Algebra, an important skill, provides a way to represent situations so they can be analyzed carefully. In the new algebra classroom, students will listen and talk to one another while learning to understand problems and devise solutions. Teachers will organize tasks (involving graphing, rating, and ranking techniques) to help students discover the…

Presents the "Food for Thought" problem and discusses different approaches used by Algebra 1 students to solve the problem. (YDS)

Outlines a lesson on the Fibonacci and Lucas sequences that captures student interest by presenting the opportunity for computation practice, mental mathematics, and proof for algebra students. Discusses an extension for solving simultaneous equations. (YDS)

Describes how student thinking about geometric patterns can be used to develop algebraic reasoning and to make sense of mathematical notation and symbols. (Contains 11 references.) (YDS)

Investigates how mathematics is used in various careers. Students explore number sense and operations, logical reasoning, data analysis, and algebra. (Author/NB)

Examines whether the embodiment of a familiar geometric system facilitates better understanding of the vector-space concept than the embodiment of a variety of unfamiliar algebraic systems. Analyzes students' responses with description, final answer, and justification of answers. Provides six problems. (YP)

Eighty-six college students studied solutions of simple and complex word problems and then used the examples to construct algebraic equations as the frequency of referral to example was recorded. Students did not always select the appropriate example, and ability to select appropriately did not interact with aptitude. (SLD)

A computer algebra system was integrated into instruction for two large classes of mathematics for business and the social sciences. Comparisons of student achievement and attitude showed no significant differences, but other implications of the study are discussed. (23 references) (LZ)

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)

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…

Presents problems from the Mathematics in Context (MiC) project with a central theme concerning the construction of a variety of formulas by students. (AIM)

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…

This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable…

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…