Students' understanding of inverse relation between addition and subtraction at primary levels

Abstract

This article presents the findings of a research which concerned with primary level students’ understanding of arithmetic principles. The objectives of this research were to investigate primary students’ understanding of inverse relation between addition and subtraction and find the possible difficulties when students using inverse relation principle. In this research, “Understanding” involved two aspects: 1. Knowing the fact and here, the fact referred to the knowledge of the inverse relation between addition and subtraction; 2. Ability to identify the situation that related to inverse relation and ability to make use of the inverse relation principle properly in related situation. With this definition, our research not just only concerned the students’ knowledge base, but also concerned how the students analyzed different problems and how they used the principle in different situations. The different situations meant the inverse related questions with different complexity and they were categorized into transparent inverse problems and non-transparent inverse problems. According to the result, students partially understood the inverse principle because they obviously underused the inverse principle in the related problems and they preferred calculating step by step with using column form. We also discovered that their understanding varied among different grades because of their arithmetic experience and the type of the inverse related questions. Basically, students did better in transparent inverse questions than non-transparent inverse questions and higher grade of students had higher level of understanding and they could use the inverse principle properly more often. But, the primary 3 students surprisingly did worse in non-transparent five-term inverse problems than primary 2 students. It may because the students experience and the attitude of analyzing the questions. These findings gave us some insight of teaching arithmetic in primary levels.