accomplish two of the principal tasks characteristic of human tutoring: (1) monitors the student's performance and providing context-specific individual instruction, and (2) monitors the student's learning and selects appropriate problem-solving activities. Both cognitive model and two underlying algorithms, model tracing and knowledge tracing, are used to monitor the student's learning. In model tracing, the cognitive tutor uses the cognitive model in complex problems to follow the student's individual path and provide prompt accuracy feedback and context-specific advice. In knowledge tracing, the cognitive tutor uses a simple Bayesian method of evaluating the student's knowledge and uses this student model to select appropriate problems for individual student. Cognitive architecture Cognitive tutor development is guided by ACT-R cognitive architecture, which specifies the underlying framework developing the cognitive model or expert component of a cognitive tutor. ACT-R, a member of the ACT family, is the most recent cognitive architecture, devoted primarily to modelling human behavior. ACT-R includes a declarative memory of factual knowledge and a procedural memory of production rules. The architecture functions by matching productions on perceptions and facts, mediated by the real-valued activation levels of objects, and executing them to affect the environment or alter declarative memory. ACT-R has been used to model psychological aspects such as memory, attention, reasoning, problem solving, and language processing. Application and utilization The first real world applications of cognitive tutors were a geometry proof tutor used by high school students and a mini course in Computer Science at Carnegie Mellon University using the LISP tutor with college students. Since then, cognitive tutors have been used in a variety of scenarios, with a few organizations developing their own cognitive tutor programs. These programs have been used with students spanning elementary school through university level, though primarily in the subject areas of Computer Programming, Mathematics, and Science. One of the first organizations to develop a system for use within the school system was the PACT Center at Carnegie Mellon University. Their aim was to "...develop systems that provide individualized assistance to students as they work on challenging real-world problems in complex domains such as computer programming, algebra and geometry". PACT's most successful product was the Cognitive Tutor Algebra course. Originally created in the early 1990s, this course was in use in 75 schools through the U.S. by 1999, and then its spin-off company, Carnegie Learning, now offers tutors to over 1400 schools in the U.S. The Carnegie Mellon