This study investigated the approaches to teaching by three fifth-grade teachers' of creative and non-creative mathematical problems for fractions. The teachers' personal constructs of the two kinds of problems were elicited by interviews through the use of the repertory grid technique. All the teaching was observed and video-recorded. Results revealed that the teachers had slightly distinctive constructs of creative and noncreative problems, and professed a greater preference for creative problems. Based on the teachers' creations of problems in classrooms and related features, the study identified three types of teaching approaches: liberal, reasoning, and skill approaches. The liberal approach appeared to indicate the most appropriate teaching methods for creative problems.Researchers have identified a variety of types of mathematical problems, such as word and time-consuming problems, and word and calculation problems (Vermeer, Boekaerts & Seegers, 2000). The consideration of these problems is more related to the length of time and the language needed for solving a problem than to the use of creativity in solving it. Another typology for mathematical problems is 'routine' and 'non-routine' problems (McLeod, 1988(McLeod, , 1994. This dichotomy, however, relates more to learners' experiences than to problem types. For example, word problems are likely to be non-routine for students used to solving calculation problems. For example, a study was described in which students were often invited by the teachers to create mathematical games and articles, such as Chinese new-year calendars in the cycle of twelve: for these students, these creative tasks were 'routine'.Well-structured and ill-structured problems are another taxonomy, as indicated by Nitko (1996) and Jonassen (1997). Well-structured problems are tasks that are clearly laid out, give students all the information they need, and usually have one correct answer that students can obtain by applying a procedure taught in class. The purpose of well-structured problems is to give students opportunities to rehearse the procedures or algorithms taught in class. In contrast, most authentic problems are illstructured. In order to solve an ill-structured problem, students have to organize, clarify, and obtain information not readily available for understanding the problem. There are likely to be a number of correct answers for an ill-structured problem. Jonassen views well-structured and ill-structured problems as 'a continuum from decontextualized problems with convergent solutions to very contextualized problems with multiple solutions' (p. 67). Jausovec's (1994) study defines well-defined problems as being clearly defined with given states, goal states, and an operator, while ill-defined problems are viewed as having vaguely defined goals, which can only be solved by creative strategies. In the present study, creative problems refer to the extreme end of problems with multiple or divergent (often limitless) solutions, while non-creative problems were those with si...