• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.11-35
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• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.377-394
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• 2019

The purpose of this study is to scrutinize the characteristics of a teacher's discursive competence on the basis of mathematical competencies. For this purpose, we observed all semester-long classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers' problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

• The Mathematical Education
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• v.59 no.2
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• pp.101-112
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• 2020

The purpose of this study is to analyze the structures of teacher's discourse according to the pattern of interaction between teachers and students in the understanding mathematical word problem. The structures of teacher's discourse could be conceptualized as a process in which the teacher starts, develops and organizes the discourse based on prior research. For this purpose, the fourth class(example, a problem of the same type as the example, formative assessment, and final assessment) was extracted from one semester of experienced teachers who have been practicing teaching methods to facilitate student participation for many years. A methodology used to develop a theory based on data collected through classroom observations. Because the purpose of the study is to identify the structures of teacher's discourse to help the problem understanding, observe the teacher's discourse and collect data based on student engagement. Results show that the structure of teacher's discourse, which consults on important aspects of interaction between teachers-students and creates mathematical meanings, helped students understand the mathematics word problem by promoting their engagement in class. Based on the structures of teacher's discourse to understand problems based on the interaction patterns between teachers and students, it can be said that teachers provided specific methodologies on how to communicate with students in order to understand problems in the future.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.179-200
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• 2020

The study investigates how two different methods of peer tutoring impact academic achievement and student affect in a high school mathematics class. The two methods include the one-on-one non-reciprocal peer tutoring and the one-on-four interactive peer-tutoring method. We looked into students' cognitive gains and their affect toward mathematics after students had experienced peer tutoring for six weeks. Further, we analyzed student responses in a survey about peer tutoring activities. A finding is that the two methods produced no statistically significant difference in both cognitive gains and student affect toward mathematics. As students expressed views about their peer tutoring experiences, their comments, however, revealed the multifaceted aspects of peer tutoring in the classroom setting. In turn, this supports the use of diverse peer tutoring methods especially when the teacher makes incremental changes in teaching practices to improve student learning. Findings also indicate that appropriate peer tutoring experiences have the potential to create intellectually safe learning environments with high student engagement. This underscores the benefit of designing and implementing diverse peer tutoring methods that are effective in engaging students in learning and increasing the opportunity to learn and create knowledge with peers.

• The Mathematical Education
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• v.60 no.1
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• pp.77-110
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• 2021

In this study, a student participation-centered class based on student mathematical thinking as a the meaningful subject was called a student thinking-based math class. And as a way to support these classes, I paid attention to lesson design. For student thinking-based mathematics classes, it is necessary not only to anticipate student thinking and teacher feedback, but also to plan in advance how to properly arrange and connect expected student responses. The student thinking-based lesson design template proposed in this study is a modified three-step(introduction, main topic, summary) lesson design template. The reason for revising the existing design template is that it has limitation that it cannot focus on mathematical thinking. Using the conceptual framework of student thinking-based mathematics lesson as a lens, the difference between the three-step lesson design prepared by pre-service teachers and the students' thinking-based lesson design prepared by the same pre-service teachers was analyzed. As a result of planning lessons using the student thinking-based lesson design, more attention was paid to the cognitive and social engagement of students. In addition, emphasis was placed in the role of teachers as formative facilitator. This study is of significant in that it recognizes the importance of classes focusing on students' mathematical thinking and provides tools to plan math classes based on students' thinking.