Instructional Explanations of Class Teachers and Primary School Mathematics Teachers about Division

Abstract

This study is a qualitative research which was conducted in order to reveal the instructional explanations of class teachers and primary school mathematics teachers working in state schools about division. A semi-structured interview form with three open-ended questions about division, prepared for this purpose, was examined by the experts. The semi-structured interview form inluded three questions asking the teachers to solve the long division operations of 3385: 13 = ?, 1238: 12 =? and 102102: 12 =? using the mathematical table of digits with a descriptive language as if they were telling the primary school students the solutions. While the first two questions were suitable with the 5th grade learning outcomes, the third question was suitable with a high level learning outcome. The main purpose of asking the 3rd question was to evaluate the instructional explanation of the teachers in a problem of different difficulty. The study group consisted of 34 teachers, 16 of whom were primary school mathematics teachers and 18 of whom were class teachers, working at central primary schools in a province located in Eastern Anatolia region of Turkey. The content analysis of the data showed that not all of the teachers could interpret the operation of division regarding the concept of digit accurately, and their division was result and reasoning oriented. However, it was found that few teachers made generalizations in a similar way. It was also seen that teachers who were at problem-solving level according to Kinach’s (2002b) comprehension level framework could not make sense of the logic underlying the division. In addition, the reason why zero (0) was moved to the quotient and when the divisor sought in remaining number should be completed by the teachers could not be clarified because they did not know the logic of the division.