• 한국수학교육학회지시리즈A:수학교육
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• 제54권3호
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• pp.207-222
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• 2015

Mathematics preservice teachers' Mathematical Content Knowledge ("MCK") includes not only knowledge for mathematics, but also academic knowledge for school mathematics and mathematical process knowledge. We can consider the items in PISA 2012 as suitable tools to assess process knowledge as well as mathematical content knowledge because these items are developed by competent international educational experts. Therefore, the responses to items with the low percentage of correct answers in conjunction with the mathematical contents were analyzed with focus on FMC. The results showed the reasoning competency in responses using the conditions of the problem and of understanding the conditions after reading the complex problems within the context (i.e. the reasoning and argumentation competency, and communication competency) requires improvements. Furthermore the results indicated the errors due to a lack of ability of devising strategies for problem solving. Based on the foregoing results, the implications towards the directions of the education for the preservice mathematics teachers have been derived.

• 대한수학회지
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• 제58권6호
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• pp.1311-1325
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• 2021

One says that a ring homomorphism R → S is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element f ∈ S, there is a unique smallest ideal of R whose extension to S contains f, called the content of f. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically 'yes' in dimension one, but 'no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권3호
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• pp.261-282
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• 2015

The purpose of this study was to provide insights on making Korean mathematics framework by analytical comparison of three major assessments such as the NAEP 2015, the TIMSS 2015 and the PISA 2015. This study focused on the key differences and common themes of mathematics frameworks among three major assessments. In order to achieve this purpose, mathematical frameworks of the NAEP 2015, the TIMSS 2015, and the PISA 2015 were analyzed and compared. The criteria of the comparison were content domain and cognitive domain. The comparing criteria of content domain were based on NCTM content standards and cognitive domain were used the three understanding levels of Jan de Lange's pyramid model. Based on these comparisons, researchers discussed that Korea mathematical framework was needed to have a set of content categories that reflect the range of underlying mathematical phenomena and a set of cognitive levels which contain the range of underlying fundamental mathematical capabilities including consideration of contexts.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권3호
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• pp.281-300
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• 2015

본 연구의 목적은 스토리텔링 수학 교과서 개발과 학교 현장에서 스토리텔링 교과서 활용의 방향성을 제시하기 위해, 2009 개정 교육과정에 따른 중학교 2학년 수학 교과서 5종을 연구 대상으로 수학 과제 유형에 따른 인지적 노력 수준, 답안 유형, 스토리텔링 유형을 분석하였다. 연구 결과, 첫째, 수학 과제의 인지적 노력 수준은 공통적으로 모든 교과 내용 영역에서 PNC(Procedures without Connections) 과제가 가장 많은 비중을 차지하였고, 수학적 내용 과제에서는 인지적 노력이 낮은 수준의 과제(Low-Level)가 많았고, 수학적 활동 과제에서는 인지적 노력이 높은 수준의 과제(High-Level)가 더 많았다. 둘째, 학생들에게 요구하는 답안 유형은 모든 영역에서 단답형이 가장 많았고, 수학적 내용 과제의 대부분은 단답형, 수학적 활동 과제는 단답형과 설명형이 많았다. 마지막으로 스토리텔링의 유형은 실생활 연계형이 가장 많은 비중을 차지하고 있었고, 수학적 활동 과제의 수가 수학적 내용 과제의 수보다 휠씬 적었다. 그러나 스토리텔링 유형이 반영된 과제에서는 수학적 활동 과제의 비율이 수학적 내용 과제의 비율보다 더 높았다. 이러한 연구 결과를 바탕으로 향후 다른 학년의 스토리텔링 수학 교과서를 개발하고 학교 현장에 적용할 때, 수학 과제 유형에 따른 인지적 노력 수준, 답안 유형, 스토리텔링 유형에 대해서 균형성과 다양성을 고려해야할 필요성을 제시할 수 있다.

• East Asian mathematical journal
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• 제36권2호
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• pp.229-251
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• 2020

Problem Based learning(PBL) is a teaching and learning method to increase mathematical ability and help achieving mathematical concepts and principles through problem solving using the learner's mathematical prerequisite knowledge. In addition, the recent instructional situations or environments have focused on the learner's self construction of his learning and its process. In spite of such a quite attention, it is not easy to apply and execute PBL program actually in class. Especially, there are some difficulties in actually applying and practicing PBL in the areas of mathematics education in not only secondary school but also in college. Its reason is that in order to conduct PBL instruction constantly in real or experimental class there is no more concrete and detailed instructional content during the consistent and long period. However, to whom is related to mathematics education including instructors called scaffolders, investigation and recognition on the degree of the learner's acquisition of mathematical thinking skills and strategies is an very important work. By the reason, in this study, the instructional content was to be explored and developed to be conducted during 15 weeks in one semester, which was based on Problem Based Learning environment by the subject of the theories relevant to mathematics education in the college of education.

• East Asian mathematical journal
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• 제38권4호
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• pp.517-532
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• 2022

This study looked at how content reviews with mathematical games in class would influence the mathematical disposition of middle school students. In doing so, three games adapted from prior research were used as a supplementary instruction after school hours over three months. The mathematical topics of the games involved concepts of probability and trigonometry at the middle school level. The results of the pre- and post-survey on mathematical disposition indicate that incorporating mathematical games appeared to have some positive impacts on whether students might be more eager to learn mathematics and actually put more effort in learning materials.

• East Asian mathematical journal
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• 제27권4호
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• pp.471-483
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• 2011

The purpose of this study is to introduce the Common Core State Standards (CCSS) for mathematics which is released on June 2, 2010 in the U.S.A. The common core state standards are aligned with college and work expectations, and include rigorous content and application of knowledge through high-order skills. The most distinguishable differences between the CCSS standards and the NCTM standards are that the CCSS standards considers the mathematical modeling as one of the mathematical content domains such as algebra, geometry, ets, and the standards are designed by working together with school leaders of all states.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권1호
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• pp.47-61
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• 2013

This paper aims to explore whether Learning Study improves teachers' subject content knowledge, pedagogical content knowledge, and attitude toward teaching mathematics. A Learning Study was conducted in a Hong Kong primary school for a research lesson on comparing the size of fractions to explore the new teacher roles.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권3호
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• pp.257-273
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• 2004

In this paper, we analyze what the components of mathematics teacher` knowledge are, and find that mathematics teacher need knowledge of three areas: subject matter knowledge, pedagogical knowledge, and pedagogical content knowledge. Studies of practicing teachers suggest that When teachers lack understanding in their respective disciplines, it inhibits them from providing students the best learning opportunities, but that a teacher possessing pedagogical content knowledge provides learners with multiple approaches into learning. Some teachers having sound knowledge of mathematics and students were able to respond appropriately to students' questions, design appropriate learning activities involving a variety of mathematical representations, and orchestrate mathematical discourse in the classroom. Thus, it appears that mathematics teachers' knowledge positively affect teaching and student learning..

• East Asian mathematical journal
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• 제39권2호
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• pp.141-166
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• 2023

The purpose of this study is to confirm the MKT(Mathematical Knowledge for Teaching) of the in-service mathematics teachers on the statistics(Representative value, Degree of scattering) through the comparative analysis between the sub-elements of the MKT. In addition, it is to examine the factors that cause the difference of the subjects' MKT. To accomplish this, by the subject of 12 secondary in-service mathematics teachers, in this study the test items of the MKT on the statistics were developed and data were collected and analyzed. As a result of the analysis of the MKT test sheet, the CCK(Common Content Knowledge) and SCK(Specialized Content Knowledge) of the mathematics teacher was confirmed as a high score, whereas the and KCS(Knowledge of Content and Students) and KCT(Knowldge of Curriculum and teaching) were confirmed as low scores. In addition, through these results, it was shown that the difference in MKT's elements the middle school and high school teachers obtain occurred slightly.