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)

Traces a student's use of different types of imagery over an extended period of time in order to determine why the student seldom used imagery to solve problems. Concludes that for most of her school life, the student had been able to rely on analytic processing to complete mathematical tasks and could do so quite successfully. (Contains 30…

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)

Reviews visualization research concerning the objects of visualization, the visualization process, and visualization in educational situations. Teaching procedures, the role of material and the social environment, and how the individual interacts with that environment are described. (YP)

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)

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)

Discusses students' use of visual considerations in doing geometrical proofs. Studies ninth-grade students (n=17) in an academically-selective high school in Jerusalem. Concludes that only three out of 16 students who turned in their papers chose symmetry considerations when working on a proof. Contains 16 references. (ASK)

Two authors introduce the topic of visualization in mathematics education. Fourteen articles are briefly described. (YP)

Examines the relationship between visualization and the middle school mathematics curriculum. Gives an overview of where and how visualization interacts with the curriculum. Investigates the role of visualization in developing inductive/deductive and proportional reasoning. (YP)

Introduces an introductory module for analysis. Describes stock of basic functions and their graphs as part one and three methods as part two: transformations of simple graphs, the sum of stock functions, and upper and lower bounds. (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)

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)

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…

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…