## 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`

**BORG Akademiestrasse**

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.

© ATCM, Inc. 2001.