An Approach to Promote Learning by Problem-Based Problem-Posing Sho YAMAMOTO, Hiromi WAKI, Tsukasa HIRASHIMA Department of Information Engineering, Hiroshima University, Japan {sho, waki, tsukasa}@isl.hiroshima-u.ac.jp Abstract: In this paper, an interactive learning environment for learning by problem-based problem-posing has been described. In the method of learning by problem-posing, a learner is required to create the problems, since it is useful to understand the problems and their solution methods. There are several ways to pose problems, such as, solution-based problems, story-based problem posing and problem-based problem-posing. However, in the problem-based problem- posing, a learner is required to create new problems by changing the original one. This problem- posing has been expected to especially promote to understand the relation among problems. We have designed and implemented a learning environment for the learner where a learner could make new problems by changing the original problem and receive feedback on its changes. The learning environment has the facilities to diagnose the changes and generate the feedback based on the results of the diagnosis. The results of preliminary experimental use of the learning environment have also been reported. Introduction An interactive learning environment for learning by problem-based problem-posing has been described in this paper. Learning by problem-posing requires learners to create new problems. Several investigations have already been suggested that the effective way to create problems is to promote learners to reflect their knowledge and problem-solving abilities (G. Polya, 1957; Brown, S.I. et al, 1993; Silver, E.A. et al, 1996). Then it is also useful to learn how to use the solution methods that can be applied to the posed problems. There are several ways to pose problems, such as, solution-based problems, story-based problem posing and problem-based problem posing (Nakano, A. et al, 1999). In the problem-based problem-posing, a learner is required to make new problems by changing the original one. This problem-posing is expected to especially promote to understand the relation among problems. We call this understanding “external problem understanding”. We have designed and implemented a learning environment where a learner could make new problems by changing the original one and receive feedback about the changes. The environment has the facilities to diagnose the changes and generate the feedback based on the results of the diagnosis. In addition, the results of preliminary experimental use of the learning environment have also been reported. Learning by Problem-based Problem-Posing In this section, the characteristics of problem-based problem-posing are explained by comparing solution- based problem-posing with Figures 1 and 2. The framework of solution-based problem-posing is shown in Figure 1. In this learning, a learner is provided with a solution method and is required to make new problems that can be solved by using the method. It is very effective to understand the applicable range of a solution method. We have already developed an interactive environment for learning by solution-based problem-posing in the domain of arithmetical word problems and also been confirmed its impact through experimental use in several elementary schools (Nakano, A. et al, 1999; T. Hirashima et al, 2007; T. Hirashima et al, 2008). In contrast to Figure 1, the framework of problem-based problem-posing is shown in Figure 2. In this learning, a learner is required to make new problems by changing the original problem. Besides, the learner is requested to solve the new problems and compare their solution methods with the original one. The change means that the solution method sometimes changes or does not change. This learning is expected to promote to understand the relation among problems from the viewpoint of solution methods. Several investigations have suggested that experts or good problem solvers comprehend the relation among problems from the viewpoint of solution methods (Chi,M.T.H. et al, 1981; Larkin, J.H., 1983; de Jong et al, 1986). Based on these considerations, we are investigating computer-based learning environment for interactive problem-based problem-posing that is composed of (1) problem change interface, (2) diagnosis function of the changes, and (3) help function for correcting or completing the change.