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

The benefits of high-level mathematics packages such as Matlab include both a computer algebra system and the ability to provide students with concrete visual examples. This paper discusses how both capabilities of Matlab were used in a multivariate calculus class. Graphical user interfaces which display three-dimensional surfaces, contour plots,…

Describes the experimental intelligent computer algebra system STRAMS which can solve problems using a set of methods and techniques traditionally taught, learn new mathematical problem solving methods, and generate different kinds of explanations. Analyzes these features of STRAMS to give reasons for its potential applicability in building…

Discusses common misconceptions in algebra, including: grouping symbols and order of operations; equations, inequalities, and expressions; and domains. Offers recommendations to help students avoid these mistakes. (MKR)

Describes the use of data sets from ultraracing--foot races that are longer than a marathon--with second-year algebra students in data-analysis projects. (JRH)

Discusses the benefits of new technologies, especially graphing calculators, in the teaching and learning of mathematics. Presents two activities for teaching algebra and regression using graphing calculators. (ASK)

Reports on a study in which three volunteer teachers helped design and then taught an experimental program of introductory differential calculus in which students had full access to calculators with a computer algebra system (CAS) in the classroom, at home, and during tests. Test scores indicated that the classes had learned similar amounts of…

Details the authors' investigation of journal writing in first-year algebra and unveils journal writing's connections with the National Council of Teachers of Mathematics Professional Standards for Teaching Mathematics. (MKR)

Presents activities that combine astronomy problems with algebra, geometry, trigonometry, data analysis, and physics. Provides experiences for students in making distance measurements themselves by using the method of parallax. (ASK)

Approximately 1,200 students in years 7 to 10 were tested on recognizing, using, and describing rules relating 2 variables. Fourteen interviewed students saw a variety of patterns, many of which were not helpful for algebra. Outlines critical steps in moving from a table to an algebraic rule. (MKR)

Introduces a strategy for writing equations of graphs to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. (Author/MKR)

Explores the ramifications of two three-year-long experiences with different pedagogical approaches to beginning algebra. Focuses on differences in the nature of subject matter understandings and explores the impact on the teacher to support students' classroom exploration of mathematical ideas. (Contains 58 references.) (Author/ASK)

Finds that students taking algebra-based introductory physics have difficulty with one- and two-body problems in particle mechanics. Provides graded exercises for drawing and utilizing free-body diagrams. (CCM)

Discussed are assumptions about technology and classroom equipment, teaching methods, getting started, pitfalls, and the role of algebra and calculus. Suggestions are given for implementing the spirit and vision of the standards. (YP)

A review of six published studies on algebra interventions for students with learning disabilities revealed that successful interventions included instruction on domain-specific knowledge, as well as general problem-solving and self-regulation strategies. Promising practices include sequential introduction of work problems through concrete,…