There has been an increasing attention on the interrelationship between mathematical problem solving and mathematical learning. Mathematical problem solving has been recognized as a process of inquiry whereby calculating and deriving the correct answers is only one of several phases. Several studies in mathematics education have identified the use of strategies to be central to solving mathematical problems (Pape & Wang, 2003; Verschaffel et al., 1999). Cai (2003) found that when students use problem- solving strategies, they are more successful in solving a mathematical problem. These problem-solving strategies, or heuristics strategies, are procedures that students should take before reaching the calculation phase of problem solving. They are designed to help students understand and organize their responses to answer the problems. While there is evidence that heuristic strategies have enhanced learners’ responses to verbal mathematical problems, there should be more attention given to study of heuristic strategies in mathematical non-routine problem solving, especially among primary school children (Kaizer & Shore, 1995).
Problem solving in Singapore
Research in mathematics education in Singapore has a relatively short history (Foong, 2007). Given the decreasing trend of research on problem solving internationally, Foong suggested that the large number of local degree studies on problem solving could be due to the fact that problem solving has been the central theme of Singapore school mathematics curriculum since 1990. Developing students’ ability in problem solving only started to be one of the mathematics learning objectives in the curriculum in the 1970s (Fan, 2007). As part of processes, heuristics for problem solving were first explicitly listed in the syllabus. The primary level syllabus listed 11 problem solving heuristics while the secondary level syllabus listed 13 heuristics with 2 not included at the primary level, that is, “using equation” and “thinking of a related problem”. Students are required to use heuristics in mathematical problem solving and thinking, and not just application of algorithmic skills or factual recall. Though these heuristics are listed in the syllabus, the use of these heuristics is not fully reflected in Singapore published textbooks (Fan & Zhu, 2000), and it is not clear how and when these heuristics should be taught in the mathematics curriculum.
Mathematics Education in Singapore
Singapore had emerged top or one of the top few in Mathematics for the Third International Mathematics and Science Study (TIMSS) for several times. This achievement could be due to the influence of national curriculum with problem solving as its central theme. Kaur and Yap (1998, 1999) has conducted an international study to compare progress in mathematics attainment by examining the performance of 8650 lower secondary pupils. They found that Singapore’s overall performance in mathematics was commendable...