Abstract: Computer-based learning tools can be exploited to make physics teaching and learning interactive, self-paced, and meaningful. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while learning physics concepts.

The diversity of students' preparation and backgrounds in introductory physics courses for science and engineering majors has increased significantly. Even a conscientious instructor cannot gear the level of classroom instruction for all students and perhaps focuses on an average student. Those with inadequate preparation may struggle to learn basic concepts and skills. Insufficient background is detrimental for learning physics because of the hierarchical knowledge structure of the discipline and the need for learning strategies for solving problems effectively.

Technology can be exploited to help students learn if it is used in a pedagogical manner commensurate with the need and prior knowledge of students. Online homework systems such as Web-Assign, LON-CAPA, and Mastering Physics are already being exploited extensively in introductory physics courses to grade students' homework [1]. Here, we describe computer-based tutorials which are self-paced and focus on helping students with a wide range of content knowledge and skills, including those at risk. Textbook publishers are increasingly providing tutorials with their online homework systems.

The computer-based interactive problem solving tutorials that we have been developing for introductory physics combine quantitative and conceptual problem solving. They focus on helping students develop a functional understanding of physics while learning useful skills [2]. If only quantitative problems are asked, students often view them as "plug-and-chug" exercises, while conceptual problems alone are often viewed as guessing tasks with little connection to physics content. The interactive tutorials combine quantitative and conceptual problem solving and provide guidance and support for knowledge and skill acquisition. They help students tackle quantitative problem solving not merely as a mathematical exercise but as a learning opportunity. They provide a structured approach to problem solving and promote active engagement while helping students develop self reliance.

Effective problem solving begins with a conceptual analysis of the problem, followed by planning of the problem solution, implementation and evaluation of the plan, and last but not least reflection upon the problem solving process. As the complexity of a physics problem increases, it becomes increasingly important to employ a systematic approach. In the qualitative or conceptual analysis stage, a student should draw a picture or a diagram and get a visual understanding of the problem. At this stage, a student should convert the problem to a representation that makes further analysis easier. After getting some sense of the situation, labeling all known and unknown numerical quantities is helpful in making reasonable physical assumptions. Making predictions about the solution is useful at this level of analysis and it can help to structure the decision making at the next stage. The prediction made at this stage can be compared with the problem solution in the reflection phase and can help repair, extend and organize the student's knowledge structure. Planning or decision making about the applicable physics principles is the next problem solving heuristic. This is the stage where the student brings everything together to come up with a reasonable solution. If the student performed good qualitative analysis and planning, the implementation of the plan becomes easy if the student possesses the necessary algebraic manipulation and mathematical skills.

After implementation of the plan, a student must evaluate his/her solution, e.g., by checking the dimension or the order of magnitude, or by checking whether the initial prediction made during the initial analysis stage matches the actual solution. One can also ask whether the solution is sensible and, possibly, consistent with experience. The reflection phase of problem solving is critical for learning and developing expertise. Research indicates that this is one of the most neglected phase s of problem solving. Without guidance, once a student has an answer, he/she typically moves on to the next problem. At reflection stage, the problem solver must try to distill what he or she has learned from solving the problem. This stage of problem solving should be used as an opportunity for reflecting upon why a particular principle of physics is applicable to the problem at hand and how one can determine in the future that the same principle should be applicable even if the problem has a new context.

The development of the computer-based tutorials to help students learn effective problem solving strategies is guided by a learning paradigm that involves three essential components: modeling, coaching, and weaning [3]. In this approach, "modeling" means that the instructor demonstrates and exemplifies the skills that students should learn (e.g., how to solve physics problems systematically). "Coaching" means providing students opportunities, guidance and practice so that they are actively engaged in learning the skills necessary for good performance. "Weaning" means reducing the support and feedback gradually so as to help students develop self-reliance.

Each of the tutorials starts with an overarching problem that is quantitative in nature. Before using a tutorial, students use a pre-tutorial worksheet that divides each quantitative problem given to them into different stages involved in problem solving. For example, in the conceptual analysis stage of problem solving, the worksheet explicitly asks students to draw a diagram, write down the given physical quantities, determine the target quantity, and predict some features of the solution. After attempting the problem on the worksheet to the best of their ability, students access the tutorial on the computer. The tutorial divides an overarching problem into several sub-problems, which are research-guided conceptual multiple-choice questions related to each stage of problem solving. The alternative choices in these multiple-choice questions elicit common difficulties students have with relevant concepts as determined by research in physics education. Incorrect responses direct students to appropriate help sessions where students have the choice of video, audio or only written help with suitable explanations, diagrams, and equations. Correct responses to the multiple-choice questions give students a choice of either advancing to the next sub-problem or directs them to the help session with the reasoning and explanation as to why the alternative choices are incorrect. While some reasonings are problem-specific, others focus on more general ideas.

After students work on the implementation and assessment phase sub-problems posed in the multiple-choice format, they answer reflection sub-problems. These sub-problems focus on helping students reflect upon what they have learned and apply the concepts learned in different contexts. If students have difficulty answering these sub-problems, the tutorial provides further help and feedback. Thus, the tutorials not only model or exemplify a systematic approach to problem solving, they also engage students actively in the learning process and provide feedback and guidance based upon their need.

Each tutorial problem is matched with other problems (which we call paired problems) that use similar physics principles but which are somewhat different in context. Students can be given these paired problems as quizzes so that they learn to generalize the problem solving approach and concepts learned from the tutorial. The paired problems play an important role in the weaning part of the learning model and ensure that students develop self-reliance and are able to solve problems based upon the same principle without help. These paired problems can also be assigned as homework problems and instructors can inform students that they can use the tutorials as a self-paced study tool if they have difficulty in solving the paired problems assigned as homework related to a particular topic.

We have developed computer-based tutorials related to introductory mechanics, electricity, and magnetism. Topics in mechanics include linear and rotational kinematics, Newton's laws, work and energy, and momentum. Topics in electricity and magnetism include Coulomb's law, Gauss's law, potential and potential energy, motion of charged particles in a constant electric field, motion of charged particles in an external magnetic field, Faraday's law, and Lenz's law.

Figure 1 shows screen capture from a conceptual question from a tutorial which starts with a quantitative problem in which two blocks with masses m

The computer-based self-paced tutorials that combine quantitative and conceptual problem solving are suited for a wide variety of students in introductory physics. They engage students actively in the learning process and provide feedback based upon their needs. They can be used as a self-study tool by students. The paired problems can be incorporated into regular quizzes or assigned as homework problems. This work was supported by NSF grant DUE-0442087.

2 C. Singh, "Interactive video tutorials for enhancing problem solving, reasoning, and meta-cognitive skills of introductory physics students", Proceedings of the 2003 Physics Education Research Conference, edited by J. Marx, S. Franklin and K. Cummings, AIP Conf. Proc., volume 720, Melville, New York, 177-180, 2004. Also, see http://www.phyast.pitt.edu/~cls/interactive

3 A. Collins, J. Brown, and S. Newman, {Cognitive Apprenticeship: Teaching the crafts of reading, writing and mathematics}, in L. B. Resnick (Ed.), “Knowing, learning, and instruction: Essays in honor of Robert Glaser,” Hillsdale, NJ: Lawrence Erlbaum., 453-494, (1989).