Chemical Education Today
Letters Problem Solving with Pathways
Tunneling Method As I perused my 575th issue of your Journal, I was pleased to see another “nuts-and-bolts” article, “Problem Solving with Pathways” (1). This was particularly so because I have been interested in the “Pathway Method” of solving chemistry problems for almost the whole period of my readership. At no stage did my involvement approach the sophistication of Joanne McCalla’s work, and I thank her for her in-depth review and useful literature citations. I cannot claim my introduction to the Pathway Method to have been inspired by Polya or Piaget. As a high school student, I enjoyed working out a given problem by as many methods as I could devise. A decade later, teaching high school and university, I developed the Pathway Method. Briefly, I believed this was a breakthrough, a discovery in teaching methodology. Then I came across a British textbook using this method, so most probably it was in use in many places. Further years of teaching and writing problems for textbooks, however, led me to what I would describe as a refine-
attack from both ends to establish the sequence of steps
target
direction of attack once sequence of steps has been found
mass glucose needed
number mole glucose needed
It is more efficient overall for a variety of students.
As an analogy, it is suggested that solving the problem is like getting from one side of a mountain to the other. Climbing over the top is not the easiest or most efficient way, if there already is a tunnel through. Just as the engineers building the tunnel plan to start at each end so that the excavators meet in the middle, so the student unravels the problem by starting at each end and linking up. Once the sequence of steps has been identified, the problem is solved by working forwards from the data to the target, as shown in the example below and in Figure 1. Problem: A moth of mass 1.10 g consumes 55 mL of oxygen (at 27 oC and 1.00 atm) per hour of flight. If glucose supplies the energy, what is the minimum mass of glucose that the moth must gather from plants for each hour of flight? C6H12O6 (aq) + 6O2(g) → 6CO2(g) + 6H2O(l)
1. McCalla, Joanne. J. Chem. Educ. 2003, 80, 92–98. 2. Smith, Alan; Dwyer, Christopher. Chemistry About You; Nelson: Melbourne, 1986, 1988; pp 190–191, 201–202. 3. Smith, Alan; Dwyer, Christopher. Key Chemistry, Book 1; Melbourne University Press: Melbourne, 1991; pp 463–464.
general gas equation
Alan L. H. Smith
volume O2 formed, temperature, pressure
Figure 1. Tunneling method applied to the chemistry problem in the text.
www.JCE.DivCHED.org
It helps to avoid time-wasting side tracks
Literature Cited
molar ratio in chemical equation
number mole O2
initial data
It helps save the struggling student from getting overwhelmed and lost in the problem
My approach has developed from “hands-on” experience rather than an in-depth study of learning theory, but it would be interesting to see an evaluation of the tunneling method.
m = nM
the vital link
ment of the Pathway method. I refer to what I have called the “tunneling method”. Again, I am not claiming discovery rights, but I did develop it from my own pondering on why some students just can’t think their way through a problem involving several steps. The tunneling method has been discussed in two of my textbooks (2, 3). The strategy is to start from each end, and link somewhere in the middle, rather than working backwards, stepwise from the objective or target to the data. I believe that this approach has several advantages:
•
22 Packham Street Box Hill North Melbourne, Victoria, 3129, Australia
[email protected] author replies:
Vol. 81 No. 6 June 2004
•
Journal of Chemical Education
803
Chemical Education Today
The author replies: 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. 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. Joanne McCalla St. Lawrence Campus of Champlain Regional College 790 Nérée Tremblay Ste-Foy, Québec G1V 4K2, Canada
[email protected] L O2
g glu
180 g glu mol glu u
6 mol O 2 mol glu
mol glu
mol O2
PV = nRT
55 mL O2
T = 300 K
P = 1.00 atm
Figure 1. Pathway for the problem described in Smith’s letter.
804
Journal of Chemical Education
•
Vol. 81 No. 6 June 2004
•
www.JCE.DivCHED.org
