New Approaches Using Technology for Solving Problems in Secondary Mathematics
Arne Engebretsen
arnee@execpc.com
Greendale High School
Greendale, WI 53129-2242
USA
Abstract
This paper examines the impact of technology on the problem solving methods available to students and teachers at the secondary mathematics level. It focuses on a optimization problem with rich mathematics connections and, depending upon the approach, appropriate for students in mathematics classes from Year 7 to Year 12 (prealgebra to calculus). Any type of graphing calculator could be used to investigate and solve the problem. This paper presents a variety of solutions using the TI-92 using not only its data analysis and graphing capabilities but also its interactive geometry and computer algebra capabilities.
The problem is to maximize the area of the triangle formed by folding a corner of a rectangular piece of paper so that it just touches the base of the rectangle. This paper first has the reader use a manipulative and conjecture as to where the point of optimization would be and then to try to find the solution to the problem using whatever means that they desire.
The paper then discusses the use of TI-92 Geometry to model the problem. Data is collected using this model and placed in the Data/Matrix Editor of the TI-92. The data is examined using a variety of data analysis methods. The data is plotted using Stat Plot and various functional relationships are examined to see how they fit the data. The Computer Algebra System (CAS) of the TI-92 is used to further examine relationships between the point where the vertex of the rectangle is placed on the base and the resulting area of the triangle. Over ten different methods for solving this problem using the TI-92 are presented in the paper. Many connections between the various solutions are investigated.
The problem presented in this paper is one that I have used with students in a variety of classes for the past ten years. Its solution is not obvious, yet with current hand held technology the investigation and solution of the problem is well within the reach of all students at the secondary level of mathematics. The paper also shows many of the powerful mathematical features of the TI-92 which students and their teachers will find to be exciting alternatives to paper and pencil methods for solving the problem.
© Asian Technology Conference in Mathematics, 1998. |
