Assignment 3: Will Hui

I once tutored a student for a high school algebra class. These were weekly private tutoring sessions, for a time period of a few months. The group consisted of myself and the student, and the task was to improve the student’s grades in algebra. In order to accomplish this, we went through the material together and I helped her work through some of the textbook exercises directly.

Internal representations consisted of her existing knowledge of the subject and my own knowledge and experience with algebra. External representations included words and diagrams in the textbook, any written notes or scratch work, and all verbal exchanges. Algebra knowledge was present in all of the representations mentioned above. Specific examples, solutions, and other applications of the material were given as part of the textbook representation.

Our overall goal was to transform algebraic knowledge drawn from both my internal representation and the textbook’s external representation into a form suitable for her internal representation. To do this, I first referred to the textbook to refresh my memory of the topic. During this process, any forgotten information was transformed from the textbook pages into my internal memory. I then taught the material by transforming the knowledge into verbal representations (by talking) and physical representations (by writing on paper). The student, in turn, transformed the verbal and physical information back into an internal representation, by committing it to her memory. When the student worked through practice problems, her internal representation got transformed onto paper. Through the reverse sequence of transformations, I could to verify whether or not her understanding of the material was correct. This cycle of feedback was repeated until we reached our goal.

This task was highly coupled, primarily due to the task’s uncertainty. We didn’t already share a common degree of understanding of the material (otherwise the entire interaction would have been pointless to begin with). I didn’t know beforehand what parts of the material she had trouble understanding, and she may not necessarily have known what the core problems were either. The process of determining what the troubles were is non-straightforward.