• The Mathematical Education
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• v.60 no.3
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• pp.297-319
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• 2021

The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.477-490
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• 2011

The concept of pedagogical content knowledge (PCK) has been developed and expanded to identify essential components of mathematical knowledge for teaching (MKT) by Ball and her colleagues (2008). This study proposes an alternative perspective to view MKT focusing on key developmental understandings (KDUs) that carry through an instructional sequence, that are foundational for learning other ideas. In this study we provide constructive components of KDUs in fraction multiplication by focusing on the constructs of 'three-level-of-units structure' and 'recursive partitioning operation'. Expecially, our participating preservice elementary teacher, Jane, demonstrated that recursive partitioning operations with her length model played a significant role as a KDU in fraction multiplication.

• Journal of The Korean Association For Science Education
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• v.36 no.1
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• pp.29-43
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• 2016

There have been much efforts to reconstruct the science curriculum focusing on Disciplinary Core Ideas(DCI) in many countries such as America and Europe, the most practical effort has been to design a curriculum with learning progressions(LPs). LPs describe stepwise how students can systematically move toward the understanding of more sophisticated ideas or scientific activities and explain in succession the process of understanding the ideas while the students learn. In this study, a LP for ecosystems has been developed, and the developed LP is then evaluated accordingly. The Ecosystem is one of the DCI of the life science in Next Generation Science Standards(NGSS). The development process of the LP was set at step 4(Development, Assessment, Analysis, and Amendment), and developed through an iterative process of sequences. As a result of analyzing the developed LP, an assessment based on the LP provides reliable information to identifying student ability. This study proposes the development process of the LP and its methodological aspects to use Core Achievement Standards, Ordered Multiple-Choice items and the Rasch model. In addition, using the empirically proven LP suggests a way of strengthening curriculum linked to educational content, teaching methods and assessment. Utilizing the proposed development process in this study will be to present the standard into the direction of becoming part of the curriculum. Currently, the state of domestic research for the LP is still lacking. This study determined the development process of the LP and the need to conduct future research on the LPs.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.261-272
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• 2018

In the current era of mathematics education, constructivism is a core theory of learning. For teachers, understanding and applying constructivism to their teaching practices are crucial for student centered teaching. However, some mathematics educators understand Constructivism in a different way. For example, some future teachers view Constructivism as making mathematics 'fun' by creating game without considering conceptual understanding. In this paper, the original articles of Constructivism were revisited and investigated to understand and to search for their meanings. Also several types and sources of Constructivism were identified; Radical Constructivism, Vygotsky's social-cultural theory of development, Social Constructionism, and Social Constructivism. This paper investigated arguments of the several types of Constructivism and discussed their implications for mathematics teaching.

• School Mathematics
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• v.12 no.4
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• pp.547-561
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• 2010

Even though statistics is considered as one of the areas of mathematical science in the school curriculum, it has been well documented that statistics has distinct features compared to mathematics. However, there is little empirical educational research showing distinct features of statistics, especially research into the understanding of statistical concepts which are different from other areas in school mathematics. In addition, there is little discussion of a relationship between the ability of mathematical thinking and the ability of understanding statistical concepts. This study extracted some important concepts which consist of the fundamental statistical reasoning and investigated how mathematically high achieving students understood these concepts. As a result, there were both kinds of concepts that mathematically high achieving students developed well or not. There is a weak correlation between mathematical ability and the level of understanding statistical concepts.

• School Mathematics
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• v.16 no.4
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• pp.727-743
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• 2014

The concepts of sample and sampling are central to the statistical thinking and foundations of the statistical literacy, so we need to be emphasized their importance in the statistics education. However, many researches which dealt with samples only analyze textbooks or students' responses. In this study, the concept of sample is addressed by a historical consideration which is one aspect of the didactical analysis. Moreover, developing concept of sample is analyzed from the preceding studies about the statistical literacy, considering the sample representativeness and the sampling variability. The results say that the historical process of developing the concept of sample can be divided into three step: understanding the sample representativeness; appearing the sample variance; recognizing the sampling variability. Above all, it is important to aware and control the sampling variability, but many related researches might not consider sample variability. Therefore, it implies that the awareness and control of sampling variability are needed to reflect to the teaching-learing of sample for developing the students' statistical literacy.

• Journal of Gifted/Talented Education
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• v.25 no.6
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• pp.927-949
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• 2015

The purpose of this study was to find out the difference between importance and performance regarding perception of core competence of gifted education teachers through importance-performance analysis (IPA). One hundred fourteen elementary gifted education teachers including math and science participated in the study. The collected survey data was analyzed with IPA matrix. As the result, firstly, there was significant difference between importance and performance regarding perception of core competence of gifted education teachers. Secondly, core competencies of 'understanding knowledge', 'research and instruction', 'passion and motivation', and 'ethics' are high in both perceptions of importance and performance. However, both 'communication and practices' and 'professional curriculum development' are low. Thirdly, there was a difference in core competence of gifted education teachers between math and science at the competence of 'passion and motivation'. Math gifted education teachers perceived 'passion and motivation' high in both importance and performance while science gifted education teachers perceived its importance low and performance high. In addition, math gifted education teachers showed lower performance compared to its importance in the sub-categories; 'knowledge of gifted development', 'gifted child assessment', 'information gathering and its literacy', and 'creative answers to various questions'. However, science gifted education teachers showed lower performance compared to its importance in sub-categories; 'higher-order thinking skills in its subject', 'teaching methodology for self-directed learning', 'problem behavior of the gifted', and 'counseling the gifted'.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.79-101
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• 2016

Understanding the equal sign is of great significance to the development of algebraic thinking. Given this importance, this study investigated in what ways a total of 695 students from second to sixth graders understand the equal sign. The results showed that students were successful in solving standard problems whereas they were poor at items demanding high relational thinking. It was noticeable that some of the students were based on computational thinking rather than relational understanding of the equal sign. The students had a difficulty both in understanding the structure of equations and in solving equations in non-standard problem contexts. They also had incomplete understanding of the equal sign. This paper is expected to explore the understanding of the equal sign by elementary school students in multiple problem contexts and to provide implications of how to promote students' understanding of the equal sign.

• Korean Journal of Labor Studies
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• v.14 no.2
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• pp.169-200
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• 2008

노동계급은 다양한 형태의 내적 이질성을 지니고 있으며, 신자유주의 경제정책과 구조조정 과정에서 고용형태에 따른 이질성은 계급균열로 발달하며 노동계급 내적 이질성 논의의 핵심을 구성하게 되었다. 국내의 선행 연구들도 정규직과 비정규직 사이의 물질적 존재조건의 양극화 추세와 사회적 관계의 위계적 배제적 성격을 확인해 주고 있다. 하지만 정규직과 비정규직 사이의 계급균열이 극복되고 노동계급의 내적 통합과 계급형성 과정을 이룰 수 있는지에 대한 논의로 발전하지는 못했다. 본 연구는 계급균열의 극복과 노동계급 통합의 가능성을 검토하기 위해 계급균열의 핵심인 비정규직 노동자 문제를 둘러싼 정규직 비정규직의 의식 수준의 비교연구를 실시한다. 본 연구는 민주노총 공공운수연맹 노동조합원들에 대한 설문조사와 심층면접 연구를 통해 계급균열의 존재를 확인하고 그 원인과 의미를 분석하였다. 첫째, 정규직과 비정규직 노동자들은 비정규직 문제에 대한 인식을 공유하고 있지만 구체적 해결책에 대해서는 입장 차이를 보임으로써 고용형태에 따른 계급균열은 존재하며, 경제위기 이후에도 해소되지 않고 고착화되고 있음을 확인시켜 주었다. 둘째, 고용형태에 따른 계급내적 균열이 비정규직 문제 인식과 추상적 원칙 수준에서는 유의미한 의식 차이를 보이지 않지만 비정규직 문제 해결을 위한 구체적 해결책에 대해 유의미한 입장 차이를 보이는 것은 정규직과 비정규직 사이의 물질적 이해관계의 차이 때문이다. 정규직 노동자들은 비정규직 노동자들의 고용안정성과 노동조건의 개선을 허용하더라도 자신들의 이해관계가 위협받지 않는 수준에서 이루어져야 한다고 보는 것이다. 셋째, 정규직 노동자들이 추상적 원칙 수준에서는 비정규직 노동자들과 동질성을 보이지만 구체적 대안에서 차별성을 보이는 것은 정규직 노동자들의 의식의 양면성을 표현하는 것이며, 물질적 이해관계에 기초한 개인적 수준의 합리성과 계급적 원칙에 기초한 계급적 수준의 합리성이 갈등하고 있는 것이다. 넷째, 정규직 노동자들의 주관성 속에서 개인적 합리성과 계급적 합리성이 갈등하는 정도는 노동조합 가입 여부 및 소속 노동조합의 정체성, 즉 이익집단 정체성 혹은 계급조직 정체성에 의해 결정된다. 여기에 계급조직 정체성을 지닌 민주노조들이 노동계급 계급균열을 극복하고 계급형성을 이루는데 기여할 수 있다는 실천적 함의가 있다.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.569-594
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• 2010

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out several research as follows : 1) establishment of observation elements for selecting examples of good mathematics instruction between 2001 and 2002, 2) development of the standards on teaching evaluation between 2004 and 2006, and 3) investigation on the elements of Pedagogical Content Knowledge including understanding of learners between 2007 and 2008. The purposes of development of mathematics teaching evaluation standards through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those three studies (namely, evaluation standards) focused on the teacher knowledge of learners' understanding. For this purpose, the meaning of learners' understanding was also investigated in-depth. Finally, the concrete elements on teaching evaluation focused on the teacher knowledge of learners' understanding in math class were new developed, based on the literature reviews on learners' understanding. Then, those evaluation elements were developed according to the five domains of learners' understanding such as evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies.