Testing Students with Hand-held Technology
Edward D. Laughbaum
elaughba@math.ohio-state.edu
Associate Director
Ohio Early Math Placement Testing Program
The Ohio State University
Department of Mathematics
231 West 18th Avenue
Columbus, OH 43210 USA
Abstract
Not only has hand-held graphing technology changed what we teach and how we teach, it has also changed how we test our students. For example if your students have access to graphing technology, is there any reason to ask them to graph a function? What about the graphs of functions containing discontinuities? These are quite often done incorrectly on the calculator. So, you may still want to test this skill. Hand-held graphing technology can easily graph quadratic functions. Should you ask your students to graph them? Maybe not, but could they graph the model of the volume of 1 mm of water at 4 degrees centigrade as a function of its temperature V = 0.000008059 - 0.00007999T + 1.00018?
Another approach in testing is to ask questions that allow students multiple methods for answering the questions. This usually was not a consideration before the use of hand-held technology permeated mathematics education. Teachers were usually interested in testing a particular algorithm, so the intent was to have students answer the question in only one way. Consider factoring 24 + 71x - 143 as an example. There are at least two ways of factoring the polynomial. One is the traditional method with pencil and paper, and the other is to find the zero with the zero-finder, convert it to a fraction and the student then immediately knows one factor. And if the student knows one factor, he/she knows the other factor. If the zero cannot be converted to a fraction or there are no zeros, the student knows the trinomial is not factorable over the rational numbers.
Since hand-held graphing technology does many of the traditional skills like graphing, finding zeros (solving equations), factoring, finding maximums/minimums, increasing/decreasing, confirm pencil and paper algorithmic work, etc., test questions may be directed toward concepts behind the above mentioned skills. For example, instead of asking students to graph a quadratic function, ask them to find when it is positive/negative/zero, when it is increasing/decreasing, what is the maximum or minimum, what is the range, etc.
These and other considerations will be developed in the paper.
© Asian Technology Conference in Mathematics, 1998. |
