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This study aims to investigate and compare mathematics teachers' knowledge of pedagogical content, knowledge of students' understanding and knowledge of instructional strategies, subcomponents of pedagogical content knowledge, student errors in the relationship between perimeter and areas in rectangles, squares, and parallelograms. 10 pre-secondary school in-service mathematics teachers and 10 prospective mathematics teachers participated in the study. The qualitative case research approach was used. To collect the data, an interview form consisting of four questions showing student errors related to perimeter and area was prepared. The participants were asked to comment on the questions given in the form, and their answers were recorded. Later, they were asked to write down their answers to these questions. According to the outcomes, there is a lack of knowledge of students' understanding and knowledge of instructional strategies, which are the subcomponents of the pedagogical content knowledge of prospective mathematics teachers. Moreover, prospective teachers are found to be incompetent as regards the necessary mathematical subject matter knowledge. To prevent difficulties, when the concepts of perimeter and area are taught, instead of giving formulae initially, concrete materials or real-life examples about these concepts should be provided.

The aim of this study is to investigate pre-service mathematics teachers' beliefs towards mathematics and modelling in mathematical modelling processes. To achieve this aim, a phenomenology design was utilized. The study was conducted with 30 elementary level pre-service mathematics teachers receiving mathematical modelling courses. A semi-structured interview form was used to explore teachers' beliefs. At the end of the study, it was seen that mathematical modelling applications caused an increase of application-oriented beliefs. It was also observed that pre-service teachers who had schema and formalism-oriented beliefs evaluated mathematical modelling practices as time consuming and incomprehensible. Findings imply that modelling applications should be included in all levels of mathematics instructional curricula, in addition to the undergraduate curriculum.

This study investigated whether the Science on Stage, a theatre and drama project, taught middle-school students more about the lives and discoveries of great scientists and whether it helped them develop positive views and attitudes towards the science course and scientists. This 8-month study employed an embedded design. The sample consisted of 20 eight graders. Quantitative data were collected using a Scientists Success Test, a Scale of Attitude towards the Science Course, and a Questionnaire of Views on Scientists, and then, were analysed using a one-sample t-test and Wilcoxon signed ranks test. Qualitative data were collected through interviews with a semi-structured interview form developed by the researchers, and then, were analysed using inductive content analysis. The Science on Stage helped participants learn more about the lives and discoveries of great scientists but had no impact on their attitudes towards the science course and scientists. It contributed not only to the history of science but also to academic and personal development. It helped participants recognise scientific facts and develop social and academic skills and made them more curious and motivated about science and art. The study discussed the results with reference to the literature and made suggestions for future research.

This study addressed in-class activities with concrete mathematics (math) materials developed by preservice math and primary school teachers in woodworking workshops and investigated what preservice teachers and primary and secondary school students thought about lectures with those materials. The study employed an embedded mixed design, a predominantly quantitative approach. The sample consisted of 23 preservice math and primary school teachers and 30 secondary school and primary school students in Turkey. Quantitative data were collected using the Torrance Test of Creative Thinking Test. Qualitative data were collected using a Material Design Evaluation Rubric and a Semi-Structured Interview Form. The results showed that the woodworking workshops improved the figural creativity of the preservice math teachers and both the figural and verbal creativity of the preservice primary school teachers. The preservice teachers had no idea about what woodworking workshops were and had difficulty mostly with sandpapering and cutting. The primary and secondary school students stated that they enjoyed using the math materials and learned better. In line with the results of the research, it can be suggested that woodworking workshops be expanded not only in universities but also in primary and secondary schools. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine the working of prospective mathematics teachers on a modeling problem for the real-life use of a formula taught in the analytical geometry course, within the framework of the dual modelling cycle (DMCF), and to compare their success in the questions given as theories and relations in real-life contexts. A case study was performed with six prospective mathematics teachers in Turkey. The data consisted of the solution papers of two activities, toilet paper tubes, the voice records, and classroom observations. In the dual modelling cycle framework (DMCF), participants resolved the results obtained from the working mathematically stages of the second activity by transferring them to the initial activity. Utilising the dual modelling cycle, prospective teachers could use similar and simpler activities to solve real life problems which they previously found difficult to solve. Participants were more successful in solving theoretical questions than the modelling activities. The dual modelling activities carried out in this study implies that prospective teachers can apply one of the theoretical equations they learned in field courses to real life. [ABSTRACT FROM AUTHOR]