The purpose of this study is to construct a valid and reliable mathematics related beliefs scale for determining preservice elementary mathematics teachers&rsquo / mathematics related beliefs in Turkey and investigating the impact of the gender and year level on the preservice mathematics teachers&rsquo / mathematics related beliefs. For the first purpose, the &ldquo / Mathematics Related Belief Scale (MRBS)&rdquo / was developed based on the combination of the belief frameworks in the literature. Data were collected from ten different universities from Ankara, Balikesir, Burdur, Bolu, Gaziantep, Izmir, Van, and Samsun in the spring semester of 2009-2010 academic year. A total of 584 third and fourth year preservice mathematics teachers participated in this study. Data were analyzed by descriptive and inferential statistics. The results showed that MRBS was a valid and reliable scale which measured Turkish preservice teachers&rsquo / mathematics related beliefs. MRBS had two components &ldquo / constructivist beliefs&rdquo / and &ldquo / traditional beliefs&rdquo / of mathematics and teaching mathematics. There was a significant effect of gender on preservice teachers&rsquo / mathematics related beliefs. No significant difference in preservice teachers&rsquo / mathematics related beliefs was detected in terms of year level in the teacher education program. The MRBS could be used for investigating preservice teachers&rsquo / mathematics related beliefs in order to determine effective teacher education program experiences.

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)