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 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)

Research on learner's beliefs are summarized in the areas of beliefs about mathematics as a discipline, beliefs about learning mathematics, beliefs about mathematics teaching, and beliefs about self within a social context in which mathematics teaching and learning are occurring. (PK)

Presents the major findings identified by a commission that examined research issues in diagnostic and prescriptive mathematics. Addresses the diagnostic process with regard to curriculum, instruction, learners, teacher education, clinics, and the mathematics education community. (TW)

Describes the four competencies which are argued to be necessary for being an effective remedial mathematics teacher. Describes a training model which has been developed for preservice and inservice teachers based on these competencies. (PK)

Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)

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

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)

Presented are some concerns related to the diagnostic/prescriptive approach to teaching mathematics. The author supports the view that teachers need to become aware of reasons for making professional decisions and become reflective practitioners. (RH)

Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

Differences in the meaning of the terms "learning" and "achievement" are discussed, with implications for appraisal, placement, curriculum, and instruction. Visual discrimination learning, paired associate learning, adapting to learning, and learning to learn are illustrated with references to learning disabled students. (MNS)

Provides a review of the literature related to math anxiety, indicating that society needs to eradicate the myth that females are more anxious about mathematics than males. Several options for eliminating math avoidance and math anxiety are considered. (JN)

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

Presents a teaching experiment to turn students from external observers into active participants in a game of algebra learning where students use graphs to build meaning for equivalence of algebraic expressions. Concludes that the graphic-functional approach seems to make the introduction to algebra much more meaningful for the learner. (ASK)

Describes a research methodology known as the teaching experiment and details an example of a teaching experiment aimed at the development of a process-oriented algebra curriculum. Addresses other possible variations of the teaching experiment, emphasizing the cooperation of teachers and researchers. (TW)