BOX 3.5
The Algebra Cognitive Tutor

The Algebra Cognitive Tutor is one of a set of cognitive tutors developed at Carnegie Mellon. Of great relevance to the SERP vision, the tutors are a good illustration of how to make the transition from the laboratory to the classroom. The work at Carnegie Mellon began as a project to see whether a computational theory of thought, called ACT (Anderson, 1983), could be used as a basis for delivering computer-based instruction in algebra. The ACT theory of problem-solving cognition is the basis for modeling students’ algebra knowledge. These models can be captured in a computer program that can generate or identify a range of characteristic approaches to solving an algebra problem. These cognitive models enable two sorts of instructional responses that are individualized to students:

  1. By a process called model tracing, the program will infer how a student is going about problem solving and generate help and instruction appropriate to where that student is in the problem.

  2. By a process called knowledge tracing, the program will infer where a student falls in the learning trajectory and select instruction and problems appropriately.

Developing cognitive models that accurately reflect competence and developing appropriate instructional responses is an iterative process. The success of the tutors depends on a design-test-redesign effort in which models are assessed for how well they capture competence and instructional responses are assessed for how effective they are.

In studies of cognitive tutors more generally, it was found that in controlled laboratory condition students using a cognitive tutor could go through a curriculum in a third of the time, and in carefully managed classrooms students would show about a standard deviation (approximately a letter grade) improvement in achievement compared with students receiving standard instruction (Anderson et al., 1995). In real classroom situations, the impact of the tutors tends not to be as large, varying from 0 to 1 standard deviation across more than 13 evaluations. Another third-party evaluation, focusing on the social consequences of the tutors, documented large motivational gains resulting from the active engagement of students and the successful experiences on challenging problems (Schofield et al., 1990).

However, unlike many such small-scale success stories in cognitive science, this project was able to grow to the point at which the cognitive tutors now are used in over 1,200 schools, 46 of 100 largest school districts, and interacting with about 170,000 students yearly. A number of features were critical to making this successful transition:

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