Considered are three different types of paper-and-pencil items: labeled word statements, symbolizations, and portrayals. The items are used for testing understanding of mathematical concepts. Limitations of pencil-and-paper items are noted. (RH)

Concepts of fractions from an adult perspective as well as from a child's perspective are examined. Types of students' schemes for some terms related to fractions are reported. (YP)

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)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

The focus of this article is on the verification processes children use when assessing the equality of parts produced by them when partitioning geometric shapes. Different processes and children's verbal proofs of equality are presented. Activities for mathematics instruction are suggested. (YP)

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)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Discusses the nature and importance of iconic learning (image-related) and a medium to facilitate assessment at the iconic level of knowing. The medium consists of a series of self-inking rubber stamps made with iconic representations of numeration blocks and sticks in denominations of 1, 10, and 100. (JN)

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Focuses on the language used by elementary mathematics teachers and its relationship to students' understanding of mathematical concepts, as well as their misconceptions. Describes eight situations in which the use of precise, formal mathematical terms could be replaced by informal language, particularly when introducing new concepts. (TW)

Explored were the relationships among students' mathematics language facility, procedural mathematics knowledge, and understanding and application of mathematics concepts. Findings indicate that students needed both procedural knowledge and language facility in mathematics for an acceptable level of conceptual achievement. (CW)

Describes mathematics education programs in Texas schools. Emphasizes the mastery of skills and concepts, as well as problem solving. Presents the philosophies of the mathematics programs for elementary schools, and for grades seven and eight. Addresses remediation, enrichment, time allotment, content, recommended manipulative materials, and…