Despite emphasis and progress in developing collaborative inquiry in computer-supported collaborative learning research, little attention has been given to examining how collective learning can be assessed in computer-supported collaborative learning classrooms, and how students can have agency in assessing their own collaborative process. We propose that assessments should capture both individual and collective aspects of learning and be designed in ways that foster collaboration. We describe the design of student-directed electronic portfolio assessments to characterize and "scaffold" collaborative inquiry using Knowledge Forum[TM]. Our design involved asking students to identify exemplary notes in the computer discourse depicting knowledge building episodes using four knowledge building principles as criteria. We report three studies that examined the designs and roles of knowledge building portfolios with graduate and Grade 12 students in Hong Kong and Canada. The findings suggest that knowledge building portfolios help to characterize collective knowledge advances and foster domain understanding. We discuss lessons learned regarding how knowledge building may be fostered and provide principles for designing assessments that can be used to evaluate and foster deep inquiry in asynchronous online discussion environments.