1 INCORPORATING MATHEMATICAL THINKING IN ADDITION AND SUBTRACTION OF FRACTION: REAL ISSUES AND CHALLENGES Madihah Khalid Universiti Brunei Darussalam Since the introduction of the new primary mathematics curriculum in Brunei starting January2006, more teachers of elementary schools are seeking a suitable way of incorporating mathematical thinking in each mathematics lesson that they teach. For this particular purpose, teachers were introduced to lesson study and it is hoped that with the guidance and support given by the team involved, teachers would build their confidence and make mathematical thinking a regular feature of their lessons. There are still many problems that the teachers face such as students not used to explaining their thoughts in class and some insisting on using certain procedures that they had learned before, without being able to explain how and why the procedure works. This paper will relate a classroom case and look at the real issues and challenges that Bruneian teachers faced in incorporating mathematical thinking when teaching of the topic on addition and subtraction of fractions. Introduction Mathematical thinking is the mathematical mode of thought that we use to solve any problem in our daily life including at schools (Khalid, 2006). It can be defined as applying mathematical techniques, concepts and processes, either explicitly or implicitly, in the solution of problems (Khalid, 2006). It is, according to Katagiri (2006), the most important ability that mathematics courses need to instill because it makes students able to think and make independent judgement. He also said that mathematical thinking allows for an understanding of the necessity of using knowledge and skills as well as learning how to learn by oneself, and the attainment of the abilities required for independent learning. Stacey (2006) reiterated this fact by saying that mathematical thinking is important because it is an important goal of schooling; it is important for teaching mathematics; and it is an important way of learning mathematics. In fact, the framework used by PISA shows that mathematical literacy involves many components of mathematical thinking, including reasoning, modelling and making connections between ideas. It is therefore imperative that mathematical thinking be stressed in any school curriculum and this is reflected in the new curriculum for primary mathematics of Brunei Darussalam, which was put into implementation from early 2006 (Khalid, 2006). Children are encouraged to use thinking skills and problem solving strategies during mathematics lessons and not just learn mathematical skills and concepts from listening to the teachers. It is feared that if mathematical thinking is not emphasized,