Interactive Environment for Learning by Problem-Posing for Reverse-Thinking Problems in Arithmetical Word Problems and Its Practical Use

Abstract

In this paper, interactive environment for learning by problem posing for reverse-thinking problems and its practical use are described. We have already developed several interactive learning environments for learning by problem-posing. In this research, we have paid a special attention to ``reverse-thinking problems'' in arithmetic word problems that can be solved either by addition or subtraction. In the reverse-thinking problems, since ``story operation structure'' and ``calculation operation structure'' are different, they require learners to comprehend the relations between problems and solutions more than ``forward thinking problems'' where ``story operation structure'' and ``calculation operation structure'' are the same ones. Based on a learning environment for posing the forward thinking problems developed previously, we have expanded it for reverse thinking problems. This learning environment has been used in a class of fourth grade at an elementary school for seven lesson times. We have also reported the results of this practical use.