Focuses on solutions to a single problem using both induction and deduction by utilizing a TI-82 graphing calculator to illustrate symbolic, numerical, and graphical approaches to the problem. (ASK)

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

This review of recent literature, focusing on the integration of mathematics and reading, highlights three reading stances within mathematics classrooms. The first stance, reading problems, highlights the scope-and-sequence, transmission approach to learning mathematics, where the purpose of reading is to figure out how to solve an immediate…

Mathematical language and chemical knowledge are complementary to each other and only productive use of the two enables using numbers to gain solutions rather than just answers. It is believed to be important in the understanding of science that students feel free to speak mathematics and only a few of them are willing to connect and use their…

Mathematical problems when solved with different approaches deepen the understanding of topics learned. It is reported that weighted average is commonly used in applications and the relationship between all the ratios involved in the problem emphasized could be learned from Farey sum of two fractions.

Mathematical reasoning is the cornerstone of mathematics learning and should be the focus of mathematics teaching. Two mathematical problems are presented, which describe students' responses, and highlight how students demonstrated mathematical reasoning in the midst of working on these problems.

This is the story of the first American mathematics journal. According to its title page, the journal was "adapted to the present state of learning in America" and "designed to inspire youth with the love of mathematical knowledge, by alluring their attentions to the solutions of pleasant and curious questions".

CAPTCHAs are images used on the internet by companies that want to block computer programs from their site. This article presents a method for solving some of these puzzles.

At each point of an ellipse one can attach a normal vector and a radial vector, the latter defined as the vector from the center of the ellipse. At the ends of the major and minor axes, the two vectors coincide, but at all other points they are separated by an angle [delta]. What is the maximum value that [delta] can attain, and where does it…

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

It was shown by Costa and Levine that the homogeneous differential equation (1-x[superscript N])y([superscript N]) + A[subscript N-1]x[superscript N-1)y([superscript N-1]) + A[subscript N-2]x[superscript N-2])y([superscript N-2]) + ... + A[subscript 1]xy[prime] + A[subscript 0]y = 0 has a finite polynomial solution if and only if [for…

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

Building on their knowledge of the three possible outcomes of solving 2x2 systems of equations, students use three-dimensional geometric figures to investigate the eight possible outcomes for solving 3x3 systems of equations.