Number talks as a brief instructional routine benefits students and teachers. In general, the routines consist of four steps- introducing, posing questions, collecting answers, sharing ideas. This paper focuses on the sharing ideas step in which multiple strategies are shared by students because teachers sometimes do not know what to do with these multiple ideas. One way is to support students to engage in comparison given that teachers are expected to support students to compare strategies in number talks. This paper explores whether and how 15 prospective teachers supported students in their practicum classroom to compare different strategies in their enacted number talk. In this paper, 15 videos of number talks enacted by the prospective teachers were collected. Analyzing the videos produced multiple episodes in relation to comparing strategies, including 1) where prospective teachers created pre-conditions for comparison, 2) where they invited students for comparison, 3) where they pressed students to compare, and 4) where they offered their own way to compare. There were two patterns that might limit the potential of having multiple strategies as conditions for comparison. Additionally, this paper found that even though the prospective teachers missed opportunities to support students to compare different strategies, there were two ways for teachers to support students to engage in comparison. These findings can be used for mathematics teacher educators to support prospective teachers.

In the context of Korean educational research, the number of qualitative research studies has gradually increased since 2000. It has become one of the most important research methods today. The field of math education is no exception to this trend, and qualitative approaches are now becoming one of the main research methods. This increase in qualitative research has contributed to the provision of detailed information about educational practice, but at the same time, the overall level of credibility in the results of qualitative research seems to be lower than that of quantitative research. This study started with the problem consciousness that the number of qualitative studies is increasing in the field of mathematical education, but there is a lack of discussion on the methodology of applying qualitative research methods. In this study, among the papers published in the journal related to mathematical education, papers using a qualitative approach are analyzed focusing on cross-case analysis. Based on the analysis results, the tendency to use qualitative approaches is diagnosed, ways of improving the validity and trustworthiness of qualitative research results in the field of mathematical education are examined, and implications and suggestions are presented.

Lecture theatres and computing laboratories are common types of classrooms used for teaching and learning in this study; both were equipped with a computer network through which teachers and students can access learning management system, digital library, educational software, and so on. Students were divided into groups of two or three; each group of students collaborated on the worksheets in the laboratory and naturally sat together when attending a class held in the lecture theatre. The social organization of classroom learning would promote student learning but what drives student learning; how to engage students with learning; and how to maintain their interest in learning are of research interest in the present study. The study illustrated the theoretical and empirical links, student motivation has a relation to rich collaboration with peers, communication as verbal interactions as well as teacher-student interactions. These are within socio-cultural contexts for learning to take place. The study was extended to make comparisons of the motivational orientations between student genders. It was found that female students were keener on fun or enjoyment in learning, peer communication, and teacher's intervention, whereas male students were concerned more about digital learning tools, a positive working relationship, social reciprocity, and interpersonal relationships.

With the rapid advancement of educational technology, recent studies have connected teachers' professional noticing with the use of digital resources in mathematical instructions. In this study, I examined elementary mathematics preservice teachers' attending and interpreting a mathematical software, ST Math, in the exploring and implementing phases. The findings indicate that preservice teachers paid attention to visual representations and manipulation prior to interactions with children and further took into consideration on task structures and situated context after interactions. They interpreted the events based on connected mathematical knowledge of prior interactions and further reflected on the progression of problem-solving strategies and sequence of tasks. In addition, four distinctive profiles of transitioning of evaluation on ST Math activities were identified with illustrations. Implications for noticing and teacher education were discussed.