Mathematics teachers at the secondary education in the 21st century must be able to move the students by scientific subtleness of mathematics and also be able to convince them of the usefulness of mathematics in life and work. In order to achieve this aim, the teachers are required to be well-cultured in Logos and Ars. For instance, they should be aware that the mathematics education is an art where they do play the major role and should know how are changing the trends and methodology of mathematics, particularly of applied mathematics, together with current science and technology in general, as we describe below. In order to meet these changes, there are many things to do, while we here only propose to make the approach in the secondary mathematics double-tracked in a good balance of the following two paths, locally and globally: one track Logos-emphasizing and the other Ars-oriented. In the final section, some topics selected from the ordinary syllabus are mentioned, each of which is significant either for theoretical thinking or for applicable literacy.
In this article, we report on a comprehensive learning carried out as an international cooperative distance learning (abbr. ICDL) between Japan and Thailand using a teleconference system. Junior high school students of both countries studied on the environmental destruction, and they interchanged their results via the ICDL. Environmental problems are just the suitable teaching material for the students to try to solve by themselves. Both watching and presenting the results of their studies had their own factors of creativity, which were to be fostered through this project. In our ICDL, students
could experience these two sides of activities.
In teaching functions, it is important for the students to obtain the ability to consider questions about the change of phenomena in the real world. But many students are poor hands at learning functions. We found the reason why students cannot understand the essence of the concept of functions from our preliminary studies and examinations.
The reason comes from the fact that students do not fully understand the definition of functions, the concept of the extraction of variable quantities, and the ratio of variation. So we tried to teach on the basis of our hand-made educational contents for 9th graders, which include the modern definition of functions, extraction of variable quantities, consideration of appearance of change, and functions of several variables. As a result of this project, our teaching methods could make improvements to some problems of the current function teaching
According to the new curriculum guidelines issued in March 2008, a framework for statistics and probability has newly been set up in the junior high school mathematics course. It has drawn school mathematics educators' attention to what the new curriculum guidelines imply for statistics education in the mathematics classes. In this article, I first show the current background in today's knowledge-based society where statistics education is needed and second give an explanation of a modernized framework of statistics education with a concrete example curriculum to be promoted internationally, where the focus is to have students develop the "statistical thinking" habit to explore and to solve their everyday problems with data rather than to have students know what statistics is and/or how to do statistics. Finally, I introduce an international project, CensusAtSchool, which supports such new-style statistics education.
As the role of statistics has become more and more prominent in this information age, it is both timely and fortunate that a formal decision has been made to include statistics as a part of the new mathematics curriculum in Japan. Since learning statistics requires a unique thinking process, one needs to give much thought to the teaching methodologies for statistics. In this paper, the CensusAtSchool project in the United Kingdom is introduced as an example of a successful attempt at teaching statistics to students, from kindergarten through high school.