The topic, which is proposed through the study is the consideration, which is from the algebraic perspective concerned to permutations and combinations that deal as a part of Probability and Statistics chapter in Korean high school mathematics curriculum. ??
This work, which is associated with ...
The topic, which is proposed through the study is the consideration, which is from the algebraic perspective concerned to permutations and combinations that deal as a part of Probability and Statistics chapter in Korean high school mathematics curriculum. ??
This work, which is associated with permutations and combinations, based on school mathematics, can be distinguished into two studies. The first one is the study of instructional method which is related to permutations, and combinations and the?second one is the belief and attitude of teachers and students concerning permutations and combinations. These two studies are recognized as the supporting tools rather than the principle purpose and historic-genetic principle.?Moreover, teachers have found that permutations and combinations are hard topics to be taught. Thereby, students have struggled with the permutations and combinations as well.?One of the reasons why teachers have struggled with permutations and combinations?is because of the lack of theoretical background knowledge and the disoriented text books. Among the studies of permutations and combinations based on the historic-genetic principle, the studies about learning motivation and the meaning of permutations and combinations are not easy to find.
Therefore, it is necessary to consider the current curriculum, which force to learn Probability and Statistics via permutations and combinations. Also, it is necessary to deal with other purposes of permutations and combinations. Indeed, in Algebra, permutations and combinations can be used to solve the 5th degree or higher degree polynomial equations with cofficients in the rational numbers field, without appealing continuous maps or limits. For solving such equations, the needs to be handled, and to be analyzed , permutations and combinations are required.
? This study deals with definitions and theorems, as basis for solving aforementioned equations. Also, the work consists of roles and general ideas of one-to-one onto functions, Galois connections, groups, rings, and fields that can appear in the process of solving equations. Moreover, it presents the structure of the group algebra and it also shows that in order to analyze the ?permutation groups. It is necessary to get the normal subset and cycle permutation decomposition. According to this fact, the process to get the normal subsets is connected to finding the normal subgroups. This process is required to find the conjugate class equation. Therefore, this study suggests that the one-to-one onto functions which are being used in middle school have to be importantly and carefully handled in high school, and ?representation of permutation has to be delivered for efficient calculation.
In rearrangement of teaching materials, permutation have to be treated as one-to-one onto functions from a finite set to itself. Currently, permutations and combinations are being used to introduce the number of cases for calculating the probability, but according to the fact that permutations and combinations is needed to get the conjugate class equation of , individually permutations and combinations have to be categorized to arrange one-to-one onto functions.
From this categorization, exponential functions and logarithmic functions have to deal with treatment as in permutations and combinations. From this fact, sets, groups, one-to-one onto functions, and rings have to be instructed in high school implicitly. As Analysis focuses on series and Geometry focuses on the simple closed curve, it is emphasized in Algebra the unsolvability of quintic equations by radicals.
The topic, which is proposed through the study is the consideration, which is from the algebraic perspective concerned to permutations and combinations that deal as a part of Probability and Statistics chapter in Korean high school mathematics curriculum. ??
This work, which is associated with permutations and combinations, based on school mathematics, can be distinguished into two studies. The first one is the study of instructional method which is related to permutations, and combinations and the?second one is the belief and attitude of teachers and students concerning permutations and combinations. These two studies are recognized as the supporting tools rather than the principle purpose and historic-genetic principle.?Moreover, teachers have found that permutations and combinations are hard topics to be taught. Thereby, students have struggled with the permutations and combinations as well.?One of the reasons why teachers have struggled with permutations and combinations?is because of the lack of theoretical background knowledge and the disoriented text books. Among the studies of permutations and combinations based on the historic-genetic principle, the studies about learning motivation and the meaning of permutations and combinations are not easy to find.
Therefore, it is necessary to consider the current curriculum, which force to learn Probability and Statistics via permutations and combinations. Also, it is necessary to deal with other purposes of permutations and combinations. Indeed, in Algebra, permutations and combinations can be used to solve the 5th degree or higher degree polynomial equations with cofficients in the rational numbers field, without appealing continuous maps or limits. For solving such equations, the needs to be handled, and to be analyzed , permutations and combinations are required.
? This study deals with definitions and theorems, as basis for solving aforementioned equations. Also, the work consists of roles and general ideas of one-to-one onto functions, Galois connections, groups, rings, and fields that can appear in the process of solving equations. Moreover, it presents the structure of the group algebra and it also shows that in order to analyze the ?permutation groups. It is necessary to get the normal subset and cycle permutation decomposition. According to this fact, the process to get the normal subsets is connected to finding the normal subgroups. This process is required to find the conjugate class equation. Therefore, this study suggests that the one-to-one onto functions which are being used in middle school have to be importantly and carefully handled in high school, and ?representation of permutation has to be delivered for efficient calculation.
In rearrangement of teaching materials, permutation have to be treated as one-to-one onto functions from a finite set to itself. Currently, permutations and combinations are being used to introduce the number of cases for calculating the probability, but according to the fact that permutations and combinations is needed to get the conjugate class equation of , individually permutations and combinations have to be categorized to arrange one-to-one onto functions.
From this categorization, exponential functions and logarithmic functions have to deal with treatment as in permutations and combinations. From this fact, sets, groups, one-to-one onto functions, and rings have to be instructed in high school implicitly. As Analysis focuses on series and Geometry focuses on the simple closed curve, it is emphasized in Algebra the unsolvability of quintic equations by radicals.
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