A simple learning environment improves mathematical reasoning

Abstract

ANIMATE, an interactive computer animation-based tutor, has been developed as part of an on-going test of a theory of word problem comprehension. Tutor feedback is unobtrusive and interpretive: unexpected behavior in the equation-driven animation of a situation highlights equation errors which the student resolves through iterative debugging. The student has responsibility for learning, goal-setting and diagnosis. Experimental controls (n = 96) with Motion problems show that improvement cannot be solely attributed to practice, computer use, or use of the situation-based method. Concurrent think-aloud protocols of students (n = 7) solving Motion, Work and Investment problems over two days (in a pretest-posttest design) uncover specific changes which underlie these improvements. ANIMATE is an effective problem-solving aid, and there is transfer of learning. Problems with impossible situations were acknowledged by median-level subjects (posttest scores between 77% and 85%), but solved blindly by high-level subjects (post test scores > = 95%), suggesting an automatically controlled processing dichotomy. On Day 2, subjects spent more time reviewing problem texts and correcting flawed expressions. They developed self-directed debugging skills, reminiscent of expert problem-solving in many domains, without relying on tutor feedback behaviors. The system is unintelligent by ITS standards but communicates knowledge to the students, helping them teach themselves approaches for mathematical problem-solving.