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Limin Chen: The Relationship Between Posing and Solving (Realistic) Mathematical Problems in Elementary Schools in ChinaDissertation submitted to obtain the degree of Doctor in Educational Sciences, October 2011 Supervisor: Prof. Dr. Lieven Verschaffel Co-supervisor: Prof. Dr. Wim Van Dooren It is well recognized that problem posing is an important component of the mathematics curriculum, and even lies at the heart of mathematical activity (Brown & Walter, 1993; English, 1997a, 1997b, 1998; Kilpatrick, 1987; Silver, 1994). Several theoretical and empirical studies have been undertaken, probing the relationship between problem posing and problem solving, but little or no systematic research has investigated this relationship when dealing with realistic problem situations in a Chinese cultural context. The goal of this doctoral project is divided into three sub-goals: (1) investigating Chinese students’ problem posing and problem solving abilities, as well as the relationship between them, (2) studying Chinese teachers’ problem posing abilities, problem solving abilities and general beliefs about problem posing and problem solving, as well as the relationship between these different abilities and beliefs, and (3) based on the results from these studies, designing, implementing, and evaluating a learning environment rich in problem posing and problem solving opportunities aimed at the development of Chinese elementary school students’ problem posing and problem solving abilities, as well as at the development of their beliefs about and attitudes towards problem posing and problem solving. This dissertation consists of five manuscripts, as well as an introduction chapter and a conclusion and discussion chapter.In the introduction chapter, some theoretical notions and empirical findings and observations related mathematical problem solving, realistic mathematical problem solving, and mathematical problem posing are first discussed, and then the research goals of the dissertation as well as an overview of the different studies are presented.The first two manuscripts of this dissertation are related to the first sub-goal. In Manuscript I, we report a study that investigated Chinese fourth-grade students’ abilities in posing division-with-remainder (DWR) problems in relation to their abilities in solving DWR problems. Results revealed that Chinese students held non-realistic perspectives towards problem posing and problem solving, and there was a significant positive relationship between students’ abilities in posing and solving DWR problems. In Manuscript II, the relationship between posing and solving word problems is further explored, not only through DWR problems, but also standard problems, with a more representative sample of subjects, and a methodology that overcame some methodological shortcomings of the study reported in Manuscript I. Results confirmed that Chinese students held non-realistic views on problem posing and problem solving, and there was a close relationship between their problem posing and problem solving abilities.The following two manuscripts of the dissertation are related to the second sub-goal. In Manuscript III, an investigation on Chinese pre-service and in-service teachers’ realistic problem posing and problem solving abilities and beliefs with respect to DWR problems is detailed. Results revealed that, first, teachers behaved quite realistically not only when solving and posing DWR problems themselves, but also when evaluating elementary school students’ solving and posing performance on DWR problems. Second, we found a correspondence between teachers’ own performances, and their evaluations of students’ reactions. In Manuscript IV, we investigated Chinese pre-service teachers’ realistic problem solving abilities and beliefs using contextually problematic problems (P-problems) that have been shown to elicit many more modelling difficulties among students and teachers than DWR problems such as the ones in Manuscript III. We used essentially the same methodology as in the study reported in Manuscript III. Results revealed a strong and straightforward relationship between the teachers’ realistic reactions to the P-problems and their evaluations of the students’ responses to the same P-problems. However, the congruence between teachers’ non-realistic reactions and their scorings of the students’ answers was somewhat less straightforward. The last manuscript deals with the final sub-goal of the dissertation. Manuscript V reports the design, implementation, and evaluation of a problem posing training program aimed at developing Chinese elementary school students’ problem posing and problem solving abilities and their beliefs about and attitudes towards mathematical problem posing and problem solving. Results revealed that the program had a significant positive effect on the originality of the problems posed by the students (but not on the correctness, complexity, and diversity of the problems posed), as well as on their problem solving ability and on their problem posing and problem solving beliefs and attitudes.In the conclusion and discussion chapter, the designs and findings of the five studies are critically discussed, and some challenging issues for future research and implications for educational theories and practices on the learning and teaching of problem posing and problem solvin

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