A design of learning environment and related teacher activities to foster mathematical power of individuals in mathematics education

Individuals who got any level of education from pre-school to university experience mathematical power improvement even at varying levels. However, it is desired that the improvement levels should not fall below certain standards and should be comparable to international standards and levels as much as possible.To achieve this, the first thing to do is to re-orient the ?mathematics education system? so that better individual MP improvement levels are obtained. In addition, a proper mathematics learning environment should be designed and built by taking into account physical, social and all other conditions. Secondly, it should be determined which learning approaches, methodologies, techniques and evaluation tools will best serve our purpose. Also, the roles and tasks of teachers, students, education managers, etc. who are actively participating in the mathematics educational processes, should be re-arranged and clarified.Our purpose in this research is to explain thoroughly ?what MP is together with all of its essential dimensions, elements, criteria and specific attitudes?; find out ?how to evaluate and assess MP?; and to determine the conditions for MP development. Consequently, we wish to contribute to mathematics education by researching on MP definition and development.In this research we used the experimental design type of ?post-test control group? with equalized group levels. Research studies on experiment group were done in accordance with MP theory, definitions and components with constructive learning approach. The control group was applied traditional mathematics teaching methods and techniques. The experimental study was done with one experiment and one control group during 2005-2006 educational period within 26 weeks. In the study, half-constructed interviews were done with both experiment and control group; and an in-class observation was obtained from only experiment group. Additionally, a descriptive study was done in order to determine today?s math learning assessment and evaluation objectives regarding sub-problems. We examined 9th grade test questions of 20 different math teachers and compared this with the problems specifically designed for MP assessment.The tools that were used to collect research data are MP Level Assessment Problems(MPLAP) for finding out MP improvement level, half-constructed interviews, student views, in-class observation of students and math written test results. The qualitative data were analyzed using a rubric formed with specific criteria, and then quantified as an input for SPSS statistics computer program; at last, using SPSS meaningful results regarding this research were obtained.We applied three different MPLAPs on experiment group students and found out that there was an increase in the students? average scores during the study process. This result is also supported by observation scores. In order to find out whether this result is caused by our MP oriented learning applications on experiment group or by an ordinary change in time, we applied a MPLAP post test for both student groups. As a result of the comparison of both groups? average scores, it was found out that the difference was meaningfully in favour of experimental group. Besides, we determined that today?s math assessment questions were designed to assess simple level subject/definition and procedural knowledge. Hence, when compared with MP components, we concluded that these questions could not be used for assessing MP level.Eventually, we stress that the assessment and improvement of MP is one of the main objectives of math aducation; and to reach this objective the best practice ways are needed to found.Key words: Mathematical Power, Mathematics Education, Learning Environment Assessment-Evaluation, Mathematical Thinking.