A Study on the Direction of Mathematics Education according to the Perspective of the Classroom Ecology
이대현 Dae Hyun Lee
14(1) 112, 2011
이대현 Dae Hyun Lee
DOI: JANT Vol.14(No.1) 112, 2011
This paper provides an outline of mathematics education based on the classroom ecology. Ecology is the subject that concentrates on the relations of human and environment. As mathematics education consists of many factors, it is natural that mathematics education should be interest in the perspective of ecology. This paper examines the meaning of ecology and classroom ecology of mathematics education in the perspective of ecology. And it provides the directions of ecological mathematics education. In special, I set the frame of mathematics classroom in the perspective of ecology. The ecological structure divides microsystem(teacher, student, content), mesosysten(relations of microsystems), exosystem(school), and macrosystem(the objects of mathematics education). Lastly, I suggest the ways of mathematical learning and research of classroom ecology in mathematics education. For we should focus the improvement of students` mathematical ability, we must search for the various teaching and learning methods and the ares of research in the perspective of ecology classroom. Therefore, we should be interested in the classroom environments as well as teaching methods, contents based on the ecology classroom in mathematics education.

An Analysis of Justification Process in the Proofs by Mathematically Gifted Elementary Students
김지영 Ji Young Kim , 박만구 Man Goo Park
14(1) 1326, 2011
김지영 Ji Young Kim , 박만구 Man Goo Park
DOI: JANT Vol.14(No.1) 1326, 2011
The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles`s Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students` geometric levels using the van Hieles`s theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles`s geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

A Study on the Analysis and Synthesis in Mathematics Education Based on Euclid`s “The Data” and “On Divisions”
서보억 Bo Euk Suh
14(1) 2741, 2011
서보억 Bo Euk Suh
DOI: JANT Vol.14(No.1) 2741, 2011
This study is the consideration to ``The Data`` and ``On Divisions`` of Euclid which is the historical start of analysis and synthesis. ``The Data`` and ``On Divisions`` compared to Euclid`s Elements is not interested. In this study, analysis and synthesis were examined for significance. In this study, means for ``analysis`` and ``synthesis`` were examined through an analysis of ``The Data`` and ``On Divisions``. First, the various terms including analysis and synthesis were examined and the concepts of the terms were analyzed. Then, analysis was divided into ``external analysis`` and ``internal analysis``. And synthesis was divided into ``theoretical synthesis`` and ``empirical synthesis``. On the basis of this classification problem presented in elementary textbooks and the practical applications were explored.

The Effects of Inquiry Oriented Instruction on the Learning of Area Formulas
박성선 Sung Sun Park
14(1) 4355, 2011
박성선 Sung Sun Park
DOI: JANT Vol.14(No.1) 4355, 2011
The purpose of this study was to investigate the effects of inquiry oriented instruction on the learning of area formulas. For this purpose, current elementary mathematics textbook(2007 revised version) which deal with area formulas was reviewed and then the experimental research on inquiry oriented instruction in area formulas was conducted. The results of this study as follow; First, there was no significant effect of inquiry oriented instruction on the mathematical achievement in area formula problems. Second, there was no significant effect on the memorization of area formulas. Third, there was significant effect on the generalization of area formulas. Forth, there was significant effect on the methods of generalization of area formulas. Fifth, through inquiry activities, the students can learn mathematical ideas and develop creative mathematical ideas. Finally, implications for teaching area formulas through inquiry activity was discussed. We have to introduce new area formula through prior area formulas which had been studied, and make the students inquire the connection between each area formulas.

How to Present Math Puzzles in Classroom
홍갑주 Gap Ju Hong
14(1) 5767, 2011
홍갑주 Gap Ju Hong
DOI: JANT Vol.14(No.1) 5767, 2011
The purpose of this study is to discuss the way and the purpose of presenting math puzzles in classroom. Firstly, the characteristics of math puzzles are discussed and the various uses of math puzzles are looked for. Secondly, The author illustrates models of classroom teaching with puzzles. Thirdly, The author discusses what subjects of mathematics could be dealt with in the math puzzle classroom. Finally, The author indicates that the teaching with math puzzles give chance of feeling ``mathematical composure`` not only to students but also to teachers.

3rd, 4th and 5th Graders` Probability Understanding
윤혜영 Hye Young Yoon , 이광호 Kwang Ho Lee
14(1) 6979, 2011
윤혜영 Hye Young Yoon , 이광호 Kwang Ho Lee
DOI: JANT Vol.14(No.1) 6979, 2011
The purpose of this study is to analyze 3rd, 4th and 5th graders` probability understanding and raise issues concerning instructional methods and search for the possibility of learning probability. For the purpose, a descriptive study through pencilandpaper test regarding fairness, sample space, probability of event, probability comparison, independence and conditional probability was conducted. The following conclusions were drawn from the results obtained in this study. First, the 3rd, 4th, and 5th grade students scored the highest in the sample space questions. In descending order of skill, the students scored the highest in sample space following probability of events, fairness and probability comparison. Second, however, the level of independence understanding was low. There was no meaningful differences between grades and the conditional probability was the least understood. The independence is difficult to develope naturally according to cognitive development. The conditional probability recognizing the probability of an event changes in nonreplacement situations was very difficult for these students. Third, there were significant differences between the 5th graders and the 3rd and 4th graders in the probability comparison questions. It shows that 5th graders understand the concept of proportion when they compare equal ratio probability of an event. The 3rd graders could do different ratio probability of an event more easily than equal ratio probability of an event after they were instructed on probability comparison.

A Case Study on Teaching Mathematics Underachievers Using the Textbooks of the Previous Grades
최정현 Jung Hyun Choi , 김상룡 Sang Lyong Kim
14(1) 8195, 2011
최정현 Jung Hyun Choi , 김상룡 Sang Lyong Kim
DOI: JANT Vol.14(No.1) 8195, 2011
In order to raise people with mathematical power and positive attitude toward mathematics fit for the 21st century, individual students should be provided with equal learning opportunities according to their ability and level, and the need of such mathematics education is even stronger for underachievers. As textbooks were considered the optimal learning materials at each stage, this study purposed to examine changes in students`` mathematical learning abilities and mathematical tendency brought by the activities of analyzing and reviewing the textbooks of the previous grades. The subjects of this study were 5 mathematics underachievers from 3 fifth grade classes at D Elementary School. They were sampled from those who were selected based on the results of diagnostic assessment and the records at the end of April and gave their consent to participation in this study. For the sampled children, their current state was surveyed first, and then the experimental classes were given twice a week and a total of 32 sessions. The children judged their mathematical abilities through reviewing the textbooks from the 1st grade to the 4th grade, and studied the textbook of each stage by themselves. After the self study, they had the textbook contents review activity that extracted 10 problems considered important per semester, and the textbook analysis activity that grouped units in each stage according to relevancy, identified similarities and differences, and examined hierarchy. From the results of this study was found that the mathematics underachiever teaching method using the textbooks of the previous grades gives mathematics underachievers confidence in their abilities, strengthens mathematical connection, and develops the habits of exploring key contents through self study.
