This paper is a sequel to the paper [8], where we discussed the connection between ShiShou KaiFangFa originated from JiuZhang SuanShu and ZengCheng KaiFangFa. Investigating KaiFangShu in a Chosun mathemtics book, SanHak JeongEui and ShuLi JingYun, we show that its authors, Nam ByungGil and Lee SangHyuk clearly understood the connection and gave examples to show that the KaiFangShu in the latter is not exact. We also show that Chosun mathematicians were very much selective when they brought in Chinese mathematics.

Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Seki Takakazu (1642?-1708) is the most famous one. Taking Seki's interpolation as an example, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to this problem which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. Professor Wu Wentsun says that, in the whole history of mathematics, there exist two different major trends which occupy the main stream alternately. The axiomatic deductive system of logic is the one which we are familiar with. Another, he believes, goes to the mechanical algorithm system of program. The latter featured traditional Chinese mathematics, as well as Wasan. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of the mechanical algorithm system of program deeper.

The Erlangen program is a scholastic plan by German mathematician Felix Klein, in which he, based on group theory, made a reassessment of geometry as well as an attempt to generally organize it. In this paper, I will introduce the historical and scholastic background of the Erlangen program, overview the process of its formation, and provide some comments regarding its historical significance.

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

It has been proposed since modern times that we need to consult the history of mathematics in teaching mathematics, and some modifications of this principle were made recently by Lakatos, Freudenthal, and Brousseau. It may be necessary to have a direction which we consult when modifying the history of mathematics for students. In this article, we analyse the elements of the cognitive interest in Hamilton's discovery of the quaternions and in the history of discovery of imaginary numbers, and we investigate the effects of these elements on attention of the students of nowadays. These works may give a direction to the historic-genetic principle in teaching mathematics.

It was not until the early twentieth century that statistics emerged as an independent academic discipline. The developments of statistical theory and methods would not have been possible without heated controversies among founding fathers. One of them, controversy on the statistical test between R. A. Fisher and J. Neyman, E. S. Pearson had been very fierce and long-lasting. On the other hand it was in the early twentieth century that psychologists began to utilize statistical test which was a hybrid of tests developed by Fisher and Neyman-Pearson. By considering the history of fields such as psychology, we can see distinctive characteristics specific to the history of statistics.

Although many people have recognized the importance of history of mathematics in mathematics education, there are few studies that history and mathematics educations are connected. In this paper, we present and discuss the ways of introducing the instruction with mathematics machines. This instruction use the history of mathematics as part of a class not as a tool to stimulate students' interest but as a goal that it can be targeted mathematical itself. To do this, we first analyze the characteristics of applying history of mathematics in mathematical education, second, describe the meaning and the educational value of mathematical machines, and finally explained the way of applying history of mathematics with mathematics machines. The Instruction of history of mathematics with mathematics machines has advantages that practice (manipulation and experiment) and theory (elaboration of definition, production of conjectures and constructions of proofs) are interlaced within a historic-cultural perspective.