There are some researches for international comparing of textbook and curriculum, so far. But These researches focused on comparing special region of textbook or curriculum. On the contrary, there are hardly papers how teacher's guide is consists and different with other country. In this paper, we have analyzed teacher's guide of Korea and Everyday Mathematics which is one of the teacher's guide in the many counties in the united states of America. Especially, teaching method, differentiated contents of curriculum, characteristics of consists of curriculum and so on. On the basis of this analysis, we search the improvement points of teaching of primary mathematics and also we make all the primary school teachers realize the diversity of teaching method through foreign cases and consequently they will make use of these results as a reference material such as reconstruction of textbook.

This study analyzed and discussed instruction methods of polyhedrons in elementary mathematics textbook by using the didactic transposition theory. By further segmenting instruction methods, we analyzed the period and order of teaching of polyhedrons, its definitions and presentation methods, and how instruction methods has changed so far. In elementary mathematics textbooks from the 1st to the 2007 revised curriculum, we choose the part where polyhedrons are introduced as the search-target, and analyzed instruction methods in these textbooks by using phenomenological description. The instruction period and order of polyhedrons were systemized when the system of Euclid geometry was introduced, considering the psychological condition of students, and the instruction period and order had been refined according to the curriculum. And methods of definition took into consideration both the academic systems and psychological situations. Also, the subject of learning has changed from textbook and teachers to students. Polyhedrons were connected to real life and students could build up their knowledge by themselves. Constructions were aimed at the understanding of meaning of contents, rather than at itself. Through these analyses, we have some suggestions on the teaching of polyhedrons in the elementary mathematics.

In the history of mathematics education, different opinions as to how to view the phenomenon of mathematics education have been suggested in various ways. As those conflicting opinions have caused fundamental tensions in the phenomenon of mathematics education, they remain fundamental standpoints that have been continuously advocated until now - not limited in a certain period. It can be argued that this situation was caused by partial or fragmentary understanding of the phenomenon of mathematics education. If we are pursuing not a partial knowledge but a complete understanding of mathematics education, how should it be formed to comprehensively study the entire phenomenon of mathematics education? To answer this question, Complex structure in phenomenon of Mathematics Education can be proposed. It is an explanation for the opposing opinions existing in the phenomenon of mathematics education. The purpose of this paper is to understand the phenomenon of mathematics education as a whole.

The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

We can easily see the 'cycloid slide' in the many mathematics and science museums. The educational materials, however, do not give us any mathematical principle. For this reason, we, in this thesis, first study the brachistochrone problem in the history of mathematics, and suggest a method of how to teach the principle using 'the dynamic geometry software GSP5' in order to help students understand the idea that the cycloid is the brachistochrone. Secondly, we examine the origin of the calculus of variations and apply it to prove the brachistochrone problem in order to build up the teachers' background knowledge. This allows us to increase the worth of history of mathematics and recognize how useful the learning is which uses technological tools or materials, and we can expect that the learning which makes use of cycloid slide will be meaningful.

The purpose of this thesis is to understand the relationship between the College Scholastic Ability Test(CSAT) and the Mathematics Level Assessment(MLA) which is conducted in P University. There are high correlations in grades, subject areas and college entrance types between grades of mathematics B-type of the CSAT and scores of the MLA. However, the many students showed substantial differences between the grades in the two tests. On the basis of these analysis results, we suggest plans for improving the implementation of the MLA and the teaching-learning methods about College General Mathematics.

The mathematics has moved toward the independence from unit. However, is this tendency also kept up in teaching and learning mathematics? This study starts from this question. We have illuminated this question in respects of a character of unit operation, an essential probability of unit operation and a didactical application of unit. As results, addition and subtraction are operations on identical objects and the result of operation does not also get out of operation's object. On the other hand, multiplication and division are operations on both identical objects and different objects. And the result of operation can generate new unit. We proposed a hypothesis which multiplication and division are transcendental operations from this analysis. The unit operation is not possible essentially. It seems only like unit operation is possible superficially by operational definition on unit. We could discuss on a didactical application of unit from above analysis. And we could deduct implications that the direction of developing mathematic does not necessarily match with the direction of teaching and learning mathematics.

The purpose of this thesis is to analyze mathematical errors in descriptive problems of the Mathematics Level Assessment(MLA) which is conducted in P University. We classified mathematical errors, which are easily made in solving the descriptive problems of the MLA, into nine types as misused data, misinterpreted language, logically invalid inference, misunderstood theorem or definition, unmatched solution, technical errors, omission of solving process, ambiguous errors, and unattempted errors. With classifying the errors in nine types, we analyzed the errors of students, who are in intermediate and low level grades, by descriptive problems. On the basis of these analysis results, we suggest plans for improving the implementation of the MLA and the teaching-learning methods about College General Mathematics.

This study was conducted to analyze the education theories applied to teaching-learning from the perspective of mathematical education. To this end, 41 papers regarding mathematical education theories were selected as study subjects from among 1,190 papers published in Korea between 2000 and 2013 in the Journal of the Korean Society of Mathematical Education and the Journal of the Korean Society of Educational Studies in Mathematics, which are journals that specialize in mathematics education. These papers were classified according to mathematical education theory, study method, content field, and study subject to obtain the numbers of papers and percentages by category in order to analyze their contents.

Students might find different solutions to the quadratic inequalities according to the range of the number representing the character of the inequalities. They have confusion when the roots of a quadratic inequality are complex numbers since the character of the inequalities generally represents the real number in the mathematics textbooks. Therefore we suggest that we must explain definitely the range of the number representing the character for each inequality question.