A cognitive tutor is a particular kind of intelligent tutoring system that utilizes a cognitive model to provide feedback to students as they are working through example problems. This feedback usually consists of immediately informing students of the correctness, or incorrectness, of their actions in the tutor interface; however, cognitive tutors also have the ability to provide context-sensitive hints and instruction to guide students towards reasonable next steps.
Cognitive Tutor ® is also the name of an particular cognitive tutor produced by Carnegie Learning for mathematics. A 2009 report from the Institute for Education Sciences's What Works Clearing House found Cognitive Tutor ® Algebra I to have potentially positive effects on mathematics achievement.
The Cognitive Model
Cognitive Tutors can trace their roots to the ACT-R theory of cognition, which is founded on the assertion that cognitive skills are realized by production rules. One distinguishing feature of the ACT-R model is its commitment to a separation of memory into two types: declarative, which correspond to facts (e.g., the concept of an integer) and procedural, which corresponds to the cognitive skills that operate over facts (e.g., the mental skill to add two integers). In proposing the model, John Anderson presented evidence that by modeling procedural knowledge as production rules we can directly observe student learning; the more opportunities students have to use a given production rule the faster and more accurately they can apply it.
Building on this discovery, cognitive tutors have a production rule model of the skills needed to solve problem sets. As students solve problems in the tutor interface, the tutor uses its model for two purposes. First, the model is usually used to give immediate feedback to students. For example, if a student produces a solution step that is not allowed by the tutor's model, then it might give feedback to the student—informing them that the action is incorrect. The second use of the model is to assess student ability. This assessment is performed by observing each step the student makes and applying a technique called model tracing to identify which procedural skills the students are using to produce each step. Once these skills have been identified, an approach called knowledge tracing can be used to assess each student's latent ability in each skill; this assessment is based on how many opportunities the student has had to apply the skill and how often they correctly apply the skill in these instances. Once the cognitive tutor has a model of each student's ability, it can use this model to determine pedagogically effective moments to give the students additional feedback, hints, or instruction.