Computer Problem-Solving Coaches Leon Hsu and Kenneth Heller University of Minnesota, Minneapolis, MN 55455 Abstract. Computers might be able to play an important role in physics instruction by coaching students to develop good problem-solving skills. Building on previous research on student problem solving and on designing computer programs to teach cognitive skills, we are developing a prototype computer coach to provide students with guided practice in solving problems. In addition to helping students become better problem solvers, such programs can be useful in studying how students learn to solve problems and how and if problem-solving skills can be transferred from a computer to a pencil-and-paper environment. INTRODUCTION The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. In particular, good problem-solving skills are critically important for scientists and engineers, who use these skills to create new knowledge and to apply existing knowledge to the real world. Because an introductory course in physics is a pre-requisite for study in nearly all science and engineering fields, it is an ideal venue for teaching problem solving. However, studies have shown that the majority of students emerge from such courses having made little progress toward developing good problem-solving skills [1]. One obstacle to students’ learning effective problem-solving strategies is the difficulty and expense of providing good coaching, i.e., supplying students with an environment where they receive guidance and feedback while they solve problems. Even when the instructor and textbook model good problem-solving techniques, students often continue to use previously developed weak strategies and not those that are modeled [2]. In this paper, we present a framework for combining previous research in student problem solving with research in student-computer interactions to develop a practical means of providing every student with effective coaching in problem solving. We then describe our ongoing efforts to implement
these ideas by designing a prototype of a computer problem-solving coach for students. Because this type of coaching focuses on the underlying student problem-solving process, it has little in common with existing computer homework systems that provide hints for specific problems. The work described in this paper is concerned with the practicality of building a software coach that interacts with students. After several prototypes have been constructed, we intend to test their efficacy first in small pilot studies of a few students and then in large-scale classroom trials.
RESEARCH BASE Data exists on curricular interventions designed to help students become better problem solvers [3]. Each of the successful interventions had three common features: (1) explicit teaching of a problem-solving framework, (2) modeling of the use of the framework by the instructor, and (3) students using the framework when solving problems. All of the problem-solving frameworks are based on the strategy developed by Polya [4]. The Minnesota problem-solving framework, shown in Fig. 1, is a typical example. Since real problem solving is rarely linear, Fig. 1 is meant only to outline the basic stages through which a solver might loop multiple times, and not to imply that problem solving can be reduced to a linear algorithmic process.

In the curricular applications, the instructor models good problem-solving techniques, usually during lectures, making explicit reference to the framework, and students are required to use the framework in their own problem solutions [5]. This strategy for teaching problem solving stems from the cognitive apprenticeship approach [6], in which the instructor models and makes explicit the cognitive processes necessary for performing a task and students are then expected to perform similar tasks with guidance before performing them on their own. In a standard physics class, students may have opportunities to practice solving problems in recitations, where they can receive feedback from both their peers and instructors [7,8]. Built into the framework for successful problem solving are the basic cognitive functions of deciding, implementing, and assessing. At each step in the solution process, the solver must decide on an action, implement it, and assess whether the implementation is adequate. Expert problem solvers perform these functions automatically, as an adult might tie a shoe. Novices, however, must be deliberate in their performance in order to succeed. Students usually focus on implementing and rarely make deliberate decisions or assess their performance. This failure to make deliberate decisions often results in students’ invoking inappropriate or incorrect knowledge, in not recalling useful knowledge they do have, and in applying procedures incorrectly. This process leads not only to incorrect problem solutions,
but also to a failure to learn from one’s mistakes. A good problem-solving aid should make these basic cognitive functions explicit to the student and enable the student to practice each one with feedback.
COMPUTER COACHES One fundamental limitation of the curricular methods described previously is the reliance on interactions with peers or an instructor to achieve targeted coaching. Social interaction is likely a necessary part of an efficient learning process but does not allow for enough guided practice for most students. In many large lecture classes, students have less than one hour each week of organized practice solving problems in the supportive environment of a small group discussion section with a knowledgeable instructor. The availability of powerful personal computers has led researchers to try to exploit their capabilities to provide students with individualized guidance and feedback [9]. Reif and Scott [10] developed a set of computer coaches called Personal Assistants for Learning (PALs) designed to teach students how to apply Newton’s motion law, Fnet = ma. A pilot study of the PALs found that such coaches could help students improve their ability to apply Newton’s motion law to solving problems. Our goal is to build on previous work to develop computer coaches (called PS-PALs or Problem-Solving PALs) that can help students learn to solve the full range of problems they encounter in a typical introductory physics course. PS-PALs differ from PALs in that the previous coaches by Reif and Scott were designed to help students apply Newton’s motion law to a problem for which it was already known that such an approach would lead to a successful solution. PS-PALs are designed to coach students in the more difficult and useful problem-solving practice of decision making: it is the student who must decide which physics principle(s) (e.g., kinematics, Newton’s laws, conservation of energy or momentum, etc.) are necessary for solving the problem, in addition to applying the principle(s) correctly. Following the literature on designing effective cognitive tutors [9], PS-PALs are based on a task analysis of the thought processes required to use a systematic problem-solving framework and give students guided practice performing these thought processes while solving problems. PS-PALs also give students immediate feedback on errors and gradually
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1. Focus the problem
• Draw a picture illustrating the situation
• Determine the question to be answered
• Choose which physics principle(s) to use
2. Describe the physics
• Draw physics diagrams
• Determine target quantity(ies)
• Write down quantitative relationships
3. Plan the solution
• Select equation containing the target quantity
• Identify other unknowns in equation
• Solve a sub-problem to find each unknown
• Check units
4. Execute the plan
• Calculate value of target quantity(ies)
5. Evaluate the answer
• Check if answer is properly stated
• Check if answer is unreasonable
• Check if answer is complete
Minnesota problem-solving framework
FIGURE 1. The Minnesota problem-solving framework.