IMPROVEMENT OF EFFECTIVE COMMUNICATION-THE CASE OF SUBTRACTION.

The research study this article is based on aims to implement research knowledge to teaching, that is, the concept of critical aspects and dimensions of variation used in the variation theory. To do this, the researchers worked with willing teachers to explore how to make mathematics teaching more effective. This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding of subtraction as well as their learning of it. The students' tests, examinations of students' mathematical work, the teachers' lessons plan and reports of the instructions for lessons form the data base for the article. The analysis indicates that one of the critical aspects in the process of implementation of the variation theory in the teachers' practice was to identify the critical aspects in students' learning. Another critical aspect in the implementation of the variation theory was to open up dimensions of variation in the identified critical aspects of the students. By giving teachers the possibility to develop the ability to identify critical aspects in students' learning, dimensions of variation are opened up in these aspects, and by applying this knowledge in the daily teaching, they have the possibility to improve students' learning. The findings suggest that developing an understanding of the students' critical aspects can be a productive basis in helping teachers make fundamental changes in their instructions and improve students' learning. [ABSTRACT FROM AUTHOR]