Realization of Techniques in Problem Solving: The Construction of Bijections for Enumeration Tasks.

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being cognizant of the technique, second for them to perform further mathematical modeling that should highlight the similarities in solution shared by all the tasks. In the fieldwork, a teaching sequence based on this approach is implemented for a technique involving enumeration via constructing a bijection. Certain factors in the students' behavior suggested that their realization of the technique at the end was not as secure as desired. Some modifications of the teaching sequence are proposed to counter these factors. [ABSTRACT FROM AUTHOR]