• The Mathematical Education
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• v.52 no.4
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• pp.517-529
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• 2013

The purpose of this study is to investigate pre-service teachers' perceptions and their difficulties of mathematics instruction. Pre-service teachers have positive perceptions about teaching students and teaching profession through teaching practicum. In addition, they have perceived that teaching practicum can enhance teaching methods for their students. Especially, they suggested that cooperating teachers' instruction and mathematics teachers and their colleagues' classroom observation are important factors to improve their teaching methods. In other hands, they have difficulties in application of questions encouraging mathematical thinking, attention concentration considering students' interest and planning and performing for mathematics instruction class according to levels of students' study abilities. Based upon this study's findings, teacher education institutes should make efforts to alleviate difficulties in mathematics instruction through effective teaching practicum such as regular reflection activities for their classes, programs development associated with schools, pre-training and education programs for guidance teachers.

• Research in Mathematical Education
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• v.6 no.1
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• pp.1-28
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• 2002

This study explored teachers (n = 219) from northern, central, southern and eastern Taiwan concerning their views about children's learning difficulties, mathematical instruction and school mathematics curricular. Results showed that teachers' mathematics knowledge or their instruction methods had no significant influence on their views of children's learning difficulties. Even though teachers indicated that understanding of abstract mathematical concepts was the most prominent difficulty for children, they tended to employ direct instruction rather than constructive and cooperative problem solving in their teaching. However, teachers' views of children's learning difficulties did influence their instructional practice. Results from in-dept interviews revealed that there were some obstacles that prevented teachers from putting constructiveism perspectives of instruction into teaching practice. Further investigation is needed to develop a better understanding of epistemology and teaming psychology as well as to help teachers create constructive learning situations.

• The Mathematical Education
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• v.45 no.4 s.115
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• pp.459-479
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• 2006

There has been an increasing concern of whether a real instructional change happens in a way to promote students' mathematical development. Against this background, this paper dealt with successes and difficulties an elementary school teacher went through as she moved on to student-centered instruction. The analysis drew on classroom observations for one year to illustrate how the teacher and students established social norms, sociomathematical norms, and classroom mathematical practices that could emphasize mathematical sense-making and justification of ideas. Close analysis showed many gradual but dramatic changes in terms of mathematics classroom culture. This led to consider possibly subtle but crucial issues with regard to implementing student-centered instruction.

• The Mathematical Education
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• v.61 no.1
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• pp.179-198
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• 2022

Teaching is delicate, complicated, and demanding work, and especially beginning teachers set forth their difficulties in preparing and implementing mathematics instruction. It is important to ensure the quality of beginning mathematics teachers' instruction above a consistent level because such affirmation justifies the national policy on teacher education as well as the individual efforts of preservice teachers in South Korea. The current study collected mathematics lessons of the two beginning teachers who graduated from the same teacher training institute and worked at the same high school. The findings reported what features their lessons have with regard to the learning environment, engaging students in learning, deepening student learning, and using representations of the edTPA in order to identify what can or cannot be expected in their mathematics instruction. The instruction of the one teacher was assessed middle or more than middle scores throughout the rubrics, but the other one had lower scores. Based on these findings, this study suggested the implications for teacher education in ways of improving the quality of instruction of beginning mathematics teachers.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.27-51
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• 2012

This paper analyzed the pedagogical content knowledge (PCK) presented in three novice teachers' mathematics instruction. PCK was analyzed in terms of the knowledge of mathematics content, the knowledge of students' understanding, and the knowledge of teaching methods. Teacher A executed a concept-oriented instruction with manipulative materials because she had difficulties in learning mathematics during her childhood. Teacher B attempted to implement an inquiry-centered instruction in the lesson of looking for the area of a trapezoid. Teacher C focused on the real-life connection to mathematics instruction. There were substantial differences among the teachers' PCK revealed in mathematics teaching, depending on their instructional goals. The detailed analyses of three teachers' teaching in terms of their PCK will give rise to the issues and suggestions of professional development for beginning elementary school teachers in mathematics teaching.

• Education of Primary School Mathematics
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• v.10 no.2
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• pp.141-149
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• 2007

It is undeniably important to bring up a solution capability of arithmetic word problems in the elementary mathematical education. The goal of this study is to acquire the implication for remedial instruction on arithmetic word problems solving through surveying elementary school students' difficulties in the solving of arithmetic word problems. In order to do it, this study was intended to analyze the following two aspects. First, it was analyzed that they generally felt more difficulties in which field among addition, subtraction, multiplication and division word problems. Second, with the result of the first analysis, it was examined that they solved it by imagining as which sphere of the other word problems. Also, the cause of their error on the word problem solving was analyzed by the interview. From the foregoing analyses, the following implications for remedial instruction on arithmetic word problems solving are acquired. First, the accumulation of learning deficiency must be diminished through the remedial instruction. Second, it must help students to understand the given problem and to make of what the goal of problem is. Third, it must help students to form a good habit for reading the problem and to understand the context of problem. forth, the teacher must help students to review and reflect their problem-solving processes.

• School Mathematics
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• v.3 no.2
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• pp.373-399
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• 2001

The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.127-150
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• 2006

The purpose of this study is to apply the principles of CGI(Cognitively Guided Instruction) into mathematics class in Korean elementary schools and to explore which mathematical concepts Korean students have and how they use informal knowledge and procedures to solve problems. In addition, this study tries to analyze difficulties that teachers might face when they are planning mathematics teachings based on CGI. The conclusions of this study are followings: First, the mathematics teaching based on CGI provides opportunity for students to communicate about mathematical knowledge that they know, The students are sure of their thoughts and learn from others by presentation. Second, the mathematics teaching based on CGI make students think mathematically. The students try to understand the meaning of problems and find various ways. Third, teachers should lead appropriate environment for the mathematics teaching based on CGI. They should offer proper problems and encourage their students to ask and answer questions respectively.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.295-308
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• 2007

The purpose of this paper was to investigate the pedagogical content knowledge of a middle school mathematics teacher manifested in his mathematics instruction by identifying the components of the pedagogical content knowledge of the teacher. For the purpose of the study, I conducted an interpretive case study by collecting qualitative data. The results showed that the pedagogical content knowledge of the teacher was characterized by: (a) knowledge of mathematics including connection among topics and various ways of solving problems; (b) knowledge of students' understanding involving students' misconceptions, common errors, difficulties, and confusions; and (c) knowledge of pedagogy consisting of his efforts to motivate his students by providing realistic applications of mathematical topics and his use of materials.

• School Mathematics
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• v.9 no.4
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• pp.447-466
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• 2007

Math education in schools have to enable students to understand the importance of math and nurture the capacity to resolve various problems in daily life with reasoning, which is therefore, always applicable to the actual world. Proportional reasoning capacity is being often used in daily life, and some kind of unit is not fixed. So students are considering it very difficult. This study looks into the difficulties that students have in proportional reasoning, what kind of problem solving strategy is being used, what the problems are in current textbooks, etc. Based on this, it tried to check the concept changes in students' proportional reasoning by developing the instruction program for 'proportional expression' unit in the 6th grade. Based on the results, this study analyzes the features of proportional reasoning instruction programs and the instruction results. Also it analyzes in-advance & after examination papers of the experimental class and comparison class to contribute to the instruction method and instruction contents improvement of 'proportional expression' unit.