Proof is a fundamental activity in mathematical practice (Hanna, 2000), also is a key element in school mathematics (NCTM, 2000). Although the proof and proving are expected to play much more prominent role in school mathematics, a great number of research studies conducted in the last two decades have given evidence that the students have serious difficulties with proof (Harel & Sowder, 1998). From different points of view, many authors have observed students as they attempt to solve proof problems, and identified students’ conception of proof as an important determinant of students’ proof practices (Marradez & Guiterrez, 2000). It was underlined that students’ perception of proof plays an important role not only in their thinking and reasoning, but also in the types of argument they produce (Moore, 1994). A significant portion of research on student’s conception of proof seeks to categorize the arguments produced by students as proof. An argument that convince students or which a students would use to convince someone is classified as a type of proof scheme. Researchers put forward different factors that may have role in students’ conception of proof, such as; students’ cognitive development (Tall, 1991), socio-mathematical norms (Dreyfus, 1999), poor conceptual understanding and ineffective proof strategies (Weber, 2003). However, little attention has been paid to documenting variables related to individual differences. One of the most important individual differences is the cognitive style. The construct of cognitive style is important factor in education due to its influence on students’ learning and learning outcomes (Liu & Reed, 1984; Saracho, 1997). The purpose of the present study is to identify 10th grade students’ use of proof schemes in geometry with respect to their cognitive styles.

The sample of the study was 224 tenth grade students from four secondary schools. Of those, 126 participants were female and 98 participants were males. Data was collected at the end of the academic year 2005-2006 through uses of two data collection instruments: Geometry Proof Test (GPT) and Group Embedded Figure Test (GEFT). GPT, included eleven open-ended questions on triangle concept, was developed by first researcher to investigate students’ use of proof schemes. The proof schemes reported by Harel and Sowder (1998) were used as a framework while categorizing the students’ responses. GEFT developed by Witkin, Oltman, Raskin and Karp (1971) was used to determine cognitive styles of the students as field dependent (FD), field independent (FI) and field mix (FM). To analyze data, a multivariate analysis of variance (MANOVA) with three cognitive styles (FD, FM, FI) as independent variables and three proof schemes use scores (externally-based, empirical, analytical) as the dependent variables was employed.

The results revealed that the mean of FD students’ externally based proof schemes use scores is significantly higher than the mean of FI students’ externally-based proof schemes use scores. Moreover, the mean of FI students’ analytical proof schemes use scores is significantly higher than the mean FD students’ analytical proof schemes use scores. There is no significant mean difference in empirical proof schemes use scores of FD, FI and FM students. The significant differences in students’ use of proof schemes with respect to their cognitive styles connote that cognitive styles are important individual differences and should be taken into consideration as instructional variables, while teaching and engaging in proof in geometry and in mathematics. Using appropriate methods and tools, mathematics educators can design an effective instruction that can meet the needs of students with different cognitive styles.