Explains big ideas in algebra that help students connect ideas with procedures in different mathematical topics to build a relational understanding of algebra. (Contains 10 references.) (YDS)

Analyzes data from observations of first year university mathematics tutorials to elicit characteristics of teaching using the teaching triad, a tool developed in earlier research. Explores sensitivity to students and mathematical challenges. Provides insight into related pedagogic processes and shows approaches to analyzing teaching that address…

Investigates how students interpret and analyze multivariate data organized in tables and the nature of external visual displays that they tend to create and use for this purpose. Reports that: (1) students based their conclusions on only part of the data; (2) students did not use either efficient or sufficient visual representations; and (3)…

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Presents an approach to task sequencing that is based on a component-skills view of intelligence and learning. Related research in cognitive psychology and in computer based instruction is reviewed, and a cognitive model of human task sequencing is developed and then applied to an intelligent tutoring system for algebra. (39 references)…

Challenges abstract mathematics requirements in U.S. high schools. Refutes various philosophical and psychological assumptions underlying math instruction, particularly the correlation between simple numbers and the physical world, the math/logical thinking connection, and frequency of use arguments. Suggests that high schools require only one…

Illustrates, categorizes, and analyzes typical mathematical errors in algebra and trigonometry made by high school and lower division college students. (16 references) (Author/MKR)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Explores quadratic functions using the graphing calculator. Discoveries are made graphically whereas hypotheses are proven algebraically. Includes traditional quadratics, other algebraic quadratics, nonpolynomial quadratics, transcendental quadratics, and proofs. (MKR)

Demonstrates the mathematical nature of a pollution problem in a marine environment. Includes reproducible student worksheets. (11 references) (MKR)

Presents a summary report of a discussion subgroup of the Algebra Working Group at the Seventh International Conference on Mathematics Education held in Quebec City, Canada in August 1992. Argues that pre-algebra should be viewed as a continuation of arithmetic that asks different questions about numbers. (12 references) (Author/MKR)

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Relates, in story form, how to make geometric and algebraic concepts more accessible to children by using one-dimensional grids. (MKR)

Groups of 30 students each in an algebra minicourse and semester course and 45 each in an accounting minicourse and semester course showed no significant differences in course grade point average or overall average. Students choosing the intensive minicourse format were generally older, indicating that adults find this format more useful and…

Reported is a study of types of errors exhibited by students of intermediate algebra at the college level and the effect the time of day instruction has on students' performance. Results indicated that two types of errors, conceptual and prerequisite, and that student performance is better in the morning. (MDH)