The present study examined the potential relationship between 1st and 5th year secondary school pre-service mathematics teachers' skills in understanding, method, modelling, verification, and extension dimensions of oroblem solving and their learning style characteristics. The data consisted of the skills pre-service teachers demonstrated in the solution process of open-ended problems. For this purpose, a graded scoring rubric was developed specific to each problem. Regarding the relationships between problem solving dimensions and the characteristics of McCarthy's learning styles, it was assumed that type 1 learners' skills were more dominant ir the understanding dimension, type 2 learners' skills in the method and modelling dimensions, type 3 learners skills in the verification dimension, and type 4 learners' skills in the extension dimension. On the basis of this assumption, problem-solving skills and learning style characteristics were associated and interpreted. The results obtained suggested that 5th year pre-service teachers were better in representing the skills pertaining to type 1 and type 2 learning styles, while 1st year pre-service teachers were better in representing the skills pertaining to type 1 learning style only. On the other hand, it was observed that a great majority of the pre-service teachers had a low level of the skills pertaining to type 3 and type 4 learning styles.
Problem Solving Skills, Learning Style, Pre-Service Mathematics Teachers
In order to interpret individual differences and to design educational models around these differences, individual learning styles have become an important consideration. Mutual characteristics of individual differences have been pivotal in the development of learning style models (Silver, Strong, & Perini, 1997). Kolb (1984) argued that individual differences n the learning process emerge n the perception/understanding and processing/transformation dimensions. According to Kolb's model, students are grouped in relation to their preferences for concrete experience or abstract conceptualisation (how students gain and comprehend knowledge) and active experimentation or reflective observation (how students transform and internalise knowledge) (Felder, 1996; Kolb).
According to McCarthy's (1985) learning styles model, dimensions of ndividual's understanding and processing are presented similar to Kolb's learning styles model; concrete experi-ence (feeling/sensing) - abstract conceptuali-sation (thinking) and active experimentation (doing) - reflective observation (watching), respectively. McCarthy identified four types of individual learning styles which are determined by a combination of information perception and processing dimensions; type one learners (imaginative learners), type two learners (analytic learners), type three learners (commonsense learners), and type four learners (dynamic learners) (McCarthy, 1990).
The 4MAT learning system, developed by McCarthy based on Kolb's "Experiential Le- arning Theory" and Jung's "Personality Types Theory" and findings of brain studies, is a "learning cycle" model with 8 instructional events (McCarthy, 1990). Each of McCarthy's four quadrants of learning styles includes right and leftmode brain and holistic oriented students. While a combination of alternative right and leftmode techniques in all four learning styles enables students to be relaxed in the situations that are in line with their learning styles, it also allows the students to overcome difficulties in si-tuations which are not within their learning style (McCarthy, 1990, pp. 32-33). The 8 instructional events of the 4MAT learning model are respectively: connect, attend, image, inform, practice, extend, refine, perform (McCarthy, Germain, & Lippitt, 2006, pp. 18-22).
Dunn (1983) argued that students could learn via learning methods convenient for themselves and approaches compatible to their learning styles. …