中學校 幾何敎育에서 個人差에 基盤한 敎授-學習에 대한 硏究

다국어 초록 (Multilingual Abstract)

Objective:
This study was designed to explored the relationship between changes of plasma homovanillic acid (HVA) and 5-hydroxyindoleacetic acid concentration (5-HIAA) and clinical variables in patients with schizophrenia following antipsychotics treatment.
Methods:
The author assayed HVA and 5-HIAA concentrations in plasma, using high pressure liquid chromatography-electrochemical detection method.
Thirty six subjects with schizophrenia hospitalized in two mental hospitals were enrolled in this study. First baseline plasma was obtained at 8:00 AM following 2 weeks withdrawal of antipsychotics. Single dose antipsychotics (haloperidol 5 mg, risperidone 2 mg) was administered to find out the acute changes of monoamine neurotransmitter systems. Haloperidol or risperidone was administered for 6 weeks. Consecutive sampling were done at 2, 4, and 6 weeks points after antipsychotics treatment. Clinical assessment was done at baseline, 2, 4, and 6 weeks points.
Results:
The plasma HVA level of the baseline and after single dose with antipsychotics was 9.32±4.06 ng/mL and 10.89±4.66 ng/mL. The plasma HVA levels increased significantly after 24 hours following administration of single dose antipsychotics. This increment was prominent in risperidone group. But the plasma 5-HIAA levels were not increased significantly after 24 hours following administration of single dose antipsychotics (respectively, 6.03 ±1.90 ng/mL and 6.05 ± 1.94 ng/mL). The plasma level of HVA and 5-HIAA following antipsychotics treatment were not changed significantly with compared to baseline level.
5-HIAA/HVA ratio was lower in atypical antipsychotics treatment than in typical antipsychotics treatment (Mann-Whitney test, p=0.034). This difference is a amplified by dividing the ratio with baseline ratio (Mann-Whitney test, p=0.001).b There is significant negative correlation between (5-HIAA/HVA ratio at 2 week)/baseline ratio and changes of general psychopathology score at 6 week point(r=-0.456, p=0.005).
Conclusion:
The plasma 5-HIAA and HVA levels can be used as biological markers to treatment response for schizophrenic illness.This study is to develop the methods of specifying teaching and learning that can consider individual differences in middle school geometry education. The purpose of this study is to decide the variations causing individual differences and to find the proper learning methods considering the variations and then to develop a teaching and learning models for realizing the methods in school.
To accomplish these purposes, the following questions of study were posed.
1. What are the variations causing the individual differences in mathematics education?
2. What are the specific learning methods which can realize the geometry learning adequate for various mathematical abilities and corresponding to individual differences?
3. What is the specific teaching and learning model which can realize the education based on individual differences?
Through literature review, this study made it clear that the matter of individual difference is just the matter of talent and examined what factors make up mathematical talents. On the basis of the result, five important variations and fourteen subordinate factors were determined.
I researched into the learning methods that consider the determined subordinate factors using the 'congruence' unit of middle school textbooks and developed specific learning methods for each of the subordinate factors through specific congruence problem solving situations. In addition, to realize these learning methods specifically, a particular teaching and learning model has been established and lesson plans have been developed according to this model. And the validity of them was approved through the evaluation of mathematics education experts.
The conclusions of this study can be summarized as follows :
1. To solve <study question 1>, I researched the studies of mathematical ability conducted by several educators and psychologists. This research is divided into the early study and the developed study of mathematical ability. Through this study five specific variations were determined. And fourteen subordinate factors have been made from the determined variations. Variations and subordinate factors are as follows :
1) variation 1 : Individual differences in collecting information about mathematical objects.
(subordinate factor 1) The difference of analytic and synthetic perceptibility for understanding problem structure.
(subordinate factor 2) The difference of curtail in analytic and synthetic perceptibility.
(subordinate factor 3) The difference of instrumental character to orient when understanding problem structure.
2) variation 2 : Individual differences of ability to generalize mathematical contents.
(subordinate factor 1) The difference of ability to see the specific contents and what they knew already as the same.
(subordinate factor 2) The difference of ability to find similarities of the specific contents and form a new concept.
3) variation 3 : Individual differences in mental process.
(subordinate factor 1) The difference of shortening in mental process.
(subordinate factor 2) The difference of adaptability in mental process.
(subordinate factor 3) The difference of reversibility in mental process.
4) variation 4 : Individual differences of aesthetic directivity in searching a good solution.
(subordinate factor 1) The difference of tendency to try to find the refined solution.
(subordinate factor 2) The difference of tendency to try to find the delicate solution.
(subordinate factor 3) The difference of tendency to try to reflect upon the solving process and find a better solution.
5) variation 5 : Individual differences in the mathematical knowledge stored in memory.
(subordinate factor 1) The difference of mathematical contents that is remembered.
(subordinate factor 2) The difference of remembering methods.
(subordinate factor 3) The difference of ability to use the remembered contents in a new problem situation.
2. To solve <study question 2>, 'congruence of figure' unit of middle school textbooks was chosen as the material.
The specific learning methods based on individual differences was developed according to the fourteen subordinate factors on the basis of middle school textbooks of Korea, Gusev's textbook, problem books of Russia, and etc.
1) The first subordinate factor
First, making an analysis list to help analytic perceptibility. Second, representing the given mathematical information as various symbols. Third, making a combination list to help synthetic perceptibility.
2) The second subordinate factor
First, asking questions to find what is given in the problem, background knowledge, the solution process and what needs to be found. Second, providing the detailed subordinate problems to find the relation among mathematical factors. Third, providing fundamentally the same kind of problems properly.
3) The third subordinate factor
First, leading to understand the type of the given problems. Second, leading to find out the final goal of the problems exactly. Third, leading to guess one solution method from problem-solving strategy, previous experiences and information about the problem.
4) The fourth subordinate factor
First, enumerating already known data concerned with the solution of the given problem and helping to compare the data with those found in the problem and choose the most applicable one. Second, providing systematic exercise problems to acquire applicability. Third, Guiding to think about what the main stream is for the problem solving and preparing for applying it to other similar problems.
5) The fifth subordinate factor
First, drawing the changeable and unchangeable factors out of the given problem and its solving process. Second, providing the opportunity to find the community through well organized and systematized practice problems that are of the same type. Third, leading to guess the community from the specified facts and providing the opportunity to confirm that it is true.
6) The sixth subordinate factor
First, establishing the detailed inferring process on the basis of the basic inferring process for the problem solving. Second, leading to a curtail of inferring process by providing the similar type of problems which require the same inferring process.
7) The seventh subordinate factor
First, providing the experience of inferential thinking in problem solving process. Second, providing a few typical solution methods and investigating the interrelation among them. Third, having students present their own solution process, write opinions about other presented solutions and refine their own thoughts through discussion.
8) The eighth subordinate factor
First, giving students direct problems and reverse ones simultaneously and having them to determine the way to solve problems systematically. Second, leading to find the relation to solve a reverse problem from the solution of a direct one and form a reverse combination. Third, guiding to find problem solving methods by connecting a direct problem and a reverse one.
9) The ninth subordinate factor
First, leading to compare the solution by previously learned mathematical facts with the one by the newly learned facts. Second, leading to learn new mathematical facts from what was already learned or find the interrelation between them. Third, providing various experience of solving problems using newly learned mathematical facts only.
10) The tenth subordinate factor
Providing a lot of experience of solving problems that require good logical connection links during the solution process and solving new problems systematically using preacquired mathematical concepts or principles.
11) The eleventh subordinate factor
First, leading students to reflect upon their own solution methods and check whether they are right. Second, guiding to identify the mathematical facts used in the solution and finding a new useful mathematical relation out of the given and what is needed to get. Third, providing the opportunity to solve problems in another way using a newly acquired mathematical concept.
12) The twelfth subordinate factor
First, finding and remembering the theorem or fact used in solving problems. Second, finding and remembering a typical frame or general type. Third, finding and remembering the essential, general and abstract things in solving problems.
13) The thirteenth subordinate factor
First, remembering the relation between mathematical facts used and contents that should be born in mind, while investigating it. Second, remembering the essential difference between the typical frame of the known solution and the new one to be remembered, while trying to understand it. Third, figuring out and remembering the relation between the existing knowledge and the new ones which are essential, general and abstract.
14) The fourteenth subordinate factor
First, providing new problems to settle the mathematical concepts. Second, providing the mathematical experience to gradually move the acquired concept to a higher level through problem chains. Third, providing the experience of mathematical investigation activity.
3. To solve <study question 3>, basic principles and directions for teaching and learning were set up, a teaching and learning model has been developed and lesson plans have been made accordingly. The basic principles and directions are as follows: assistance by the teacher and the peers, teacher-student conversation, student-student conversation, independent task performance.
According to these principles and directions, a teaching and learning model specified as lesson preparation stage, introduction stage, understanding stage, consolidation stage, and application stage has been developed. And ten geometry lesson plans were made.
The developed teaching and learning model and lesson plans were evaluated by mathematics education experts and the result was analyzed with weighted Kappa coefficient. And all the experts agreed that the developed teaching and learning model and lesson plans were meaningful for based on individual differences in middle school geometry education.
In conclusion, this study is about the teaching and learning methods based on individual differences in middle school geometry education. It extracted the variations of individual difference and their subordinate factors, and developed learning methods with those variations and factors reflected systematically. A specific teaching and learning model and lesson plans have also been developed to realize geometry education based on individual differences at school. The validity of the developed teaching and learning model and lesson plans were confirmed by the evaluation of experts. This study makes us expect the geometry education of middle school that corresponds to the individual psychological characters and considers individual differences.

목차 (Table of Contents)

• Abstract = ⅶ
• Ⅰ. 서론 = 1
• 1. 연구의 필요성 및 목적 = 1
• 2. 연구 문제 = 4
• 3. 용어의 정의 = 5
• 4. 논문의 구성 = 7
• Ⅱ. 문헌 검토 = 10
• 1. 개인차(individual difference) = 10
• 2. 수학적 재능 = 15
• 3. 개인차와 교수-학습 = 38
• Ⅲ. 연구 방법 및 절차 = 52
• 1. 연구의 방법과 절차 = 52
• 2. 자료 수집 = 54
• 3. 통계 처리 방법 = 55
• Ⅳ. 개인차를 고려한 학습방법 = 56
• 1. 개인차를 유발하는 변인과 하위요소 = 56
• 2. 수학적 대상에 대한 정보수집에서의 개인차를 고려한 학습 = 61
• 3. 수학적 내용을 일반화하는 능력에서의 개인차를 고려한 학습 = 72
• 4. 사고과정에서의 개인차를 고려한 학습 = 84
• 5. 풀이의 심미지향성에서의 개인차를 고려한 학습 = 96
• 6. 수학적 정보에 대한 기억에서의 개인차를 고려한 학습 = 106
• Ⅴ. 개인차를 고려한 기하단원 수업의 실제 = 125
• 1. 개인차를 고려한 교수-학습 모형 개발을 위한 기본 방향과 원칙 = 125
• 2. 개인차를 고려한 교수-학습 모형의 개발 = 126
• 3. 개인차를 고려한 교수-학습의 실제 = 135
• Ⅵ. 요약 및 결론 = 151
• 1. 요약 = 151
• 2. 결론 = 156
• 참고문헌 = 163
• 부록1. 개인차를 고려한 10차시 수업안 = 170
• 부록2. 교수-학습 모형과 그에 따른 수업안에 대한 평가 문항 = 239