Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Discusses findings regarding the academic backgrounds of students taking algebra-based physics. Four areas were examined: (1) performance in math courses; (2) high school physics background; (3) community or junior college experience; and (4) science education majors. Suggestions for improving the academic performance for students in these areas…

Discusses effectiveness of hints given to (n=100) ninth-grade students solving nonstandard problems on functions. Hints that stimulated concrete action were effective if the action modeled the required solution method. Hints that only warned against certain mistakes were ineffective. Appendix includes problems and hints. (MKR/Author)

Describes a study of eighth graders that examined the effect of the use of a linked multiple representation software program on student conceptions of algebraic functions, including graphing techniques. Results of classroom observations and paper-and-pencil tests are discussed, and the adapted curriculum used in the experiment is described. (17…

Described are materials developed to add to existing complex-number units and how they have been used in second-year algebra and precalculus classes. Discussed is software developed, objectives, and classroom materials. Two worksheets are included. A computer program is provided. (CW)

The geometry problems of finding rectangles that have numerically equal areas and perimeters knowing when the plane can be tessellated by congruent regular polygons are connected by the equation: m = 2n/(n-2). Three graphic approaches to the solution of the problem when m and n are integers are discussed. (MDH)

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

An activity in which students use manipulative materials to help solve simple algebraic equations using the operations of adding inverses, removing opposites, and sharing equally is presented. Directions, examples, the rationale, and cautions are included. (KR)

Discussed are solutions to the problem "What is the expected number of rolls for the total first to exceed 6?" Several algebraic solutions are presented. A computer program which may be used to simulate this problem is included. (CW)

The cognitive structure of an algebra test was defined and validated using the linear logistic test model (LLTM) and quadratic assignment (QA). A 29-item test was administered to 235 ninth graders. Results suggest the benefits of applying both LLTM and QA to test construction and analysis. (SLD)

Presents 24 activities related to the theme of area to illustrate how algebra can empower students, not impede their progress. Activities use grid tools, manipulatives, computational tools, and paper-and-pencil tools to facilitate access, discourse, independence, and multiple representations. Well-chosen themes offer connections, motivation,…

Discusses the study of identification codes and check-digit schemes as a way to show students a practical application of mathematics and introduce them to coding theory. Examples include postal service money orders, parcel tracking numbers, ISBN codes, bank identification numbers, and UPC codes. (MKR)

Discusses the use of computers to teach proofs. Presents some possibilities of computer use in teaching proofs. (ASK)

Emphasizes the importance of proofs and offers examples and ideas that might help educators develop students' mathematical reasoning skills. (ASK)

Describes a study that investigated the influence of small-group work on confidence level and achievement of adults in mathematics, specifically in algebra. Students who participated in the experimental (small-group) method of instruction experienced significantly greater increase in confidence level, and higher completion rate, than students who…