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)

Low ability sixth graders (n=19) participated in a teaching experiment involving fraction concepts. Results showed students were able to acquire and use semantic processes and transfer these processes to novel tasks. Semantic processing was positively associated with performance. (MKR)

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)

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…

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)

Structure of mathematical concept of multiplication and its integration into conceptual system, with respect to formal and informal aspects of understanding for 10 university students, are investigated through linear scale assessment of examples for prototypical effects and through follow-up interview which included direct explanations of…

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)

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…

The difficulties and misconceptions that many students experience when learning to visualize graphs of functions are discussed. Specifically, the inability to make accurate connections between symbolic and graphical representations, the lack of understanding about scale and scaling, and the confusion caused by transformations are examined with…

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…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)