Moutsios-Rentzos, Andreas (2009) University mathematics students: thinking styles and strategies. PhD thesis, University of Warwick.

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Abstract

This study concentrates on the relationship between the students’ thinking styles (Stenberg, 1999) and the strategies (Kirby, 1988) the students employ when dealing with exam-type questions in mathematics. Thinking styles are the “preferred way[s] of using the ability one has” (Sternberg, 1999, p. 8) and are conceptualised to be relatively stable over time and context. A strategy is the “combination of tactics, or a choice of tactics, that forms a coherent plan to solve a problem” (Kirby, 1988, p. 230-231). The students’ attainment, the nature of task and the students’ views are also considered in this study. A three-phase study including both quantitative and qualitative techniques was designed with the aim of delineating this relationship. The study was conducted with 2nd year students (N=99) following a BSc in Mathematics in the Department of Mathematics of the University of Athens, although, for methodological reasons, additional data were collected from a broader group of undergraduates (NUG=224). The students’ thinking styles were identified through a version of the Sternberg-Wagner Thinking Styles Inventory (Sternberg, 1999), translated into Greek. Two main Style Cores were identified: Core I (creative, original, critical and non-prioritised thinking) and Core II (procedural, already tested and prioritised thinking). Based on these cores, the students were assigned to two clusters: Cluster 1C2C (High Core I/Low Core II) and Cluster 3C4C (High Core II/Low Core I). In order to identify the students’ strategies, the A-B-Δ strategy classification was introduced, expanding on Weber’s (2005) semantic, syntactic and procedural strategies. The AB-Δ strategies were grouped in three Strategy Types depending on their links with truth,memory and flexibility, respectively identified as: α-type, β-type and δ-type. Students assigned to Cluster 1C2C appeared to prefer more α-type and less β-type Initial Strategies than those assigned to Cluster 3C4C. The nature of the task appeared to affect this link. On the other hand, in the context of Back-Up Strategies, stylistic preferences and ‘high’ attainment appeared to regulate a link between the nature of the task and a Back-Up Strategy, rather than forming a style-strategy link (as in the case of Initial Strategy). Drawing from Skemp’s (1979) views about reality (inner and social) and survival (respectively, internal consistency and social survival), it is argued that the students choose different strategies, because they essentially perceive the given task in qualitatively different ways. The students’ different stylistic preferences indicate differences in their inner reality, thus affecting their choice of an ascertaining argument, which in turn determines their selection of Initial Strategy. The failure of the students’ Initial Strategy leads them to re-evaluate the task itself, thus resulting in a change of the reality in which the students have to survive and this, in turn, determines the students’ Back-Up Strategies.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics L Education > LB Theory and practice of education > LB2300 Higher Education
Library of Congress Subject Headings (LCSH):	Mathematics -- Study and teaching (Higher), College students -- Psychology, Thought and thinking, Strategy (Philosophy)
Date:	February 2009
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Gray, Eddie, 1948- ; Simpson, A. (Adrian)
Sponsors:	Greek State Scholarship Foundation (GSSF)
Extent:	415 leaves : charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/2285

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