Describes the two-year Transition toward Algebra project developed to help middle grade teachers experience and think through effective teaching strategies that promote a rich and positive learning environment and transition toward algebra. Teachers engaged in problem solving, discovering relationships, and translating among mathematical…

Reports on middle school students' use of dynamic physical models to interpret functions. Includes student creations of symbolic variables and function equations. (KHR)

Examines the balance model and identifies the issues that divide scientists. Describes learning situations that were the subject of the empirical study which involved 40 students in two 8th-grade classes. Shows the presence of negative numbers gave rise to many errors. Discusses the relevance of the balance model and analyzes the arguments put…

Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)

Presents a measurement problem that can be explored by students of varying ability. Discusses aspects that make it accessible in a heterogeneous class. (YDS)

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

Describes student work with linear and nonlinear relationships illustrating algebra skills and understanding which are important to introductory algebra. (YDS)

Describes a series of lessons in which 6th grade students explore notions of rates of change and their effect on the shapes of graphs. Addresses aspects of the algebra content standard for the middle grades. (YDS)

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)