Algebra Cognitive Tutor

• Anderson’s group (Anderson, Corbett, Koedinger, & Pelletier, 1995), and has been extended and marketed by Carnegie Learning (<www.carnegielearning.com)>
• Because it is so widely used and has undergone so many positive evaluations, it is arguably the most successful ITS in the world at this time.
• Inner loop: The inner loop monitors the student’s steps while solving an algebra problem.
• Although most problems, including the one in Figure 2, involve using multiple representational tools (graphs, tables, etc.) to analyze a problem scenario, some problems focus only on specific tools, such as the equation solver. In Figure 2, the problem to be solved is shown in the upper left window. This problem has four parts, labeled 1 through 4. When the student began, the cells of the table in the worksheet window at the lower left were all empty. The student has filled every cell with a number, text or an algebraic formula. In the process of figuring out what to put in the cells, the student used the solver window (upper right) and the graphing window (lower right). Each time the student filled a table cell, plotted a point on the graph, entered an equation in the solver window, etc, the tutor gave immediate feedback that told the student whether the step was correct or incorrect.
• Outer loop: The outer loop in the Algebra I Algebra Cognitive Tutor selects an algebra problem for the student to do and makes sure that the student submits a solution. The tutor uses its fine-grained assessment to select a task that exercises a few knowledge components that the student has not yet mastered. When the student has mastered all the knowledge components in a unit (all the bars turn gold), the student is advanced to the next unit in the algebra curriculum.
• Step analysis: The tutor analyzes each student step in terms of a set of anticipated steps (S. Ritter, Blessing, & Wheeler, 2003). The set of anticipated steps for a problem is precomputed by solving the problem in all acceptable ways by running a rule-based problem solver. The rules are written to correspond to knowledge components. Each step is associated with the rules that were used to generate it during the precomputation. During tutoring, the student’s step is matched against these anticipated steps.
• When a student’s step matches an anticipated step, the student is credited in the assessment with having applied the associated knowledge components.