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)

Investigates children's cognitive structures with respect to concepts one-half, one-quarter, and one-third as these apply to continuous circular and triangular regions. Examines the effect of an intervention program with 21 children in grades three through six. (YP)

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)

Explores the extent to which presentations about multiplication and division involving decimals within three series of mathematics textbooks for grades three through eight help students to counter common learner misconceptions about multiplication and division. Results indicate that theory on conceptual change with its concomitant research have…

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)

Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (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)

Examines the role of visualization within the process of geometrical concept attainment for students in grades five through eight, preservice elementary teachers, and inservice senior elementary teachers. Investigates the "bitrian" and "biquad" examples, numbers of critical attributes, elements in triangles, judgment in quadrilateral examples, and…

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)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

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…