There are increasing calls to prepare K-12 students to use computational tools and principles when exploring scientific or mathematical phenomena. The purpose of this paper is to explore whether and how constructionist computer-supported collaborative environments can explicitly engage students in this practice. The Categorizer is a Javascript-based interactive gallery that allows members of a learning community to contribute computational artifacts they have constructed to a shared collection. Learners can then analyze the collection of artifacts, and sort them into user-defined categories. In a formative case study of the Categorizer for a fractal activity in three middle grade (ages 11-14) classrooms, there was evidence that participating students began to evaluate fractals based on structural and mathematical properties, and afterward could create algorithms that would generate fractals with particular area reduction rates. Further analysis revealed that students' construction and categorization experiences could be better integrated by explicitly scaffolding discussion and negotiation of the categorization schemes they develop. This led to the development of a new module that enables teachers and students to explore points of agreement and disagreement across student categorization schemes. I conclude with a description of limitations of the study and environment, implications for the broader community, and future work.