The purpose of this study was: (a) to develop a learning hierarchy for rational number subtraction using intraconcept analysis, and (b) to validate that hierarchy using the Walbesser technique and pattern analysis. Skills required to complete tasks within the hierarchy were operationally defined and ordered from both a mathematical and…

Whether hierarchical ordering among fraction identification problems reflects the replacement of simple rules by complex rules was investigated. Latent class techniques revealed that children applied rules that were adequate for simple problems but had to be replaced to solve more complex problems. (Author/GK)

Explores how children from kindergarten to 6th grade think about the same fraction problem and what that should mean for instruction. (Author)

This study investigated the extent to which various latent class models adequately described elementary rule-governed mathematical behaviors. Children were given a fraction concepts test. Results supported the adoption of a set of three-class models including a mastery class, a nonmastery class, and a transitional class to describe the data.…

Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

Two experiments explored the relationship between conceptual and procedural knowledge. Results revealed that fourth and sixth graders made computational errors even though they possessed conceptual knowledge. Fifth graders mastered conceptual knowledge before procedural knowledge. Results support the dynamic interaction theory. (BC)

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Current reform documents in mathematics education recommend that teachers help students develop both conceptual and procedural understandings; however, teachers often do not possess the in-depth mathematical reasoning abilities necessary to accomplish this goal. Describes one way in which preservice teachers can come to better understand the…

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…