Takayoshi Yoshioka

METHOD AND EFFECTIVENESS OF AN INDIVIDUALIZED EXERCISE OF FUNDAMENTAL MATHEMATICS

This article describes a method used to provide mathematics students in colleges of engineering in Japan with supplementary exercises to aid in their learning. The impact of this effort is also described. An online support function enables instructional personnel to individualize the exercise for students whose abilities vary widely. Individualizing exercises helps students to understand a mathematical method used to solve a problem and also the mathematical idea or concept upon which the method is based. The program described here consists of activities that supplement those in the regular lesson. They are designed to help those students who failed to meet certain course objectives or to solve the problems given in the lesson. Students using the individualized program are allowed to select the problems from among the problem exercises available based on the course objectives that they have not yet satisfied. The online support function of the learning environment that the authors developed assists teaching personnel in the otherwise time-consuming preparation of individualizing these activities. Students determine how well they did on the objectives in the regular lesson by visting the Web page for the course. Information is provided on the impact of the activities on student performance in a fundamental mathematics course in the authors college.This article describes a method used to provide mathematics students in colleges of engineering in Japan with supplementary exercises to aid in their learning. The impact of this effort is also described. An online support function enables instructional personnel to individualize the exercise for students whose abilities vary widely. Individualizing exercises helps students to understand a mathematical method used to solve a problem and also the mathematical idea or concept upon which the method is based. The program described here consists of activities that supplement those in the regular lesson. They are designed to help those students who failed to meet certain course objectives or to solve the problems given in the lesson. Students using the individualized program are allowed to select the problems from among the problem exercises available based on the course objectives that they have not yet satisfied. The online support function of the learning environment that the authors developed assists teachi...

Increasing Reality and Educational Merits of a Virtual Game

Abstract Linear algebra, especially vector equations in 3-dimensional (3D) space, was the least performed topic of fundamental mathematics for Japanese engineering students. For most of them, symbolic representations in textbooks were too abstract, 3D graphic objects took too much time to draw on notebooks, and too few verbal explanations were given in the lectures. Because they didn’t feel the reality in vectors and didn’t connect symbolic vector equations with graphic representations in their mind, the learnt knowledge evaporated easily just after the exams. A virtual game with interactively changeable 3D graphics was developed to improve this situation. The game was conducted in a classroom with a projector displaying the on-going results in front of the class. Students’ avatars had graphic icons and characteristic vectors, and team of avatars fought each other in battles. The winners of the battles were calculated using a scalar product of 3D vectors. The game was combined with a web-based learning system, where students could learn the connection between symbolic and graphic representations of lines or planes in 3D space interactively. Students earn learning points by using the system, and the points could be used advantageously in the battles. Young students felt some reality in the game, and increased experiences of handling 3D graphic objects using vectors. They learnt how an inner product of two vectors decided the winners of battles graphically through the game. And interested students increased the amount of out-of-class activities on the learning system. However, they testified that the game was too simple and had little space for them to devise their winning tactics. That is why we added several new features to the game for increasing reality of the battles and also helping the students to deepen their understanding on vector operations. Students’ reflections to the game and the learning system were collected through interviews to some students or measured through their learning histories on the system and the out-of-class exercises. According to the interviews, the game and the learning system helped them to feel more reality in linear algebra and to start learning it meaningfully.