The author replies to Silverstein:

How professors calculate α∞ should be driven by the concepts they choose to emphasize in their courses, the mathematical backgrounds of their students, and the facilities and equipment available at their institutions. Our purpose in choosing the technique described in the article was to help students visualize what time infinity is when the value of α is virtually unchanged. This particular approach emphasizes reading the graph, understanding the regression line that is used for time lag, and knowing that a 45-degree line is one where the input and output variables are identical. On our campus students typically enter physical chemistry after calculus II. The only regression they have seen in their mathematics coursework is linear regression in the precalculus course sequence taught with the graphing calculator. In fact very few undergraduate science curricula actually deal with the idea of regression at all. Unless students are taking statistics courses, very few will have had experience with nonlinear regression. This brings to light the importance for chemical educators to communicate with their mathematics’ colleagues.

When technology is used to help with mathematical calculations, the emphasis must be on the concepts being learned rather than simply the procedures (1, 2). Without this conceptual emphasis, students often blindly trust technology without questioning results, even on elementary calculations (3). In our approach we are attempting to help students learn more about the concept and also to attain data analysis skills they will need in the future. The graphing calculator is also capable of nonlinear curve fitting. While nonlinear curve fitting is a wonderful technique, it is something that should be taught so as to emphasize conceptual understanding and only after students really understand linear curve fitting. In fact, regression of any kind should only be introduced after students really understand the mathematical nature of the curves and the chemical reasons the curves display those mathematical properties.

Although there are easier and more accurate methods to calculate α∞ we used the approach printed in the article for the students’ benefit. While in the article we gave the exact feedback of the calculator to show its output, we agree that the k values in our method are accurate only to three or four significant figures. However for our educational purposes, the number of significant digits was less important than the students’ understanding of the concept.

Literature Cited

1. Davis, B.; Porta, H.; Uhl, H. Calculus & Mathematica. Addison-Wesley: Reading, MA, 1994.
2. Roddick, C. D. Primus 2001, 11, 161-184.
3. Glasgow, B.; Reys, B. J. School Science and Mathematics 2001, 98, 383-388.