This document shows the use of the calculator to assist in solving different divisions of students in fourth grade of elementary school, through the interaction in its components (divisor, dividend, quotient and remainder). Worksheets were used with a constructivist approach, which provided the student self-assessment tests. The teacher's role was…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

This study addressed the problem of why students with learning disabilities in mathematics too often fail to develop multiplicative and divisional concepts/operations. We conducted a constructivist teaching experiment with 12 students (nine 5th and three 4th graders). This report focuses on three students' conceptual progress, particularly on…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

Effects of guided (GI) and direct instruction (DI) in solving subtraction problems for mathematically low performers in regular schools were compared. In the GI condition, self-development of solution procedures was encouraged whereas in the DI condition one prescribed strategy was to be used. Forty children (M[subscript age] = 9.3 years) were…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth-grade students' multiplicative structures and their construction of improper fractions. Students' multiplicative structures are the units coordinations that they can take as given prior to activity--i.e., the units…

The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

This study sought to provide an explanation of (n=13) university students' understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of the analysis of the data, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examines the differences in the…

This monograph chronicles a field-based investigation of children's learning in a second grade mathematics classroom over the course of a school year. The interrelated aspects of the processes by which children learn mathematics with meaning are illustrated here. The investigation was expanded to include a sociological analysis in an attempt to…

Analyzes one third grader's participation in mathematics class discussions, his beliefs about class discussion, and his arithmetical development throughout a school year in a problem-centered learning classroom. Concludes that a fruitful classroom discussion both necessitates and, conversely, is facilitated by the negotiation of social norms and…

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented)…

Compared project (n=79) and nonproject (n=111) third-grade students on their conceptual development in arithmetic, their personal goals in mathematics, and their beliefs about reasons for success in mathematics. Project students attained more advanced levels of conceptual understanding and held stronger beliefs about the importance of working…