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identifier% Y P D \ Yլ i pȬ ̸ Research on the Uses of the History of Mathematics Through the Analysis of Secondary School Mathematics Textbooks and the Supporting Data2015P!Y YP!
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YP!X Yլ \֩iD LD0 \ P | t L @ `D . , Y Yլ ̸X Dt DՔ\ t . X, ٳYլ@ ( ̸ T ιt DՔ . K, 䲑\ PY )D \֩X l1\ Yլ ̸X DՔX. 7, Yt 8| p l` ǔ Yլ ̸| ` DՔ . l YP Yլ ̸ X x 䲔 Yt 䲑\ )<\ YD ` ǔ )<\ Dt t踴8| hD L . 0| Yլ ̸| P \֩ Xĳ] l1XՔ t ɍ<\ ɉ DՔ . l Yt Yլ| X D ǔ P!x D X Yլ ̸X D tǔ )X l ɉ|hD ¬\.; By studying the history of mathematics, one can learn about its evolution and how it has taken its form as we know today. One can also learn about the historical values of mathematics and its usefulness from studying its history. The history of mathematics portrays the culture and the civilization of a society. Numerous educators in mathematical fields suggested that the study on the history of mathematics can be one of the useful tools to understand mathematics, and therefore it should be incorporated into the mathematics curriculum. First, it is necessary to look into how these suggestions are being applied to mathematical e< ducation in real life. The bases of Korean Mathematics curriculum are the textbooks, hence we can indirectly confirm the uses of history of mathematics in real life classroom by analyzing the textbooks. After I examined the previous studies done on the analysis of the textbooks, I found out that the scopes of the analysis and the standards of the analysis vary, so they are not suitable to be used as supporting data to find out about the uses of the history of mathematics in secondary education. Therefore, in this paper, I have examined all the secondary school textbooks that had been published following the mathematical curriculum established in the year of 2009. Then, the following research problems have been chosen in order to figure out the uses of the history of mathematics and to provide the supporting data:
Research Question 1. How is the history of mathematics being incorporated into secondary school textbooks in general and in each grade?
1-1 How is the contents related to the history of mathematics distributed in each unit of the mathematics curriculum?
1-2 How is the contents related to the history of mathematics distributed differently according to who or what the subject is and the varying regional group?
1-3 How is the history of mathematics contents introduced in the textbooks using the pedagogic methods?
Research Question 2. From the analysis on two of the least used pedagogic methods in the secondary school textbooks, what can be used as the data on the history of mathematics ?
As stated in the research question 1-1 middle school's mathematics curriculum can be divided into different units which includes: Number and Operation, Character and Expression, Function, Probability and Statistics and Geometry. High School's mathematics curriculum can be divided into Basic Mathematics, Mathematics I, Mathematics II, Probability and Statistics, Calculus I, Calculus II, Geometry and Vectors, Advanced Mathematics I and Advanced Mathematics II. As a result, in Character and Expression unit and in Geometry unit from the middle school's mathematics curriculum, the history of mathematics has been introduced more compared to the other units of the textbooks. On the other hand, Function unit and Probability and Statistics unit focused less on the history of mathematics. In high school's mathematics curriculum, the contents distribution varied for every subject, and in Advanced Mathematics I and Advanced Mathematics II, some portion of the subjects did not mention about the history of mathematics. Subjects like Calculus I, Calculus II and Geometry and Vectors have hierarchical nature, and higher up the hierarchical level, less data regarding the history of mathematics was presented.
For research question 1-2, I have classified the regional groups into the Western countries, Eastern countries and Korea, and I have classified the subject as historical figure in mathematics, mathematical legacy and historical facts about mathematics. Also, I have further analyzed the regional groups and the subject using 9 different categories. The results showed that the data on the history of mathematics originated mostly from Western countries, and the subjects were mostly people. When I have combined both results of the data, the largest portion of the subject was historical figures in mathematics who were from Western countries.
For research question 1-3, I have looked into pedagogic methods and whether problems have been resolved. Pedagogic methods have been divided into six categories: problems from mathematical texts, historical tools for mathematical education, comparisons, finding of errors, usage of engineering tools and the means of a mathematician. As a result, 21% included problem solving, and a lot of reading materials are provided. I learned that all 6 of the pedagogic methods had been used in all the textbooks I have analyzed, and problems from mathematical texts and the means of a mathematician took up about 8~9%. However, historical tools for mathematical education, comparisons, finding of errors, usage of< engineering tools were presented in less than 3% of the entire data.
As for research question 2, I have analyzed the data on history of mathematics regarding 'problem solving' and 'finding of errors' which were the least likely used pedagogic methods in the secondary school textbooks. In the end, I was able to find the pattern from some of the data, and through the data regarding the history of mathematics, I was able to indirectly experience the mathematician's idea. Also, I realized how mathematics is still in the process of development.
In the process of finding out the current state of how the history of mathematics is used in the mathematical education, I was able to come up with this conclusion. First, there are sections which require additional data regarding the history of mathematics. Second, there is a need to include more data related to the historical figures of mathematics from Eastern countries. Third, there is a need for data on the history of mathematics using diverse pedagogic methods. Fourth, it is necessary to present the problems that the students can solve themselves or urge the students to do their own research. This research seeks to reflect the educational benefits which the students can gain from studying the history of mathematics, and it points out the necessity of how a research must be conducted in a way which enhances the quality of the data.~http://dspace.ewha.ac.kr/handle/2015.oak/212026;
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