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Results show greater experienced groups prefer originality and freedom, with low structure and complex information processing, while postgraduates also favor implementing rules and instructions. 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A crosssectional quantitative study (N = 238) was conducted in a large Greek university, identifying the thinking styles of second, third and fourth year undergraduates, as well as those of students following a postgraduate degree in mathematics. The analysis revealed that the more experienced undergraduates and the postgraduates showed a stronger preference for originality and freedom in thinking, low degrees of structure, high levels of freedom and more complex information processing, combined with non-prioritised thinking. However, the postgraduates combine these preferences with a stronger preference for implementing rules and instructions. A discussion on these findings and on the factors that may account for them is presented.  \nKey words: university mathematics, thinking styles, undergraduates, postgraduates, MSC 97C30  \n1. Thinking and mathematical thinking  \nIn the general educational and psychological research, various researchers argue for the existence of general cognitive preferences, usually described by the construct of cognitive style, which can be defined as “an individual's characteristic and consistent approach to organizing and processing information”(Tennant, 1988, p. 89) . Little research has been conducted into the interaction between these cognitive styles and studying mathematics and/or advanced mathematics (Duffin & Simpson, 2002; Pitta-Pantazi & Christou, 2009) .  \nAlthough there appear to be variations in the conceptualisation of cognitive styles, most theorists agree that cognitive style is relatively stable over time and context (Zhang & Sternberg, 2001). Therefore, by focussing on students’ thinking styles, we essentially look for the medium-to-long term interactions between university education and the student’s way of thinking and for relatively stable thinking characteristics that the undergraduates and the postgraduates may share. Such a study will help us in finding out more about the outcomes of the existing university educational system on the thinking of the students who form the ‘pool’ from which future mathematics teachers and mathematicians derive. This is crucial both for the mathematical community and for the general community as the majority of future mathematics teachers will be amongst these graduates.  \nIn a previous study (Moutsios-Rentzos & Simpson, 2005) we focussed on the transition from university mathematics to a taught postgraduate degree in mathematics. In that study, we highlighted two apparently conflicting conjectures. The first conjecture was that the existing undergraduate educational system, with the rapid delivery of new material, might favour students who have a preference for absorbing new information without any particular short-term search for links with existing knowledge (Duffin & Simpson, 2002) and so postgraduates, having been successful in that environment, would maintain most of those thinking styles. The second conjecture, suggests that the students who choose to follow a postgraduate degree are distinct in their approaches to study from the general graduate population and, therefore, the postgraduates “become increasingly surface and decreasingly deep in their orientation to learning”(Biggs, 2001 p. 91) .  \nReceived 24 December 2010, accepted 30 December 2010, published 31 December 2010.  \nIn this paper, we further consider this apparent conflict. We adopt one conceptualisation of the general construct of cognitive style, Sternberg’s (1999) thinking style (the “preferred way of using the ability one has”, p. 8) to identify the links, if any, between studying university mathematics and the students’general thinking preferences. In particular we ask t","cbCaim7D6lsJwKaj","https://ap.wps.com/l/cbCaim7D6lsJwKaj","pdf",109509,"English","# Abstract\n# Thinking and mathematical thinking\n## Cognitive style and research background\n## Stability and educational interactions\n## Prior study and research question\n# Theoretical framework\n## Cognitive consistencies in thinking and in mathematical thinking","[{\"question\":\"What research question does the paper focus on?\",\"answer\":\"It asks what differences and similarities exist in thinking style among undergraduate mathematics students across different year groups, and how those students compare with postgraduate mathematics students.\"},{\"question\":\"How was the study conducted?\",\"answer\":\"A cross-sectional quantitative study was conducted in a large Greek university with a sample size of N=238.\"},{\"question\":\"What major differences in thinking styles were found?\",\"answer\":\"More experienced undergraduates and postgraduates showed stronger preference for originality and freedom and for low degrees of structure, along with complex information processing. Postgraduates additionally showed a stronger preference for implementing rules and instructions.\"}]","The Thinking Styles of University Mathematics Students - Volume 3 - Number 4 - 2010 | PDF",1792065400,25]