Learning by Posing Problems Using Illustrations Instead of Words

Abstract

Learning by posing arithmetic word problems is well-recognized as an effective means to mastering the use of solution methods; however, several learners cannot pose problems using words. In problem-solving exercises, if a learner cannot understand what is expressed in a problem statement, an illustration of the scene expressed in the statement can help the learner understand. Therefore, in this paper, we propose learning by posing problems with illustrations instead of words. One of the purposes of learning mathematics is to acquire the ability to derive a numerical relation from a scene and to associate a calculation expression with various scenes. We expect that posing problems via illustration and without words is an effective way for beginners to learn. In the problem-posing exercises, learners construct various types of problems. Teachers have to evaluate each posed problem and advise learners on the basis of the evaluations. This task places a heavy burden on teachers. Therefore, we developed a computer-based environment for posing problems using illustrations. The environment provides a learner with a calculation expression and illustrations. The illustrations can be disassembled into several figures. A learner assembles an illustration that describes a story of arithmetic problem that correspond to the calculation expression by combining the figures. The learner uses no sentences in this problem-posing exercise. The environment diagnoses the illustration problem and produces advice to the learner. We conducted a preliminary evaluation of the environment to confirm that a learner who cannot pose problems via words was able to pose problems using illustrations. Our results were promising, indicating that our environment provides a means for learners who cannot pose problems via words.