Presents a summary report of the Algebra Working Group's discussion subgroup on secondary algebra at the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Three appendixes include the reactions to the keynote addresses in this issue. (MKR)

Three experiments investigated the ability of 79 college students to solve similar algebra word problems. Data indicate that students are able to perceive and use similarities in such problems at the level of a conceptual structure. A training session to explain relevant structural principles was effective in improving performance. (SLD)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Data from students in grades 8-10 in suburban schools were presented to show that errors in formulating algebraic equations are not primarily the result of syntactic translation, as has been assumed in the literature. A theory of cognitive models is offered as an explanation for the errors. (Contains 37 references.) (MLN)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

Discusses the objectives, organization, assessment, student reactions, and evaluation of an abstract algebra course in which small-group instruction was used. Concludes that better understanding is achieved and the students assimilate more concepts using this method, although the pace is slower than that in a traditional classroom setting.…

Reviews three geometry textbooks in order to examine both the quantity and content of algebra review. Concludes that although the books incorporate a great deal of algebra, much of it is noncontextual review. (ASK)

Focuses on changes in attitude toward mathematics and calculator use and changes in how general mathematics students naturalistically solve algebraic problems. Uses a survey to determine whether a student is rule-based. Concludes that the rule-based students used an equation to solve the algebraic word problem whereas the non-rule-based students…

Investigates whether three cognitive components of language proficiency--metalinguistic awareness of symbol, syntax, and ambiguity--are associated with students' success in learning algebraic notation. Reports that very few students with low metalinguistic awareness scores achieved high algebra scores in a total sample of more than 1500 students.…

Presents a method for introducing students to broken-line functions with unbroken domains. Concludes that a unit on broken-line functions should enhance students' understanding of the function concept. (ASK)

Describes teacher and student experiences in a college algebra course at a high school when assessment practices changed. (ASK)

Demonstrates a change in the goals of teaching the algebra of equation-solving in Victoria, Australia that requires a transition from a way of solving problems in arithmetic to a conceptually new algebraic way. Contains 20 references. (Author/ASK)

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and…

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Examined beliefs of elementary, middle, and high school mathematics teachers regarding algebra development. Found that teachers held a symbol-precedence view of student mathematical development. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performance, whereas middle school…