## Remedial Education of Symbolic Fractional Calculations: Focused on Each Calculating Step

Takayoshi Yoshioka
yoshioka@toyota-ct.ac.jp

Toyota National College of Technology

Japan

Karl Fuchs
yoshioka@toyota-ct.ac.jp

Salzburg University

Austria

Alfred Dominik
yoshioka@toyota-ct.ac.jp

Austria

Hitoshi Nishizawa
yoshioka@toyota-ct.ac.jp

Toyota National College of Technology

Japan

### Abstract

A remedial education of symbolic fractional calculations using a WWW-based instruction system is described in this paper. Manual calculation skill of young Japanese students is declining gradually in the recent five years, at least at the institutions some of the authors are working for. Their calculations are loosing accuracy and consistency. For example, although they can add or multiply two fractions numerically, the same students struggle to find the very first step of the addition or multiplication for symbolic fractional expressions. What they lack, in our observation, is to think about the reasoning of each calculating step and to describe it externally. Repeated exercises do not improve the situation of some students. They have the tendency to repeat inappropriate calculations induced from their misconceptions in the exercises even after they are pointed out by the teacher. They recognize the mistakes as they are but do not seem to reconsider their methods that produced the mistakes. To compensate their weakness and to provide them with the opportunity to think of the reasoning, weユve introduced a step-by-step instruction system into the remedial education for the students in trouble. The system requests the students to select one of the operations in a list on the computer display for forwarding a step of the calculation, and calculates only the step instead of the student.

Students were embarrassed at the first time since they were forced to think of the reasoning for the calculation. It took a long way to accomplish the very simple calculation in step-by-step manner for the first time. However, as they got used to the method, they seemed to recognize what the system requested them. After the series of trials using the system, their calculation skills were improved remarkably.