The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

Investigated was the relation between student ability to translate sentences into equations, equations into sentences, and student performance in formal operational reasoning, proportional reasoning, and introductory-level chemistry. Results indicate that students who lack formal operational skills may experience problems in the translation of…

Assessed was the level of thinking of 140 students who had been placed in developmental algebra as entering college freshmen. Scores on the Group Assessment of Logical Thinking, Scholastic Aptitude Tests, college placement tests; high school grade point average, and developmental algebra final grade were analyzed. Group characteristics are…

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Provided is an example of the use of the Pythagorean Theorem to give learners experience in applying mathematical rules. A proof for the theorem is included. Precautions and alternatives are discussed. (CW)

Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)

Math Notebook is a publication issued 10 times a year, with each issue focusing on a particular learning problem in mathematics and its diagnosis and remediation through practical, workable strategies for use by teaches, parents, and tutors. All the articles were written by Mahesh C. Sharma, with the exception of "The Japanese Soroban," by Frances…

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)

Discussed is the use of a program called MathCAD which allows students to solve higher order polynomial equations and geometry problems. The use of cooperative learning is emphasized. Included are graphs and part of a printout generated while solving problems with MathCAD. (KR)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

This is volume 6 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This book contains both a theoretical examination of the connection between instruction and the development of children, and experimental data on a definite…