Individual human tutoring is perhaps the oldest form of instruction. Countless millennia since its introduction, it remains the most effective—and most expensive—form of instruction. In late 1970s and early 1980s there was a surge of interest in the potential of artificial intelligence to capture some of the benefits of human tutors in computer-based tutoring systems (Sleeman & Brown, 1982; Wenger, 1987). Intelligent tutoring systems (ITSs) are problem-solving environments that variously employ expert systems to (a) reason about the problem-solving domain and analyze student activity, (b) make decisions about instructional interventions, and (c) reason about the student’s knowledge state. Early support for ITSs arose largely among artificial intelligence researchers who recognized them as rich environments in which to develop artificial intelligence algorithms. The principal measure of success was the proportion of student behaviors that an ITS could interpret and respond to meaningfully.
In the mid 1980s, our research lab began to develop a type of intelligent tutoring system called a cognitive tutor. Cognitive tutors are distinguished from the larger class of intelligent tutoring systems by their grounding in cognitive psychology. Each cognitive tutor is developed around a cognitive model of the problem-solving knowledge students are acquiring. A cognitive model is a type of rule-based expert system that is intended to solve problems in the same ways students solve them (e.g., Brownston, Farrell, Kant, &
Martin, 1985). The initial motivation was to evaluate and develop Anderson’s (1983) ACT* theory, a unified theory of the nature, acquisition, and use of human knowledge.
As a result, cognitive tutors are grounded in empirical evaluations and empirically driven cognitive theory. Our tutor evaluation criteria have been educational effectiveness (Anderson, Corbett, Koedinger, & Pelletier, 1995; Koedinger, Anderson, Hadley, &
Mark, 1997) and success in predicting student performance (Corbett & Anderson, 1995).
Cognitive tutor research has served to validate ACT*’s fundamental assumption that problem-solving knowledge can be represented as a set of independent if-then production rules (Anderson, Conrad & Corbett, 1989) and has served to refine the learning assumptions in the more recent ACT-R theory (Anderson, 1993; Anderson &
Lebiere, 1998).
Students working with a cognitive tutor interact with computer interfaces that support them in complex problem-solving activities. Under the surface, the Cognitive Tutor is
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tracking student problem solving actions using its cognitive model of the knowledge students are acquiring. Through a process we call model tracing, cognitive tutors can follow different students working through a problem in different ways and provide student-centered learning support that is adapted to each individual’s approach and needs.
Completing a Problem
Figure 9.1 displays the problem-solving interface of our Algebra I Cognitive Tutor near the end of a problem. The problem statement in the upper left corner of the screen presents a situation and asks several questions. Students answer the questions by filling in the worksheet in the lower left corner. The worksheet starts out as an unlabeled table of empty cells. Students first identify relevant quantities in the problem and label columns accordingly, then enter appropriate units in the first row of the worksheet, enter a symbolic formula for each quantity in the second row, and answer the questions in successive rows of the table. Students also graph corresponding functions with the graphing tool in the upper right corner. Again, the grapher tool is an unlabeled grid at the
FIG. 9.1. The Algebra I Cognitive Tutor screen near the end of a problem.
beginning of the problem. Students label the axes, adjust the bounds and scale for each axis, plot the points from the worksheet, plot the linear functions, and compute the intersection. A symbol manipulation tool (middle bottom window) is available for students to use in answering the questions and finding the intersection of the functions. In
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this figure, the student has completed three of the questions in the worksheet, used the symbol manipulation tool to solve an equation in answering one question, and graphed one of the two linear functions.
Note that at any point in time, the student may pursue a variety of problem solving goals. For example, this problem describes a hot air balloon that is ascending and a blimp that is descending, and the fourth question asks: “At this rate, when will the blimp land?”
The student might plausibly take four different problem-solving actions to begin tackling this question. She might:
1. Recognize that landing translates to a height of 0 and enter the given value 0 in the blimp column of row 4 in the worksheet;
2. Graph the blimp descent function to read off the elapsed minutes associated with a height of 0.
3. Use the equation solver to find the elapsed minutes associated with a height of 0 by solving 0=8500–250X.
4. Unwind the equation 0=8500–250X in her head to find the elapsed time and type the arithmetic expression -8500/250 in the Time column of row 4.
In model tracing, the cognitive model can be used to trace the student’s solution path no matter which of these options she pursues. The cognitive model runs in step-by-step synchrony with the student. At each step, the student’s action (e.g., typing in a worksheet cell) is compared to all the actions the model is capable of generating at the time. As with effective human tutors, cognitive tutor feedback is brief and focused on the students’
problem solving context. If the student action is correct it is simply accepted by the tutor.
If the student action is incorrect, it is rejected and flagged (either in red or bold font). If the incorrect action matches a common misconception, the tutor also displays a brief just- in-time error message in the messages window (the lower left window of Fig. 9.1). The tutor does not automatically provide detailed advice, but instead offers students the opportunity to reflect on and correct their own mistakes. However, the cognitive model provides problem solving advice if the student asks. There are generally three levels of advice available for each problem-solving goal. The first level reminds or advises the student of an appropriate goal to accomplish. The second level provides general advice on solving the goal. Finally, the third level provides concrete advice on solving the goal in the current context.
Figure 9.2 displays some snapshots of characteristic student-tutor interactions. In the left panel of Fig. 9.2.1 the student has read the problem description and correctly typed
“Time” at the top of the first column to label one of the relevant quantities. The student proceeded to label the second column, but typed a unit of measure—feet—instead of typing in the quantity that is being measured in feet. The tutor presents a just-in-time error message displayed in the right panel: “Feet is a unit to measure something in this problem. Try using a more descriptive phrase. What is measured in feet?” In the left panel of Fig. 9.2.2 the student has filled in the problem headers and requested help on the given value of the first question: “How long does it take for the blimp to descend to the height of one mile?” The right panel displays the three help messages that are displayed successively if the student asks for one, two, or three levels of help. When the second and third messages are presented, the words “blimp” and “height of one mile” are highlighted in question 1 of the problem statement window. In the left panel of Fig. 9.2.3 the student
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has entered the given value 0 for question 3: “Assuming the balloon has been climbing steadily, when did it leave the ground?” The student inadvertently entered the value in the blimp column instead of the balloon column and the tutor provides the just-in-time error message: “You have entered the given 0 in the wrong column of the worksheet.”
FIG. 9.2. Example student-tutor interactions.
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The cognitive model also is employed to monitor the student’s growing knowledge during learning, in a process we call knowledge tracing. The tutor infers the student’s knowledge of component problem-solving rules in the cognitive model from the student’s performance and uses these estimates to individualize the problem-solving sequence.
This student model is displayed on the screen in the “skillmeter” in the bottom right corner of Fig. 9.1. Each histogram represents a problem-solving rule in the model, and the shading represents the probability that the student knows the rule. Check marks indicate that the student has mastered the rule. Knowledge tracing is employed to individualize the problem sequence and help the student achieve mastery of the component problem-solving rules. Within each curriculum section, successive problems are selected to provide students the greatest opportunity to apply rules they have not yet mastered.
Cognitive Tutors in Context
Cognitive tutors are not intended to stand alone in education, but to serve as one tool in a full course curriculum. They do not provide declarative instruction, which is typically provided through class activities and reading. In our Cognitive Tutor Algebra and Geometry courses, 60% of class periods are organized around disposable looseleaf text materials. These class periods primarily consist of small-group problem-solving activities that are in turn reported to the full class. In the remaining 40% of class periods, students develop their individual problem-solving skills working with the cognitive tutor, which provides some of the benefits of an individual human tutor. Because help is available as needed on a step-by-step basis, students are able to advance at their own rate in the cognitive tutor lab and reach a successful conclusion to each task.
Cognitive tutors are not intended to replace the classroom teacher, but cognitive tutor courses offer most teachers new challenges and opportunities. While whole-group lecturing is the norm in American classrooms, learning is student-centered in our cognitive tutor courses and students learn by doing, rather than solely by listening and watching—both in the classroom and in the cognitive tutor lab. In the classroom, the teacher facilitates small-group problem-solving and whole-class discussions. In the computer lab, the tutors act as a set of classroom assistants that enable students to progress through the most common difficulties and free the teacher for more extensive individual interactions with students than are typically possible in a classroom setting.
Perhaps the most common concerns that teachers express in preservice training are their own unfamiliarity with the cognitive tutor technology and classroom management issues that may arise with students moving at their own pace in the cognitive tutor laboratory. In practice, however, these concerns do not materialize. Students easily become familiar with the technology, and the tutors provide just the support students need to move successfully at their own pace. When we hold in-service training sessions after the courses have started, teachers have more questions about managing small-group problem- solving than about managing the cognitive tutor lab.
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