| The mathematics reform calls teachers to encourage and accept a variety of different solution methods in the classroom. When examining these different solutions, a distinction can be made between those that more directly model the action suggested in the problem and those that are non-modeling solution methods. In this study, five teaching scenarios were created and twenty pre-service teachers were individually interviewed. Each scenario involved a student presenting a non-modeling solution method that caused confusion for other students in the class. Pre-service teachers' responses to the interview were analyzed according to how they might deal with these scenarios in their own classroom. Specifically, the responses were analyzed by comparing the pre-service teachers' mathematical knowledge, knowledge of student's thinking, and pedagogical knowledge. The teaching and learning experiences that most influenced the way the pre-service teachers responded were also explored.; The findings suggest that while the pre-service teachers generally encouraged different types of solution methods, many did not attend to the distinction between a more modeling or non-modeling method. Two important aspects used in the analysis were whether pre-service teachers attempted to connect solution methods to each other and whether they centralized the non-modeling nature of the solution when dealing with student confusion. The study suggests that scenarios such as the ones used in the interviews might be used as "teaching tools" to help pre-service teachers identify student confusion and understand differences between modeling and non-modeling solution methods. |
