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This study aimed at studying the sequence of the Figure Transformation Learning, inquiring relationship among these transformations and then researching whether there is the difference of the learning ability or not between by teaching them as it is independent and by teaching them as it is contains. (Hypothesis 1) It may be more effective to teach The Sequence of Transformation Learning by beginning with peculiar field, ending with general field than vice versa At the result of verification-CR_M=2.59, 0.005<p<0.01-significant difference appeared. At the sight of the above it is proved more effective to teach them by beginning with peculiar field, ending with general field. (Hypothesis 2) It may be more effective to teach the Figure Transformation Learning the way it contains than the way it is independent At the result of verification-CR_M=5.19, p<0.005-significant difference appeared. It is proved more effective to teach the Figure Transformation Learning the way it contains than the way it is independent. Synthesizing two hypothesises of the above, the conclusion is following The Figure Transformation Learning should be taught by beginning with peculiar field, ending with general field (congruent transformation→similar transformation→projective transformation→topological transformation). To teach it the way it contains is more effective.
The purpose of this study is to develop the dual teaching materials of mathematics textbooks according to the scholastic abilities of students. The contents of this study are as follows; (1) Analyzing the mathematics curriculums, we organized a learning hierarchy for the contents of teaching materials distinguished in the grades and the areas. (2) We developed a viewpoint composing the dual teaching materials of mathematics textbooks. (3) We found a plane of instructional strategies dealing with the dual teaching materials of mathematics textbooks.
Children must develop mathematical Concepts from operations they perform on physical objects. Such real learning based on first-hand experiences in the physical world places mathematics in the realm of something that is fun, that can be enjoyed, and that can be understood. Attention must be given both to methods of teaching and to stages of development of children if true understanding is to occur. Thus, Critical thinking, Creative thinking and Problem Solving must be stressed in teaching-learning situations.
The purpose of this paper is to sequentialize Mathematics-learning contents, and to explore teaching-learning model for mathematics, with on the basis of the theory of cognitive development and the period of conservation formation for children. The Specific topics are as follows: (1) Systemizing those theories of cognitive development which are related to Mathematics - learning for children. (2) Organizing a sequence of Mathematics-learning, on the basis of experimental research for the period of conservation formation for children. (3) Comparing the effects of 4 types of teaching-learning model, on the basis of inference activity and operational learning principle. ① Induction-operation(IO) ② Induction-explanation(IE) ③ Deduction-operation(DO) ④ Deduction-explanation(DE) The results of the subjects are as follows: (1) Cognitive development theory and Mathematics education. ① Cognitive development can be achieved by constant space and Mathematics knowledge is obtained by the interaction of experience and reason. ② The stages of cognitive development for children form a hierarchical system, its function has a continuity and acts orderly. Therefore we need to apply cognitive development for children to teach mathematics systematically and orderly. (2) Sequence of mathematical concepts. ① The learning effect of mathematical concepts occurs when this coincides with the period of conservation formation for children. ② Mathematics Curriculum of Elementary Schools in Korea matches with the experimental research about the period of Piaget's conservation formation. (3) Exploration of a teaching-learning model for mathematics. ① Mathematics learning is to be centered on learning by experience such as observation, operation, experiment and actual measurement. ② Mathematical learning has better results in from inductional inference rather than deductional inference, and from operational inference rather than explanatory inference.