• The Mathematical Education
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• v.62 no.4
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• pp.515-529
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• 2023

The purpose of this study is to analyze teachers' understanding of the number and operations area of grades 3 to 6 in elementary school mathematics curriculum and to derive implications for improving teachers' understanding of the mathematics curriculum. To this end, elementary school teachers were asked to develop items to evaluate curriculum achievement standards at each grade level, and then the teachers' understanding of the curriculum was examined based on the collected items. As a result of the study, there was a misinterpretation of the achievement standards in approximately 25% of the questions collected. Typically, cases where the content covered by each grade was confused when using textbooks as a standard, or cases where the difference between the content covered by the two achievement standards could not be completely distinguished were found.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.865-884
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• 2010

The purpose of this research was to analyze the characteristics of teachers' questionings in the geometry field and suggest the characteristics of teacher questioning to enhance students' mathematical creativity. Teacher questioning plays a role to students' mathematical achievements, mathematical thinking, and their attitudes toward mathematics. However, there has been little research on the roles of teacher questioning on students' mathematical creativity. In this research, researchers analyzed teachers' questions concerning the concepts of triangles in the geometric areas of 4th grade Korean revised 2007 mathematics textbooks. We also analyzed teachers' questionings in the three lessons provided by the Jeju Educational Internet Broadcasting System. We classified and analyzed teachers' questionings by the sub-factors of creativity. The results showed that the teachers did not use the questionings that appropriately enhances students' mathematical creativity. We suggested that teachers need to be prepared to ask questions such as stimulating students' various mathematical thinking, encouraging many possible responses, and not responding with yes/no. Instead, teachers need to encourage students to explain the reasons of their responses and to take part in learning activities with interest.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.465-492
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• 2014

In this study, through the analysis of the mathematics curriculum and textbooks, we produce the cooperative learning activity sheets which was appropriate instructional content for various levels. And, by using them appropriately at the levels of student learning on their own interest, we enhance academic achievement and cooperative learning attitudes. Specific for details for this study are as follows: First, through the applying a variety of the differentiated cooperative learning activity sheets and developing instruction learning, we improve the academic achievement. Second, through the making and utilizing the differentiated cooperative learning activity sheets and the interest and attitudes in mathematics, we improve the cooperative learning attitude. Third, through the levels of the subgroup cooperative learning, we improve the math learning abilities through a learner-centered. Further the purpose of this study is to bring up complementary cooperative spirit among colleagues.

• School Mathematics
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• v.4 no.4
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• pp.565-580
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• 2002

연구자들은 학생들에게 문제해결 전략을 지도하는 것이 학생들의 문제해결력을 신장시켜 준다는 보고하고 있다. 이와 같은 연구결과를 배경으로 수학 교과서를 통하여 문제해결 전략을 지도하려는 시도들이 미국을 비롯하여 한국에서도 있어 왔다. 본 논문은 문제해결 전략을 교과서에 제시할 수 있는 가능한 세 가지 모델들을 논의하고, 미국과 한국의 수학교과서에서 문제해결 전략을 제시하는 방법을 분석하였다. 한 가지 모델은 문제해결 전략에 한 단원을 할애하는 것이다. 두 번째 모델은 각 수학내용을 지도하는 단원에 문제해결 전략의 지도를 위한 하위단원을 할당하는 것이다. 마지막, 세 번째 모델은 문제해결 전략 지도를 위한 특정 단원이나 하위 단원을 설정하는 것이 아니라 가능한 많은 쪽에 전략을 제시하는 것이다. 위에 언급한 세 가지 가능한 모델을 바탕으로 미국과 한국의 초등학교 수학교과서에서 문제해결 전략을 제시하는 양상을 비교하였다. 이 비교를 위하여 각 학년별로 제시되는 모든 전략들을 교과서와 교사용 지도서를 토대로 추출하였다. 각 교과서에서 전략을 제시한 양식을 비교한 결과 다음과 같은 결론을 얻게 되었다. 한국의 수학교과서는 전형적으로 첫 번째 모델의 양식으로 문제해결전략을 제시하고 있었다. 각 단원마다 별개의 문제해결 전략이 제시되었다. 또한, 학년별 지도 전략을 살펴보면 학년별로 연계성이 있게 전략이 제시 되었다기 보다는 학년별로 다른 다양한 전자의 지도에 중점을 둔 듯하다. 미국의 수학교과서는 두 번째 모델과 세 번째 모델의 중간적인 양식으로 문제해결 전략을 제시하고 있다. 즉, 각 단원마다 문제해결 전략 지도를 위한 하위 단원을 지정하였으며 필요한 경우에는 본 단원의 주 학습요소와 관련된 문제해결 전략은 단원 중에도 제시되고 있었다. 따라서, 차기 수학교과서 개정시기에는 세 번째 모델을 그 모형으로 삼아 문제해결 전략들을 제시하는 방안을 강구해야 할 것으로 기대된다.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.407-434
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• 2008

This research is to analyze the descriptions in the statistic chapter of the grade 7's current textbooks. The analysis is based on the distribution concepts suggested by Nam(2007). Thus we assumed that the goal of this statistic chapter is to establish concepts on the distributions and to learn ways of communication and comparison through distributional presentations. What we learned and wanted to suggest through the study is the followings. 1) Students are to learn what the distribution is and what are not. 2) Every kinds of presentational form of distributions is to given its own right to learn so that students are more encouraged to learn them and use them more adequately. 3) Density histogram is to be introduced to extend student's experiences viewing an area as 3 relative frequency, which is later to be progressed into a probability density. 4) Comparison of two distributions, especially through frequency polygons, is to be an hot issue among educational stakeholder whether to include or not. It is very important when stochastic correlations be learned, because it is nothing but a comparison between conditional distributions. 5) Statistical literacy is also an important issue for student's daily life. Especially the process ahead of the data collection must be introduced so that students acknowledge the importance of accurate and object-oriented data.

• Journal of the Korean Society of Earth Science Education
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• v.16 no.2
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• pp.291-301
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• 2023

In this study, the STEAM elements and convergence types which appeared in the creative and convergent activities in authorized elementary school science textbooks for 5^th and 6^th graders were analyzed. For this study, creative and convergence activities presented in 9 different science textbooks for 5^th and 6^th graders were selected and the STEAM elements and convergence types were analyzed by each publisher, grade-semester, and science field. The results of this study are as follows. First, there was a large variation by publisher in the total frequency of STEAM elements and the frequency of each element in creative and convergence activities. Second, the ratio of convergence type consisting of two elements was very high, and the higher the number of fused elements, the lower the ratio appeared in overall. Third, the art (A) element had the highest frequency in all grade-semesters, and the technology (T), engineering (E), mathematics (M) elements differed in the distribution of frequency by grade-semesters. Fourth, the engineering (E) element in the 'integration' field, and the art (A) element in the fields of 'movement and energy', 'material', 'earth and universe', and 'life' had the highest frequency.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Journal of Science Education
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• v.48 no.1
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• pp.15-30
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• 2024

This study aimed to analyze students' cognitive levels and the cognitive demands of mathematical concepts related to science to understand why students struggle to comprehend scientific concepts and tend to avoid learning them. Initially, the mathematics and science curricula of the 2015 revised curriculum were examined to extract learning elements related to mathematics within middle school science content. The Curriculum Analysis Taxonomy (CAT) was then employed to analyze the cognitive levels required by the learning content. In the domain of chemistry, among a total of 20 learning elements related to mathematics, 12 required an understanding at the level of initial formal manipulation (3A), while 3 necessitated comprehension at the level of later formal manipulation (3B). It was noted that cognitive logic types such as proportional reasoning, mathematical manipulation, and measurement skills were prominently employed in elements corresponding to both 3A and 3B. As for biology, out of 7 learning elements related to mathematics, 3 required an understanding at the level of initial formal manipulation (3A), and 2 necessitated comprehension at the level of later formal manipulation (3B). Elements corresponding to both 3A and 3B in biology predominantly involved correlational logic, indicating a somewhat different cognitive challenge compared to the domain of chemistry. Considering that the average percentage of middle school students capable of formal thinking, as analyzed through the GALT short form, was 12.1% for the first year, 16.6% for the second year, and 29.3% for the third year, it can be concluded that the cognitive demands of mathematics-related chemistry and biology learning content are relatively high compared to students' cognitive levels.

• The Mathematical Education
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• v.50 no.4
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• pp.489-505
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• 2011

This study is an analysis on the focus of textbooks regarding the statistical chapters of "measures of representative(central tendency) and of the spread". Applying the summary-concept criteria of Juhyeon Nam(2007), 4 kinds of aspect of the chapter; (1) definition and its teleological validity of the measures of representative, (2) definition and practical value of the measures of spread (3) distributional form on the measures of representative and of spread (4) location and scale preservation or invariance of the measures of representative and of spread were observed. On the measures of representative, some definitions were insufficient to check the teleological validity of the measure. Most definitions of the measure of spread were based on the practical view points but no preparation for the future statistical inferences were found even by implication. Some books mention about the measures of representative and of spread for distributions, but we could not find any comments on the correspondence between the sample mean and the expectation of a distribution or population mean. However it is stimulant that some books check the validity of corresponding measures with the location and scale preservation or invariant property, that were not found in the previous curriculum.

• 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.