models of development can be…

The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small…

Computational models are tools for testing mechanistic theories of learning and development. Formal models allow us to instantiate theories of cognitive development in computer simulations. Model behavior can then be compared to real performance. Connectionist models, loosely based on neural information processing, have been successful in…

Nonreading tasks that share some (but not all) of the task demands of reading have often been used to make inferences about how cognition influences when the eyes move during reading. In this article, we use variants of the E-Z Reader model of eye-movement control in reading to simulate eye-movement behavior in several of these tasks, including…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

Computational models have played a central role in the debate over language learnability. This article discusses how they have been used in different "stances", from generative views to more recently introduced explanatory frameworks based on embodiment, cognitive development and cultural evolution. By digging into the details of certain specific…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of…

Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

In the first chapter Brownell critically examines the psychological bases of the three most common theories of arithmetic instruction: drill, incidental learning, and meaning. In chapter 2 the results of a nation-wide survey of actual teaching practices are reported. Chapter 3 presents a contrast between "informational arithmetic" and…

Proposes that teachers should examine the elements of mathematical understandings that precede conservation and one-to-one correspondence and tailor classroom instruction to benefit both conserving and nonconserving students. (PK)