I really enjoyed reading articles about mindful learning by Ellen J. Langer. The results of experiments in the article (pay attention vs. notice new things, and tasks vs. play) were very interesting but not surprising. I have already experienced this behavior in some classes. Here is an example. I was teaching assistant for an undergraduate course. The first semester, the instructor told students that we will have 4 exams before the final exam. That semester, some students were always complaining about the number of exams in my office hours! Next semester, the instructor changed the syllabus and told students we do not have any in-class exams. Instead, we will have only four quizzes. In the second semester, students never complained about the number of quizzes, although the workloads and quizzes were similar to the previous semester’s exams!
I think mathematical modeling of a problem is one of the most difficult skills to teach in my field. Here is a very simple example: we have four employees and four different jobs. Employees have different skills. How to assign the employees to the jobs in order to have maximum efficiency? This is a simple problem that students learn to model it (See the following picture for a more complicated mathematical model).
One difficulty of the mathematical modeling is that the problems do not have one unique model and each person can model a problem differently. In addition, the number and type of problems are not limited. There are complicated problems that scientists still cannot model it mathematically. Therefore, we cannot teach a specific technique to the students and tell them that use this technique in order to model all types of problems (there is only a general guideline). Students should learn to be creative facing with different problems. Teaching the modeling skill to new students in the field is a very difficult and challenging job. I have seen many students struggling to learn mathematical modeling and complaining about instructors. I also have seen a student used the YouTube to learn mathematical modeling and said that this is more helpful than the class and I should not go to the class anymore!
Teaching the modeling skill is not possible without engaging students and encouraging them to learn mindfully. In my opinion, this is why some instructors are more successful in teaching this skill even through the YouTube. I definitely will think and read more about encouraging mindful learning and ways to improve it in the classes. Thanks to Dr. Langer for the amazing articles.