This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any…

Excel assignments were used as extra credit in an intermediate algebra course. Ninety percent of the students had a home computer and seventy per cent were familiar with Excel. There was not a significant linear correlation between the amount of Excel that the students performed and their achievement in algebra. One-third of the students did less…

Three proofs are given for the fact that the derivative of an everywhere-positive non-constant real polynomial function must change sign. This self-contained note could find classroom use in courses on calculus or abstract algebra.

This article investigates a specific instance when the textbook answer for finding a root of a complex number differed with the answer given by the TI-83. After explaining the reason for the difference the article then expands the definition of the integral root of a complex number to an arbitrary complex power of a complex number.

This article describes activities that introduce basic trigonometric functions in a smooth and natural way. The only requirements are basic algebra, the Pythagorean theorem, and the concept of area.

This article describes a way to use color to help students develop formulas for functions that describe growing patterns. (Contains 4 figures.)

Brooks (1999) compared algebra achievement of students enrolled in the intervention group (I CAN Learn[R] classes) to that of students enrolled in the comparison group (traditional classes) at pretest, midyear, and posttest. Brooks found that students in the I CAN Learn[R] classes achieved higher scores in algebra than students in traditional…

The inability of students to become proficient in algebra seems to be widespread in American schools. One of the reasons often cited for this inability is that instruction seldom builds on prior knowledge. Research suggests that teacher effectiveness is the most critical controllable variable in improving student achievement. This report details a…

In overcrowded urban high schools, students are dealing with many issues in and out of school. Issues at home paired with math curriculum that does not seem relevant to their lives, leads to a lack of engagement in the classroom. This research poses the question: How can project-based algebra engage low-socioeconomic status high school students?…

Within the context of a mathematics reform effort to implement algebra in elementary schools, there is a pressure to provide results in the form of student achievement scores. However, widely-used measures of student achievement may be unrelated to the ideas and instructional practices encouraged by the reform effort. The inappropriate use of…

This study of student performance in an online Algebra course looked at the development, implementation, and evaluation of interactive tools for graphing linear equations. The study focused on an interactive tool that was evaluated with virtual school Algebra students for a challenging component of the course. The performance of these students in…

This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

A whimsical mathematics event for children and adults, derived from Lewis Carroll's Alice's Adventures in Wonderland, was held at the Providence Children's Museum in Rhode Island. NCTM's Standards were the basis of all the activities. (Contains 10 figures and 1 table.)