A cognitive tutor is a tutoring system that has students solve multi-step tasks on a user-interface that allows them to enter those steps. The tutor gives immedaite feedback on each step, indicating whether it is correct or incorrect. Students can ask for hints, and often do so immediately after the cognitive tutor has told them that the step they just entered is wrong. Cognitive tutors are known to be more effective than having students solve the same problems without the aid of a tutor, and they are the central components of some highly effective mathematics interventions. Early work on cognitive tutors is summarized in Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The Journal of the Learning Sciences, 4, 167-207.
On the basis of these successes, a company, Carnegie Learning has developed a series of mathematics curricula that include cognitive tutors. Their web site includes many reports of evaluations, most of which show impressive positive results when students use the tutor-based controls, compared to control instruction. The PSLC Algebra and Geometry LearnLabs are the results of a collaboration between PSLC, Carnegie Learning and several school system.