Presents a device for sketching the graph of the composite and inverse of single variable real-valued functions. Discusses some didactic methods of paths. (YP)

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Proposes elements of a model of knowledge structures used in comprehending and generating graphs. Uses the competence model to attempt to organize and interpret findings on misconceptions in graphing. Discusses two types of common misconceptions; treating the graph as a picture and slope-height confusions. (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)

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)

Discusses a technique for graphically composing functions. Describes three-step composition procedures in two- and three-dimensional rectangular coordinate systems. Provides three examples. (YP)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (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)

Discusses the use of the computer to encourage a versatile approach to learning involving both symbolic/logical and visual/holistic types of mental activity. Provides experimental data showing the effect of an enhanced Socratic mode of teaching. (YP)

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…