Recently, Joanne McCalla published a very interesting and thought-provoking article (1), "Problem Solving with Pathways", about a problem solving method based on a visual pattern. I have some remarks and comments on her work.

First, the method mentioned in the article belongs to the concept-oriented teaching methods. (I note that it is possible to use another teaching method belonging to the group of strategy-oriented methods. However, for beginners concept-oriented teaching methods may be more helpful than strategy-oriented ones.) The concept-oriented teaching methods focus on the construction of a concept-network (pathway) between the "Given" and the "Objective". This construction may be a linear thinking process especially for beginners. They usually try to build this pathway going from the Given to the Objective (Given → Objective), or simply they calculate something from the Given without building any pathway. The other possibility for building the network between the Given and the Objective by linear thinking way is the Pathway method (Objective → Given) elaborated nicely by the author. However, the problem solving of the experts usually is a non-linear process. Therefore the goal of any teaching method should be in developing this non-linear process: how to build the pathway between the Given and the Objective going from the Given to the Objective and vice versa simultaneously (Given → … ← Objective). For this purpose the teaching of Pathway method is very useful, because most of the students are familiar with building from the Given to the Objective, but they usually have no practice in the reverse way of thinking.

Second, the visual representation of the concept-network between the Given and the Objective is very important and useful not only from point of view of teaching, but in evaluating the students' answers and furthermore, in constructing databases for different types of problems. From this visual representation we can conclude, for example, that the concept-networks (pathways) of chemical problems contain mostly three- and two-unit blocks as it is shown in Figure 1 of the article. So we can establish that the starting point of any teaching method (concept-oriented or strategy-oriented) should be in preparing the students to be familiar with these blocks. Furthermore, this visual representation gives the possibility to construct chemical puzzles, in which students must complete a partly incomplete concept-network. Building the visual representation of the pathway may help to identify the unnecessary or missing information.

Third, the author defined a "Pathway-use parameter" (0–3) in order to evaluate the quality of the student's pathway construction, and this parameter was used in the Kolmogorov–Smirnov test. She divided the students into two groups. Students using Pathway-method successfully (their "Pathway-use parameter" is 2 or 3) belong to the first group, and students using another method (score 0) or using the Pathway but not successfully enough ("Pathway-use parameter" is 1) belong to the "control" group. In my opinion the later students should be considered in the first group, because they tried to use the Pathway method, but didn't do it successfully.

Finally, I would like to remark that this Pathway method and its visual representation is a very useful tool in teaching numerical problems in chemistry.

Literature Cited

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

See the author's reply.