Assessment in Computer Supported Collaborative Learning (CSCL) is an implicit issue, and most assessments are summative in nature. Process-oriented methods of assessment can vary significantly in their indicators and typically only partially address the complexity of group learning. Moreover, the majority of these assessment methods require time-intensive coding of qualitative data. Our study explores the operationalization of activity theory to frame group activity in a CSCL context by breaking group work into six dimensions. We map log data generated by a collaborative software, Virtual Math Teams with Geogebra, with these dimensions and construct six measures to lay the groundwork for automating CSCL assessment. Next, we move beyond identification and analysis of those measures to infer group learning using human judgment and employ a clustering algorithm to categorize groups with similar performance, allowing us to consider the six indicators simultaneously and to step further toward assessment automation. Last, in terms of the complexity of group learning in a socio-technical context, we discuss a web-based tool that not only shows group-level assessment but also integrates with our previous work on individual assessment, thus providing teachers with a diverse of group learning.