• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.177-199
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• 2008

In the Netherlands, Streefland(Elbers, 2003) gave a solution on how teachers can help students to participate in the process of knowledge construction by investigating constructions and activities of a community of inquiry for a primary school students(between 11 and 13 years of age). In Australia, Goos(2004) analyzed the teacher's role in creating a classroom culture of inquiry, which appeared to be taken for granted by the Grade 12 group, for the Grade 11 students by classroom observation and interviews. In Korea, because of diverse obstacles with a university entrance examination, a study about teacher's role in inquiry-oriented instruction for high school mathematics schooling has rarely appeared in the literature. The purpose of this study is to investigate teacher's role for promoting and managing inquiry-oriented mathematics instruction effectively by a case study. To fulfill this purpose, we develop inquiry-oriented instruction model by investigating teacher's role as an assistant for helping students to do mathematical activity.

• The Mathematical Education
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• v.49 no.2
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• pp.223-246
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• 2010

Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.

• Education of Primary School Mathematics
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• v.6 no.2
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• pp.65-74
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• 2002

In this paper, inquiry-oriented mathematics instruction was suggested as a teaching method to foster mathematical creativity. And it is argued that inquiry learning assist students to explore the mathematical problem actively and thus participate in mathematical activities like mathematicians. Through inquiry activities, the students learn mathematical ideas and develop new and creative mathematical ideas. Although creativity is often viewed as being associated with exceptional ability, for mathematics teacher who want to develop students' mathematical creativity, it is productive to view mathematical creativity as a mathematical ability that can be fostered in general school education. And also, both teacher and student have to think that they can develop mathematical ideas by themselves. That is very important to foster mathematical creativity in the mathematics class.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.43-55
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• 2011

The purpose of this study was to investigate the effects of inquiry oriented instruction on the learning of area formulas. For this purpose, current elementary mathematics textbook(2007 revised version) which deal with area formulas was reviewed and then the experimental research on inquiry oriented instruction in area formulas was conducted. The results of this study as follow; First, there was no significant effect of inquiry oriented instruction on the mathematical achievement in area formula problems. Second, there was no significant effect on the memorization of area formulas. Third, there was significant effect on the generalization of area formulas. Forth, there was significant effect on the methods of generalization of area formulas. Fifth, through inquiry activities, the students can learn mathematical ideas and develop creative mathematical ideas. Finally, implications for teaching area formulas through inquiry activity was discussed. We have to introduce new area formula through prior area formulas which had been studied, and make the students inquire the connection between each area formulas.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• The Mathematical Education
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• v.41 no.2
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• pp.173-187
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• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.75-92
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• 1999

Many educators say that one of the key theory which is widely accepted teaching-learning process in the 7th mathematics curriculum is constructivism. They believe constructivism is very powerful as a background theory in teaching-learning mathematics and in this point of view, each student can construct knowledge by himself in the inner world. Therefore, the aspect of teaching-learning methods in the 7th mathematics curriculum focused on inquiry learning, self-directed learning, cooperative learning. Through this methods, the 7th mathematics text also composed of ease, interesting and dynamic activity oriented subjects. And constructive teaching-learning methods in mathematics is implemented variously by those whom attracted in constructivism. Thus, the purpose of this study is to build up a model that is required to systematize teaching-learning process in mathematics as a guideline for teachers. Another purpose of this study is to make clear that the presented model is appropriate process for teaching-learning in mathematics.