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The purpose of this study was to examine the mathematical modelling competencies of student mathematics teachers within a learning environment that was based on a holistic approach to instruction. The participants were student mathematics teachers enrolled in undergraduate programmes at two different universities. In one of the university programmes, the participants took a mathematical modelling course that was taught according to a holistic approach, while the participants at the other university followed the standardized undergraduate programme that did not include a mathematical modelling course. The sub-competencies of mathematical modelling of the student mathematics teachers who participated in the mathematical modelling course were examined using an analytic rubric that was designed according to the holistic approach applied within the context of the study. In order to determine whether the observed changes were related to the experiences of mathematical modelling, these results were compared to the sub-competencies of mathematical modelling of the control group. The findings showed that experience within a learning environment based on mathematical modelling, as well as affective factors, supported the development of modelling competencies. On the other hand, it was observed that certain sub-competencies were difficult to develop; while many sub-competencies were enhanced by the modelling experiences, others were adversely affected. Furthermore, a certain group of sub-competencies was found not to be directly linked to modelling experiences.

In the current study, the subject of beats is addressed as a context to teach the subject of superposition of sound waves. In addition to this, by revealing the mathematical aspect of the subject, the context of beats was first investigated mathematically and then interpreted from a physical point of view. WolframAlpha was used for graphical drawing and Tone Generator was used for perceiving by hearing.

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-The aim of this study is to investigate of solution approaches of elementary mathematics prospective teachers in order to solve analytical problems on the lines and the circles which are presented visual and algebraic forms. 63 third-grade prospective teachers who were studying in the Department of Elementary Mathematics Teaching, Education Faculty participated in the study. Solution approaches of the prospective teachers were determined by analyzing the solutions of four problems which included visual and algebraic analytic problems on lines and circles. When the answers of prospective teachers were examined, it was found that most of the participants adopted geometric approaches in order to solve the analytic problems on both lines and circles and the problems in visual and algebraic forms. So, as geometric approach is not enough for solution of every problem, the study recommends that students should learn different solution approaches and raise awareness of necessity of various approaches.

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