This paper reports an empirical study which investigates a disparity between student-teacher rated scores in a criterion-referenced assessment (CRA) of a critical thinking and writing module for engineering undergraduates. Using the rubric as a self-assessment tool, students rated their self-confidence level and performance in terms of the critical thinking skills identified in Goldberg's Seven Missing Basics of Engineering Education, namely: "Inquiry," "Labelling," "Modelling," "Gathering Data," "Decomposition," "Visualization" and "Communication." Despite students' reports of high confidence levels in the acquisition of skills, weak positive correlations were observed between student and teacher-rated scores. This confirms the disparity between student-teacher assessments. Focus-group interviews with students revealed a lack of clarity in the rubric, and no provision of exemplary work as the two underlying reasons for the disparity. The findings provide pedagogical implications for effective rubric use and insights on issues in the development of rubric for self-assessment to enhance learning in higher education.