Once an instructor has made explicit the mental operations that students must master in order to get past a bottleneck (STEP 2), it is necessary to devise strategies to help students learn each of these steps. It very important to :
Focus on the most essential mental operations. It is important to decide which mental operations should be modelled and which have already been mastered by all or almost all of the students. Obviously, it is not necessary to devote valuable class time to going over skills that have already been thoroughly mastered. Therefore, it is often useful to use assessments early in a course to see which mental operations it is necessary to focus on. If a small number of students are lacking an understanding of operations already mastered by the rest of the class, it may be advisable to give them pathways to mastering these skills outside the regular course, e.g, special web sites or tutoring sessions.
Model each mental operation by itself. It is much more difficult for students to learn when a number of steps are being presented at the same time. Therefore, it is generally important to break them down into their component parts and to model each separately.
Think strategically about the order in which modeling occurs and consider its connection to other elements in the course. Some attention should be devoted to deciding the logical order in which to model these operations and, when possible, the modeling should be integrated with the content of the course. The modeling of specific steps should also be coordinated with specific opportunities for students to practice these skills and receive feedback (STEP 4).
Model the same mental operations repeatedly and in different forms. In most cases these operations will need to be modeled repeatedly across the course and, ideally, in different forms. The goal should be to make the modeling process such a central part of a class that it informs every aspect of the course from the course description to the form of assessments, thereby reinforcing the learning.
In many cases show students how to bring the steps together in more complex tasks. In some cases it will be necessary to model, not only the individual mental operations, but also the process of combining these in more complex class activities, such as writing a paper or conducting an experiment.
Modeling in the Classroom (Face-to-face or virtual)
A good deal of the modeling described above will occur in formal settings, in which the focus of the activity will be upon showing students just what they need to do to overcome potential bottlenecks to learning. We have found that such presentations are generally more effective, if instructors do three things:
- Present a clear metaphor or analogy that makes clear the kind of thinking required to overcome the bottleneck;
- Perform the kinds of thinking students must be able to replicate, in a form that makes the necessary steps clearly visible to them;
- Make explicit the relevance of the process that is being performed by the instructor to the learning in the course — i.e. to not only do the task in front of them, but also to make meta-comments about the steps that are being done and how they relate to the kinds of tasks that students face in the course at hand.
NOTA BENE: modeling is generally not sufficient by itself to allow students to master difficult mental operations. Therefore, in most cases it needs to be supplemented by opportunities for students to practice these skills and receive feedback on them (STEP 4).