This paper describes the AI Drawing Partner, which is a co-creative drawing agent that also serves as a research platform to model co-creation. The AI Drawing Partner is an early example of a quantified co-creative AI system that automatically models the co-creation that happens on the system. The method the system uses to capture this data is based on a new cognitive science framework called co-creative sense-making (CCSM). The CCSM is based on the cognitive theory of enaction, which describes how meaning emerges through interaction with the environment and other people in that environment in a process of sense-making. The CCSM quantifies elements of interaction dynamics to identify sense-making patterns and interaction trends. This paper describes a new technique for modeling the interaction and collaboration dynamics of co-creative AI systems with the co-creative sense-making (CCSM) framework. A case study is conducted of ten co-creative drawing sessions between a human user and the co-creative agent. The analysis includes showing the artworks produced, the quantified data from the AI Drawing Partner, the curves describing interaction dynamics, and a visualization of interaction trend sequences. The primary contribution of this paper is presenting the AI Drawing Partner, which is a unique co-creative AI system and research platform that collaborates with the user in addition to quantifying, modeling, and visualizing the co-creative process using the CCSM framework.