The 5-stage model of Ross was used to examine the role of instruction in facilitating children's acquisition of place value knowledge. Compares children from 2 samples on 10 tasks designed to reveal their thinking about place value. Discusses implications for theory and classroom. (YP)

Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Describes three activities of imaging, including constructing an image, representation-presenting the image, and transforming the image. Discusses a link between imaging and number sense, teaching students to image, and assessing imaging. Contains 25 references. (ASK)

Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

Describes a teaching experiment conducted over a period of four consecutive days with 13 fourth grade students who had already completed a unit of fractions to determine whether problematic size was the ordering criteria. Concludes that children can indeed order fractions as they do natural numbers. (Contains 11 references.) (ASK)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Describes a study that explores secondary school students' conceptions of division by zero. Examines whether students identify expressions involving division by zero as undefined or tend to assign them numerical values. Studies students' justifications and analyzes the effects of age and level of achievement in mathematics on students' responses…

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

What makes a fraction meaningful and a definition of the quantitative notion of fractions are discussed. Then observations from teaching experiments are presented. (MNS)

The work of Ladislav Kosc on dyscalculia is presented. His work on meanings, forms, terminology, diagnosis, correction principles, factors in mathematical ability, language dysfunctions, and publications are each included. (MNS)

The purpose of this study was to assess the ability of students in grades 6 and 7 to order rational numbers in both decimal and fraction form, including the identification of their thinking strategies. Implications for instruction are included. (MNS)

This research was designed to document the ability of Down's Syndrome children aged 5-10 to perform equivalence tasks, and to investigate possible relationships between such performance and the presence of certain potentially confounding task variables. (MNS)

Identifies four causes of confusion in reading mathematics related to numbers, symbols and sentences, vocabulary, and directionality. Discusses techniques for overcoming each type of the confusion. (YP)

Ways in which children think of 10 are considered first. Then a study with 14 second graders is reported; students were placed at three levels with respect to their addition and subtraction concepts. Findings are detailed, along with implications for instruction. (MNS)