At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

Provided is an examination of the methodology used to study the problems of learning addition and subtraction skills used by developmental researchers. The report has sections on categories of theory and their methodologies, which review: (1) Behaviorist, Neo-Behaviorist and Piagetian Theories; (2) the Behaviorist and Piagetian Paradigms; (3)…

Limitations of the retrieval strategy dimension of Siegler's (1982, 1984) distributions-of-associations model of young children's estimation of sums are delineated, an alternative model is described, and findings of two studies designed to test key assumptions of the models are reported. In Study 1, kindergarten children with normal IQ and no…

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a…