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The Nine Chapters on the Art of Mathematics has played a very important role and been considered as a classic in the history of Chinese mathematics. We formed a research team which used this material to introduce to high school students the setting of an equation, explaining its problem and method using the Fangcheng chapter of the Chinese classic. The main goal of this lesson plan was to introduce the Fangcheng method of solving systems of linear equations, so that students can naturally develop understanding of the concept of the matrix and its operations, and appreciate the Chinese cultural heritage as well. Thus, helping them realize that mathematics came from real life, we aroused students' interests. Among 33 respondents of the survey, 29 thought this course helped them understand the methods and basic concepts, and 28 said it enhanced their mathematical literacy. Obviously, introducing the Fangcheng chapter and Fangcheng method from the Chinese classic, and linking them to the learning of the matrix, we can enhance students' understanding and their beliefs about the cultural aspects of mathematics., "The study of the history of mathematics 2017". September 19-22, 2017. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

In this paper, we discuss features of geometrical diagrams in different cultures, especially representations of 3-D objects in East Asia. There is no Chinese diagram in the first millennium or earlier that survives to this day. In the second millennium, there are some interesting features. In the first half of the second millennium, Chinese diagrams for 3-D objects are usually contextualised; in the second half, the diagrams became more abstract. Korean and Japanese mathematicians used very creative ways, such as parallel line segments or shadows, to draw 3-D objects. Japanese scholars also put a middle curve in a 2-D diagram to create the sense of the third dimension. For sangaku diagrams, they also put different colours on the two regions divided by the middle curve, as if those regions are different "faces"., "The study of the history of mathematics 2017". September 19-22, 2017. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

International audience; Mathematical narrative is a concept that has gradually been attracting the attention of school teachers and mathematics educators in especially recent years. The term ‘mathematical narrative' in this workshop proposal refers to a form of narrative that is used to communicate or construct mathematical meaning or understanding. By introducing certain metaphors, a narrator may induce or promote learners' or listeners' mathematical understanding. This teaching tool can be used, for instance, to encourage further reflections upon some mathematical concepts or for alternative remedial learning, especially after conventional classroom teaching. Moreover, this can be applied in liberal arts courses at the university level. One straight forward way to introduce mathematical narrative into teaching is to use stories, arguments, problems, and their solutions from history, but one can also use literary metaphors to improve understanding. In this workshop, two school teachers and two mathematics educators will share their experiences in using mathematical narrative in their teaching, and also exchange teaching ideas with other participants in the workshop. The four presenters and the topics they will be discussing are described below. Presenter 1: Yi-Wen Su, Department of Mathematics, University of Taipei. The starting point of HPM is always history, and so is the beginning of this workshop. The first presenter is also the organiser of this workshop, and she shall share her experiences on how to design an activity to help improve undergraduate mathematics majors' reading comprehension using pre-modern mathematical arguments. The main material in this activity is the original proof of Heron's formula by Heron, and also another procedure that is equivalent to Heron's formula found in a thirteenth-century Chinese mathematical text written by Qin Jiushao. Presenter 2: Jyun-Wei Huang, Taipei Municipal Heping High School. The second presenter shall discuss his teaching in an elective mathematics course in senior high school in Taiwan (10th–12th grade). The core of this course is the use of the five most beautiful mathematical equations. The teacher tries to integrate mathematics discourse and mathematics writing in his teaching, and guides students in creating artistic works such as mathematical fictions, poems, games, and movies. In this way, he can help his students discover the beauty of mathematics and enhance their motives in learning. Presenter 3: Yuh-Fen Chen, New Taipei Municipal Mingder High School. The third presenter mainly teaches junior high school in Taiwan (7th–9th grade). She will share many activities designed by the team of mathematics teachers in her school, including publishing a school mathematical magazine, engaging students in mathematical games they created, decorating the school with ‘mathematical tablets' that have their origins in the mathematical writings from Japan's Edo period, and encouraging students to write popular science novels after some mathematical reading. Presenter 4: Wann-Sheng Horng, Department of Mathematics, National Taiwan Normal University. Last but definitely not the least, history is transformed into narratives. The final presenter will introduce his experience in combining literary metaphor in teaching for undergraduate liberal art courses in mathematics. The main example he shall use is a questionnaire he employs to help students reflect upon mathematical concepts. He uses a metaphor quoted from Eli Maor's popular work, The Pythagorean Theorem: A 4,000-Year History. Maor uses the metaphor of ‘democracy' to talk about a theorem related to chords in a circle. The presenter's questionnaire guides students to reflect upon many aspects of Euclidean geometry and helps many university students, who are relatively weak in mathematics, to gain a new perspective about the discipline. Keywords: mathematical narrative, history of mathematics, reading, HPM