• Journal of the Korean School Mathematics Society
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• v.18 no.1
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• pp.1-14
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• 2015

In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.333-357
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• 2014

This study resulted from a study regarding creative STEAM System based upon an experiment with the center of gravity. The results of the study are constructed by a fusion of mathematics and physics, showing that they are the same as mathematical calculations. Also, students can find that center of gravity of an object is in equilibrium on a metal rod when the center of gravity exactly is placed on the rod. The fact that an experimental results are correspond to calculations can maximize the effectiveness of teaching. And also this study has the following effectiveness. First, the exact construction and calculations arouses good competition among students. Second, this experiment can give students a motivation for study and increase their thinking in classes because the theoretical background of center of gravity experiment is basically attributed to math and science classes in school. This study includes three different types of center-of-gravity experiments. One is a simple type of experiment in which center of gravity exists inside of an object. Another is a complicated one in which the center of gravity is also inside of an object. However, the third type is an experiment in where the center of gravity is outside of an object. Therefore, it gives students an opportunity to discuss how to confirm equilibrium on a metal rod when the object has its center of gravity outside. Having discussions in class will allow students to have a critical way of thinking. In addition, searching for a way to solve a problem will increase creativity of students as well. And the last type is finding the center of gravity of a big acrylic panel where multiple objects are on the panel. According to the survey and interview conducted by students who participated in this program, teaching based on creative STEAM system helps students to get a better understanding and more fast acquisition of knowledge. We can expect that a well-planned creative STEAM system through a continuous study will be both effective and efficient in educating critical and creative students.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.1-22
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• 2012

The purpose of this study is to understand Korea students' characteristics as well as to give important information of improving our education using comparative analysis of framework, test booklets, test results between PISA 2009 and NAEA 2009. PISA 2009 was administered on May of 2009 and NAEA was administered on October of same year. The summary of the results of comparing two assessment is as follows First, cut score of NAEA Advance level is bigger than the cut score of level 5, which is considered as high achievement level. The cut score of Basic level of NAEA is also higher than the level 2 of PISA, which is considered as basic achievement level. This phenomenon can show that NAEA achievement level is set little bit higher than the achievement level of PISA in mathematics domain. Second, the percentage of female students on higher level was higher than that of male students. In suburban area, the percentage of high level was small and the percentage of low level was big. Third, students of Advanced level are distributed concentrating in PISA levels 4~6, Proficient achievement level concentrating in PISA levels 3~5, Basic achievement level concentrating in PISA levels 2~4, and below basic achievement levels concentrating in below level 1 and level 3 of PISA. Fourth, the correlation between NAEA 2009 and PISA 2009 achievement scores are significantly positive. However, the correlation of subscales were low. Fifth, analysis of non-equivalent group, 11 items located in 'change and relationship', 'uncertainty', 'connection cluster' domains found to be significantly different. The percent correct showed very big difference. The analysis results presents the implication of mathematics curriculum, teaching and learning methods as well as National Assessment of Educational Achievement.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.501-525
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• 2015

This study analyzes arithmetic word problem of multiplication and division in the mathematics textbooks and workbooks of 3rd grade in elementary school according to 2009 revised curriculum. And we analyzes type of the problem solving ability which 4th graders prefer in the course of arithmetic word problem solving and the problem solving ability as per the type in order to seek efficient teaching methods on arithmetic word problem solving of students. First, in the mathematics textbook and workbook of 3rd grade, arithmetic word problem of multiplication and division suggested various things such as thought opening, activities, finish, and let's check. As per the semantic element, multiplication was classified into 5 types of cumulated addition of same number, rate, comparison, arrayal and combination while division was classified into 2 types of division into equal parts and division by equal part. According to result of analysis, the type of cumulated addition of same number was the most one for multiplication while 2 types of division into equal parts and division by equal part were evenly spread in division. Second, according to 1st test result of arithmetic word problem solving ability in the element of arithmetic operation meaning, 4th grade showed type of cumulated addition of same number as the highest correct answer ratio for multiplication. As for division, 4th grade showed 90% correct answer ratio in 4 questionnaires out of 5 questionnaires. And 2nd test showed arithmetic word problem solving ability in the element of arithmetic operation construction, as for multiplication and division, correct answer ratio was higher in the case that 4th grade students did not know the result than the case they did not know changed amount or initial amount. This was because the case of asking the result was suggested in the mathematics textbook and workbook and therefore, it was difficult for students to understand such questions as changed amount or initial amount which they did not see frequently. Therefore, it is required for students to experience more varied types of problems so that they can more easily recognize problems seen from a textbook and then, improve their understanding of problems and problem solving ability.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.321-350
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• 2013

The purpose of this study to analysis of problem posing in 5th and 6th grade mathematics textbooks and to comprehend errors in the problem posing activity of 6th graders in elementary school. For solving the research problems, problem posing contents were extracted from mathematics textbooks and practice books for the 5th and 6th grade of elementary school in the 2007 revised national curriculum, and they were analyzed, according to each grade, domain and type. Based on the analysis results, 10 problem posing questions which were extracted and developed, were modified and supplemented through a pre-examination, and a questionnaire that problem posing questions are evenly distributed, according to each grade, domain and type, was produced. This examination was conducted with 129 6th graders, and types of error in problem posing were analyzed using collected data. The implications from the research results are as follows. First, it was found that there was a big numerical difference of problem posing questions in the 5th and 6th grade, and problem posing questions weren't properly suggested in even some domains and types, because the serious concentration in each grade, type and domain. Therefore, textbooks to be developed in the future would need to suggest more various and systematic of problem posing teaching learning activity for each domain and type. Second, the 'error resulting from the lack of information' occurred the most in the problems that 6th graders posed, followed by the 'error in the understanding of problems', 'technical errors', 'logical errors' and 'others'. This implies that a majority of students missed conditions necessary for problem solving, because they have been used to finding answers to given questions only. For such reason, there should be an environment in which students can pose problems by themselves, breaking from the way of learning to only solve given problems.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.1-17
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• 2014

Recently a student's mathematical thinking and problem-solving skills are emphasized. Nevertheless, the students solved the problem associated with a given type of problem solving using mechanical algorithms. With this algorithm, It's hard to achieve the goal that are recently emphasized. Furthermore It may be formed error or misconception. However, consistent errors have positive aspects to identify of the current cognitive state of the learner and to provide information about the cause of the error. Thus, this study tried to analyze the error happening in the process of solving gearwheel-involved problem and to propose the correct teaching method. The result of student's error analysis, the student tends to solve the gear-wheel problem with proportional expression only. And the student did not check for the proportional expression whether they are right or wrong. This may be occurred by textbook and curriculum which suggests only best possible conditioned problems. This paper close with implications on the discussion and revision of the concepts presented in the curriculum and sequence related to the gearwheel-involved problem as well as methodological suggested of textbook.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.693-734
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• 2011

The purpose of this research is to analyze the pedagogical content knowledge on the natural number concepts of Korean Elementary School Teachers. Shulman(1986b) had developed a tool in order to understand teachers' knowledge, as he defined three types of knowledge in teaching ; Subject Matter Knowledge, Curricular Knowledge, and Pedagogical Content Knowledge. Pang(2002) defined two types of elements including in the ways of teaching ; individual element, and sociocultural element. Two research questions are addressed; (1) What is the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? ; (2) What factors are included in the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? Findings reveal that (1) the Korean Elementary School Teachers had three types of the pedagogical content knowledge on the natural number concepts; (2) Teacher Factors were more included than Social-Cultural Factors in the pedagogical content knowledge on the natural number concepts of the Korean Elementary School Teachers. Further suggestions were made for future researches to include (1) a comparative study on teachers between ordinary teachers and those who majored mathematics education in the graduate school. (2) an analysis on the classroom activities about the natural number concepts.

• The Mathematical Education
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• v.42 no.1
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• pp.19-39
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• 2003

The purpose of this study is to find out effective ways to take care of the 8th and 10th graders' disposition causing math. disliking. To accomplish this goal, we proceeded as follows : First we categorized the 11 factors recognized as the reasons of math. disliking into 4 math. disliking causes such as psychological f: environmental cause, conceptual cause, relational cause and application related cause. Second, to take care of these tow causes, we developed materials which are closely related with the contents of the 8th and 10th graders' school mathematics. Third with these materials we taught the students who had proved to have the math. disliking trend, for one semester. As a consequence of this experiment we arrived at the following results. As for psychological & environmental causes, 35.7% of the 8th graders and 17% of the 10th graders proved to have been improved significantly. This result shows that the curing of the psychological & environmental causes is more effective in the 8th graders than in the 10th graders. i.e., the curing effects of the students' psychological & environmental cause for disliking math. decline as they get older. As for conceptual causes, 35% of the 5th graders and 30% of the 10th graders proved to have been improved significantly. In case of the 8th graders this ratio was similar to that of the other causes. But as for the 10th graders this ratio was a little low compared with that of the case of relation causes and application related causes. As for relational causes, 35% of the 5th graders and 49% of the 10th graders proved to have been improved significantly. Especially the 10th graders improved greatly. Among the four factors that compose this cause, especially hierarchy and connection factors were effectively cured. On application related causes, 47% of the 5th graders and 57% of the 10th graders proved to have been cured significantly. And among the four types of causes listed above, this was the most successfully cured one. Of the two factors of this cause, the basic application factor appeared to have been improved in all experimental groups. In connection with teaching methods, we found out the followings two facts. First, the more teachers push students to solve their tasks with their own efforts, the higher is the ratio of owe. Second, the more teachers teach students personally, the more effective are the teaching results.

• Journal of The Korean Association For Science Education
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• v.27 no.4
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• pp.346-353
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• 2007

In order to be efficient in teaching, a teacher should understand the current learner's level through diagnostic evaluation. This study has examined the major issues arising from the noble diagnostic assessment tool based on the theory of knowledge space. The knowledge state analysis method is actualizing the theory of knowledge space for practical use. The knowledge state analysis method is very advantageous when a certain group or individual student's knowledge structure is analyzed especially for strong hierarchical subjects such as mathematics, physics, chemistry, etc. Students' knowledge state helps design an efficient teaching plan by referring their hierarchical knowledge structure. The knowledge state analysis method can be enhanced by computer due to fast data processing. In addition, each student's knowledge can be improved effectively through individualistic feedback depending on individualized knowledge structure. In this study, we have developed a diagnostic assessment test for measuring student's learning outcome which is unattainable from the conventional examination. The diagnostic assessment test was administered to middle school students and analyzed by the knowledge state analysis method. The analyzed results show that students' knowledge structure after learning found to be more structured and well-defined than the knowledge structure before the learning.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.305-322
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• 2010

The epistemological obstacles in the area learning of plane figure can be categorized into two types that is closely related to an attribute of measurement and is strongly connected with unit square. First, reasons for the obstacle related to an attribute of measurement are that 'area' is in conflict. with 'length' and the definition of 'plane figure' is not accordance with that of 'measurement'. Second, the causes of epistemological obstacles related to unit square are that unit square is not a basic unit to students and students have little understanding of the conception of the two dimensions. Thus, To overcome the obstacle related to an attribute of measurement, students must be able to distinguish between 'area' and 'length' through a variety of measurement activities. And, the definition of area needs to be redefined with the conception of measurement. Also, the textbook should make it possible to help students to induce the formula with the conception of 'array' and facilitate the application of formula in an integrated way. Meanwhile, To overcome obstacles related to unit square, authentic subject matter of real life and the various shapes of area need to be introduced in order for students to practice sufficient activities of each measure stage. Furthermore, teachers should seek for the pedagogical ways such as concrete manipulable activities to help them to grasp the continuous feature of the conception of area. Finally, it must be study on epistemological obstacles for good understanding. As present the cause and the teaching implication of epistemological obstacles through the research of epistemological obstacles, it must be solved.