The author replies to Smith.

As a "nuts and bolts" kind of person, I was interested to read of Alan Smith's involvement in teaching problem solving in Australia. This is truly a global endeavor. It seems clear that the "tunneling method" that he describes has some elements in common with the Pathway method as I have developed it (1). Both methods insist on thinking through the problem before any calculations are attempted. The tunneling method shares with the Pathway method a process of focussing, at least partially, on the Objective of the problem. Where we differ is that Smith would encourage students to develop the logic from both the Objective and the Given, to join the two partial pathways in the middle, in the analogy of building a tunnel from both ends. The Pathway method, on the other hand, restricts its focus to the Objective, each successive link becoming a new objective until the information in the Given is encountered. Both approaches have advantages, but I would wonder if it ever happens that the excavators digging the tunnel from the two ends fail to meet in the middle. If this happened, would the tunnel being built from the Objective then simply continue until it reached the Given? If this were to happen, would we not then be back to the Pathway method?

Figure 1 shows a Pathway for the problem described in Smith's letter. Clearly the logic connections are identical. Smith uses more words, and works from top to bottom (and bottom to top) of the page, to reach the meeting point. The Pathway has an advantage in working left to right, in that the students have long training in this mode of perusal, and it is easy to integrate this into their work on the page. When this process is carried out with the older "technology" of pen and paper, it is even more compact than it appears here: the boxes are only necessary because of the demands of word processing.

Figure 1. Pathway for the problem described in Smith's letter.

I would agree with Smith that it can be very efficient to work the logic from both ends, but I would add that this is more likely to be the case as the problem solver becomes more expert. As the learner understands more fully the material on which the problems are based, more and more "chunks" of Pathway come to be regarded as single units, with the result that problem solvers become more adept at thinking from both the Given and the Objective.

Despite these differences, it should be clear that both approaches are attempting to help our students become more independent in their problem solving behavior, and that is the main point in all of this.

Literature Cited

1. McCalla, Joanne. J. Chem. Educ. 2003, 80, 92-98.