Systematic integration of a rubric in first-year engineering calculus courses

Abstract

ABSTRACT For many first-year engineering students, their first calculus or pre-calculus courses can be a substantial barrier for initial success and persistence to subsequent engineering courses. One approach that may mitigate this challenge for some students is to support their development as stronger metacognitive learners – learning how to self-evaluate and improve based on informed feedback. A structured mathematical problem-solving rubric designed to offer feedback on how to develop and communicate mathematical solutions to engineering problems can be a helpful tool to support metacognitive development. After a semester of careful and systematic instruction, practice, and use of such a rubric in engineering calculus courses, we found significant improvement in pre-calculus students' metacognitive awareness. A median split analysis showed that for both calculus and pre-calculus courses, the lower metacognitive half of each class improved significantly in their metacognitive abilities, as was the intent for the rubric. Students reported an overwhelmingly positive perception of the value of the rubric for their own learning, and the subset of calculus I students who improved in their sophistication of rubric use had significantly higher (12.5%) final exam scores compared to those who did not improve.