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To transform the knowledge and skills they develop through teacher education programmes into successful instructional practices, preservice teachers should strongly believe in their capabilities. T...

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of real life problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students' ways of thinking. The researchers' conceptual development, on the other hand, involved realizing the critical aspect of the teacher role played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.

This study investigated how prospective teachers notice student mathematical thinking in a video-based learning environment and in analyzing students’ thinking when they conduct a research in their practice schools in the scope of a 14-week elective course program. Instructional process of the course had two phases. In the first phase, a group of eight prospective mathematics teachers analysed video cases related to students’ mathematical thinking. In the second phase, they explored actual students’ mathematical thinking through diagnostic interviews in their practice schools in order to conduct a small-scale research project. The results indicated that while prospective teachers tended to be more simplistic in analysing students’ thinking in their early video-case analyses, they came up with deeper analysis of student thinking by making sound inferences from data and proposing pedagogical strategies. Moreover, prospective teachers stated that micro-case videos functioned as a catalyst for enhancing their noticing of student thinking before conducting small-scale research projects.

This research provides the instructional exploration of analytic geometry pattern based on van Hiele thinking pattern, and the potential of GeoGebra effect on experimental group along with its nested group (high and low achievers) in comparison with control group in analytic geometry. To investigate the significant effect of GeoGebra, the two match groups were constructed on their previous grade-11 mathematics records with almost equal statistical background and with the same compatibility in the biological age. Further, six-week experiments of 22 lessons were prepared and two teaching methods (tradition vs DGS aided instructions) were tested. Three hypotheses were carried out i.e. Treatment does not significantly affect, the two groups in mathematical achievement mean scores and, the higher and low achievers of the two groups in mathematical achievement mean scores. To measure the treatment effect, t-test was used by SPSS. Analyses of the research revealed that experimental group performed well, while; GeoGebra was influential in favor of low achievers in comparison to control low achievers.

Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students' higher-level thinking through effective questions. However, teachers' utilization of effective and higher-level questions is usually limited in traditional settings. The goal of this study is to investigate how secondary mathematics teachers' knowledge and skills of questioning change when they are engaged in professional development activities based on the modeling perspective. The program included five cycles each of which lasted a month. Each cycle consisted of meetings before and after the implementation of a model-eliciting activity and its implementation. The results showed that the professional development program had a positive effect on teachers' ability to ask qualitatively different questions in order to move students' thinking forward.

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students. mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers. knowledge to use modeling in mathematics education and how this knowledge evolves. The aim of this study is to investigate how teachers. pedagogical knowledge to use modeling in the classroom is formed and modified through professional development activities based on lesson study cycle from modeling perspective. The professional development program reported in this study included five monthly cycles consisted of meeting before the implementation, implementation of the activity and a follow up meeting. The participants were four in-service mathematics teachers. Results showed that the program provided opportunities for teachers to test, revise, and refine their knowledge. More specifically, teachers generated effective strategies for proper implementation of the modeling activities in the classroom.

This study investigated students’ scientific epistemological beliefs in relation to socio-economic status (SES) and gender. Data were obtained from 1,152 eight grade Turkish elementary school students using Scientific Epistemological Beliefs instrument. Canonical correlation analysis indicated that students with a working mother and educated parents as well as greater number of books at home together with a separate study room are more likely to have tentative views and less likely to have fixed views about science compared to students with unemployed mother, uneducated parents, less books at home, and no separate study room. Generally, results revealed while family SES correlated positively with tentative views, it was negatively associated with fixed views, implying that students from high SES family were more likely to believe that knowledge is uncertain and not handed down by authority compared to students from low SES family. This study, however, failed to indicate any relationship between father work-status, buying daily newspaper and epistemological beliefs. In addition, Multivariate Analysis of Variance indicated that boys more likely to have tentative beliefs compared to girls.

Researchers point out the importance of teachers’ knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students’ ways of thinking. This study investigated prospective secondary mathematics teachers’ interpretations of students’ thinking as manifested in students’ work that embodied solutions of mathematical modelling tasks. The data were collected from 25 prospective mathematics teachers enrolled in an undergraduate course through four 2-week-long cycles. Analysis of data revealed that the prospective teachers interpreted students’ thinking in four ways: describing, questioning, explaining, and comparing. Moreover, whereas some of the prospective teachers showed a tendency to increase their attention to the meaning of students’ ways of thinking more while they engaged in students’ work in depth over time and experience, some of them continued to focus on only judging the accuracy of students’ thinking. The implications of the findings for understanding and developing prospective teachers’ ways of interpreting students’ thinking are discussed.