The aim of this study was to determine the how pre-service mathematics teachers respond to unexpected questions from students about the second derivative. A qualitative research method was used for this purpose, applying a case study framed as an in-depth analysis of how pre-service mathematics teachers respond to students' ideas. The participants were 39 pre-service mathematics teachers who were in their final year of their mathematics teacher education program. The pre-service teachers, who participated voluntarily, were asked to respond to open-ended questions relating to a scenario that included a teacher, as well as her 12th-grade students. The written responses that the participants provided constitute the data of this study. The results revealed that most of the participants could not effectively answer an unexpected question from students. Nearly half of the participants stated that they could not answer the question. Others ignored it, while some acknowledged the question and attempted to give an answer. Moreover, a small number of the participants made an effort to explain and demonstrate the concept of concavity by drawing the graphs of the function and relating them to the first derivative.

The aim of the study is to investigate the actions of prospective mathematics teachers while solving Distance Problem in the technology-aided mathematical modeling process. The study was conducted with twenty-one secondary prospective mathematics teachers. The participants selected by the criteria sampling method were divided into seven study groups of three persons an worked on the Distance Problem. The data were gathered from written response papers and GeoGebra solution files that included the approaches of the participants while solving the Distance Problem. The analysis of the data was carried out by means of content analysis based on the theoretical framework. The results showed that the participants used mathematics and physics knowledge in solution. GeoGebra played a role in solution from the second stage of the modeling process. GeoGebra was been important in establishing algebraic and geometric representations of mathematical models and establishing relations between them to arrive at mathematical solutions and results. In validation, only one group compared the data on the written paper with the data in GeoGebra. The students should encouraged to in overcome their difficulties during the modeling process and to include to the rich learning environments in which they can organize their knowledge of technology, mathematics and physics.

The purpose of the study is to analyze the mathematics student teachers' solutions on the Eşme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were collected from the participants' written solutions related to the problem. To analyze the students' answers through mathematical modelling process, the researchers compiled 7-stage mathematical modelling process from the literature. It was observed that the problem created an appropriate process for mathematical modelling. While examining the solutions of the participants who were informed about this 7-stage mathematical modelling process, it was generally observed that their solution approaches toward the problem decreased while progressing in modelling stages.

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these problems and the groups' reflective diaries regarding their problem posing and solution processes. The data were analyzed by using content analysis and the codes were constructed according to the problems' contents. The participants' diaries were examined in terms of generated codes and the expressions supporting/relating the codes were determined. While designing the problems, the participants considered the factors such as being interesting, understandable, appropriateness to real life and modelling process, model construction, and usability of different mathematical concepts. Their solutions were generally handled in terms of usage of the mathematical statements, appropriateness to the modelling process and being meaningful for real life. Modelling training should be provided to enable the student teachers to develop modelling problems and their designs should be examined and the feedbacks should be given.

The purpose of this study was to investigate how pre-service mathematics teachers’ pedagogical content knowledge was reflected in their microteaching. Twenty preservice secondary mathematics teachers participated in the study. The participants formed groups of two, three or four people of their choice, resulting in six groups in total. Each group designed and conducted a microteaching on a topic of their choice. The videotapes of the groups’ microteaching and their lesson plans constituted the data set for the study. We analyzed the data per the components of the pedagogical content knowledge framework outlined by various researchers. We found that the preservice mathematics teachers in general were knowledgeable about different instructional strategies and the curriculum about the topic of their microteaching, but their knowledge of learners was relatively poor. Implications for teacher education are discussed.