Abstract: This article reports the experience of a group of pre-service teachers when they discussed effective models for integer operations. While the participants proposed various models, analogies, and metaphors, it was difficult to find effective models that explain all the cases of integer operations and that were acceptable to all of them. This experience of discussing the rules for integer operations provided the participants with an opportunity to refine their prior knowledge and rediscover extant findings regarding effective mathematical models. However, their experience also revealed uncertainties about the mathematical and pedagogical nature of integer operations. Those uncertainties include the issues of convention versus understanding, the unnecessary complexity of the models, and the possibility of using models in a rote manner. The opportunity to discuss these models of integer operations helped the pre-service teachers to unpack their perceptions and understanding. For teacher educators, this work emphasizes the value of offering this type of activity in their mathematics teacher preparation courses.

Key words: Pre-service teacher education; Integers; Metaphors; Explanation