This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

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…

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 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…

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

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…

It is over 25 years since Wood, Bruner and Ross (1976, "Journal of Child Psychology and Psychiatry," 17, 89-100) introduced the idea of "scaffolding" to represent the way children's learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing…

Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…

This computer software is a tool designed to help teachers help children in grades 1 through 7 construct their own knowledge of whole numbers and fractions. This software is the first in a series of new, dynamic computer microworlds that allow teachers to interact with students and students to interact with each other as they engage in…

Discusses ways teachers can encourage students to construct useful meanings for the fractional unit. Provides three examples of representations of common fractions and illustrates misconceptions in fraction problems. Includes a brief summary of constructivist mathematics education and an example in which a teacher misunderstands a fractional unit.…

As universities strive to produce the best mathematics teachers possible through both graduate and undergraduate programs, teacher educators must constantly work towards helping teacher candidates create their own conceptual understanding of mathematics. This pilot study examined the effect teaching in a constructivist manner had on teacher…