• School Mathematics
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• v.4 no.1
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• pp.79-95
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• 2002

This paper is to make strides toward an enriched understanding of student learning and performance in mathematics that acknowledges the roles social and cultural contexts play in what students learn as well as what we are able to team about student learning. A student's mathematical practice over a year and a half is presented in detail in order to explore the relationships between classroom contexts and student performance. This study was situated at a K-4 urban elementary school in the United States. The data used for this study included classroom observations, interviews with the teachers and the student, and document collection. The data were analyzed by characterizing each classroom context and exploring the student's practice both in the classrooms and in the interviews. Despite the student's ongoing status as a struggling student, there were tremendous changes in his level of engagement in and persistence with mathematical tasks. The student was substantially more engaged in and enthusiastic about the daily mathematics lessons in third grade than he had been in second. However, we found little improvement in his mathematical understanding and performance during class or in the interviews. This highlights that increased engagement in the mathematical tasks does not necessarily signal increased learning. This paper discusses several issues of learning and performance raised by the student, looking at the relationship between classroom context and student performance. This paper also considers implications for how students' performances are interpreted and how learning is assessed.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.163-192
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• 2018

The purpose of this study was to examine the relations among mathematics teachers' beliefs, classroom norms and discourse, and equity issues in mathematics classrooms. In order to achieve this purpose, three teachers who work in the same school were analyzed. The analysis revealed that the participating teachers' beliefs about mathematics teaching and learning and about their students' abilities and motivation influenced the establishment of classroom norms and discourses that defined what students needed to do to be successful mathematics learners. Also, classroom norms and discourse affected the development of students' identity and power and the level of equity in the classroom.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.487-509
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• 2022

The purpose of this study is to analyze classroom discourse in the math classroom of middle school in China, which has a unique math classroom background of entrance examination for high school. To this end, this study analyzed teacher question statistics and episodes by teacher question type as starting speech in mathematics classroom discourse, and five IRF subtypes were especially identified by class discourse structure analysis. The data were analyzed focusing on a total of 15 transcripts of math classes recorded by three math teachers at H School in Guiyang, Guizhou Province, China, and written interviews of teachers. According to the results of this study, an average of 20 teacher questions were observed for each class, and the teacher question type was classified into confirmation question (understanding confirmation question, explanation request question, and double check question) and information question (information presentation question). In addition, according to classroom discourse analysis, the IRF discourse structure was divided into fragmentary evaluation, evaluation+reason, evidence of explanation, evaluation+student response re-statement, guidance on other thoughts or solutions, and student answer correction or teacher opinion presentation.

• Research in Mathematical Education
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• v.16 no.2
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• pp.107-123
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• 2012

A group of twenty-nine high school student-teachers were given a set of mathematical propositions focusing on shape-to-shape transformations. Their task was to determine through hands-on manipulation and use of dynamic software that each shape be transformed into an area equivalent rectangular region. This paper reports on a classroom-based research.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.229-238
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• 2006

During World War II there was a statistical analysis conducted by the Allied analysts to estimate the German war productions, including their tank productions. This article revisits the analysis of the tank productions as a classroom activity format. Various reformed ideas are proposed in order to enhance students' perspectives of the point estimation. Comprehensive simulation works and actual classroom discussions will be provided along with the theoretical investigations.

• School Mathematics
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• v.19 no.1
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• pp.19-41
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• 2017

The purpose of this article was to a) identify how preservice teachers conceive feedbacks and subsequent classroom discourses, and b) compare them with those in reform-oriented mathematics classroom video for mathematics teachers' professional development about classroom discourse. This article analyzes feedback patterns and subsequent classroom discourses in preservice teachers' imaginary classroom scripts (lesson plays) and compares them with those in the reform-oriented classroom video dealing with the same teaching situation. Most of the preservice teachers' feedbacks focused the evaluation of students' responses and transmission of meaning (univocal function), whereas the teacher's feedback in the reform-oriented classroom allowed the whole class to validate or challenge the answers, thereby facilitating students' generation of meaning (dialogic function). The comparison analysis between the univocal discourse in a preservice teacher's lesson play and the dialogical discourse in the reform-oriented classroom video shows that teacher feedback serves as an important indicator for the main function of classroom discourse and the levels of students' cognitive participation, and also as a variable that determines and changes them. This case study suggests that to improve the quality of classroom discourse, preservice and in-service teachers need experience of perceiving the variety of feedback patterns available in specific teaching contexts and exploring ways to balance the univocal and dialogical functioning in their feedback move during the teacher training courses.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.523-545
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• 2010

Mathematical communication has been emphasized not only as the process of learning mathematics but also as the objective of mathematics education. However, little studies have been conducted with regard to what to consider and how to implement in the actual classroom for promoting mathematical communication. Given this background, this paper implemented a mathematics instruction in each of 2nd, 4th, and 6th grade classrooms in which specific learning objectives were considered to promote discourse-based mathematical communication. It then analyzed the degree by which such learning objectives were achieved and the linguistic interactions between the teacher and students in each classroom. This paper finally provided issues and suggestions for effective discourse-based instruction in mathematics classroom by analyzing similarities and differences among the three classrooms.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.521-536
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• 2017

One of difficulties with which teachers meet is to have underachievers with no willingness and motivation for study involved in class. Mathematics underachiever are average or above average in their intelligence but their actual achievement in mathematics did not coincide to their intellectual capabilities. The teaching strategy for them is to motivate them to try to study mathematics and to experience the improvement in their mathematics grade. In this paper, we choose flipped classroom as the strategy of teaching basic mathematics to math underachievers and applied it to them. Then we wanted to make sure the possibility for applying flipped classroom to teaching math underachievers through the analysis of change in the scholastic achievement of students in mathematics and mathematical disposition. The results of this study are as followings; First, when we taught basic math to underachievers using a flipped classroom, we confirm that math underachievers with active participation improved scholastic achievements significantly. Second, the flipped classroom was led to positive effects in an affective domain. In particular, it showed the most noticeable change in the area of willingness to math problem-solving and perception about the value of mathematics.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.261-275
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• 2016

Many students have dualistic beliefs about mathematics and its learning- for example, there is always just one right answer in mathematics and their role in the classroom is receiving and absorbing knowledge from teacher and textbook. This article investigated some epistemic implications and limitations of common mathematics teaching practices, which often present mathematical facts(or procedures) and treat students' errors in a certain and absolute way. Langer and Piper's (1987) experiment and Oliveira et al.'s (2012) study suggested that presenting knowledge in conditional language which allows uncertainty can foster students' productive epistemological beliefs. Changing the focus and patterns of classroom communication about students' errors could help students to overcome their dualistic beliefs. This discussion will contribute to analyze the implicit epistemic messages conveyed by mathematics instructions and to investigate teaching strategies for stimulating students' epistemic development in mathematics.

• Research in Mathematical Education
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• v.15 no.2
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• pp.105-114
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• 2011

During the 20th century, the secondary school mathematics teaching in China had been developing from the an old-style private school form with individual instruction to classroom teaching with Chinese characteristics, which experienced three stages of development; the stage for the formation of modern teaching system (1902-1949), the stage for development (1950-1976), and the stage for innovation (1977-2000). The characteristics and journey for the transformation will exert great for reference and effects for the reform of secondary school mathematics teaching nowadays.