• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.291-313
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• 2018

This study aims to analyze Pardies' ${\ll}$Elements of geometry${\gg}$. This book is very interesting from the perspectives of mathematical history as well as of mathematical education. Because it was used for teaching Kangxi emperor geometry in the Qing Dynasty in China instead of Euclid's which was considered as too difficult to study geometry. It is expected that this book suggests historical and educational implications because it appeared in the context of instruction of geometry in the seventeenth century of mathematical history. This study includes the analyses on the contents of Pardies' ${\ll}$Elements of geometry${\gg}$, the author's advice for geometry learning, several geometrical features, and some features from the view of elementary school mathematics, of which the latter two contain the comparisons with other authors' as well as school mathematics. Moreover, some didactical implications were induced based on the results of the study.

• Journal for History of Mathematics
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• v.33 no.1
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• pp.55-71
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• 2020

In this study, the situation of publishing middle and high school mathematics textbooks used at the period of the first curriculum were investigated. In the period of the first curriculum, middle and high school textbooks were used from 1956, and middle school textbooks were used until 1965, and high school textbooks were used until 1967. First of all, the announcements of the ministry of education related to the textbook authorization were examined in the government official gazettes of 1956~1967. However, there were considerable typographical errors in these announcements of the ministry of education. So textbooks used at that period were examined, and typographical errors were corrected by cross-checking the bibliographic information.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• Journal for History of Mathematics
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• v.34 no.2
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• pp.75-87
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• 2021

Hirabayashi Ichiei has sought theoretical improvement of educational studies in mathematics from the standpoint that educational studies in mathematics should be practical. His beliefs and subsequent attempts have many implications for Korean educational studies in mathematics. In this regard, it is meaningful to examine his theory of mathematics education. But he is not well-known in Korean community of educational studies in mathematics today. For this reason, His life and theory of mathematics education are outlined.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.13-30
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• 2006

The purpose of this study is to investigate the meaning and roles of rhymes in oriental mathematics. To do this, we consider the rhymes in traditional chinese, korean, indian, arabian mathematical books and the mathematical knowledge which they implicate. And we discuss the reasons for which they were often used and the roles which they played. In addition, we suggest how to use them in teaching mathematics.

• Journal for History of Mathematics
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• v.32 no.2
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• pp.61-77
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• 2019

The study was conducted based on the 'method of mathematical exploration through history'. In recent school education, 'Probability and Statistics' education has been emphasized, and as a result, the study has conducted a study on permutations. Permutation is used in a variety of fields, and in this study, we looked at the Derangement. The results of this study are as follows. First, analysis was made at current school mathematics level and academic mathematics level for Derangement. Second, the historical development process of derangement was examined. Third, based on this, the research direction of this study was decided to be 'Derangement number's triangle(Rencontres number's triangle)', and the inquiry for education expansion was carried out. Fourth, we have presented data on concrete educational expansion by discovering various mathematical facts of the Derangement number's triangle. We hope that the results of this study will provide meaningful implications for the application of mathematics and the presentation of new inquiry directions.

• Research in Mathematical Education
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• v.20 no.1
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• pp.51-56
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• 2016

This paper is devoted to evaluate the effect of bilingual mathematics learning of Mongolian students in the primary school of Inner Mongolia. The study used tests and examined 305 Mongolian students' math achievement from Mongolian school and 277 Mongolian students from Mongolian and Han mixed school, at the same time 301 students from Guangxi regular primary school for comparison. Multivariate statistical analysis shows that there is no significant difference between these students. The results showed that the implementation of bilingual mathematics education in Inner Mongolia have achieved the desired effect. The reasons leading to the observed results are analyzed. There is a long history of bilingual education in Inner Mongolia, so the bilingual education system is complete, and the bilingual teaching resources are relatively abundant, especially the mathematics term translation between Mongolian and Chinese is standardized and unified.

• The Mathematical Education
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• v.47 no.3
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• pp.337-351
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• 2008

The intersection between mathematics and biology is rapidly expanding. The purpose of this paper is to develop college mathematics curriculum to improve the quantitative and mathematical skills of life & biological science students, and to help them better appreciate the importance and utility of mathematics. We deal with 4 questions. We first study how mathematics plays an important role in biological education and the history of biology. Secondly, we do a case study about partnership between mathematics and biology societies not only in university but in highschool of US, specially via Bio2010 and Math & Bio2010. We then investigate a way to enhance new mathematics curriculum as a service in biological science. Finally, we survey university students' basic background in order to determine the level of curriculum. From our investigation, we suggest some points to renew curriculum.

• The Mathematical Education
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• v.54 no.1
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• pp.31-47
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• 2015

School Math Field Trips(SMFT) for School Mathematics can be defined as teaching and learning activity of mathematics going into the field of Korean history, culture, science and technology. This is a literature analysis study to systemize teaching and learning method of mathematics based on literature analysis and real SMFT activity. First, SMFT was introduced to improve cognitive affective and cultural-mathematical teaching and learning method of mathematics. Second, SMFT has three purposes of cognitive, affective and cultural-mathematical. Third, to conduct mathematical education activity the direction of teaching was set. Forth, the progressing way of developing material and SMFT was researched. Fifth, developing the evaluation standard of SMFT and evaluation method was suggested.