In this note we propose a 10 hour-program for gifted students. A special feature of this program is to utilize the computer for the topics on cryptography. During the program the students are required to read some books. It is possible for some parts of the program may not be attractive to the students who are not interested in computers.

The aim of this study is to investigate future teachers' skills that can make problem solving methods concrete for 7-11 year old students. For the students in the concrete operations level, solutions of word problems should also be taught by concreting. But most of teacher candidates can not solve the problems without algebra because they got used to solve the word problems with algebra during their high school and university education. In this study, whether the teacher candidates have the skills of solving the primary school level problems without using algebra or not are being observed. At the end of this observation it is determinated that primary level teacher candidates generally prefer using algebra operations because of their former habits. The results show that in the education of the primary level teacher candidates, there is the need of developing the solving skills using figures and diagrams without algebra rather than algebraic solutions in word problems.

Based on author's practice of instructing Chinese gifted students to join the Chinese Mathematics Olympic (CMO), the paper adopted test analysis model of the Scholastic Aptitude Test of Mathematics (SAT-M), tested mathematics ability of 212 mathematical gifted students to join the CMO, applied correlation analysis and factor analysis and proposed the mathematics ability structure in Chinese gifted students including comprehensive operation ability, logic thinking ability, abstract generalization ability, spatial imagination ability, memory ability, transfer ability and intuition thinking ability. And it analyzed the expression form of these abilities respectively and gave some suggestion on mathematics teaching about gifted Chinese students.

According to the mathematics educational practice and research about gifted children in some secondary schools in China, the paper presented some relevant problems: 1. Missing or mistaken selecting in gifted children in China. It included the limitations of identifying standard and the fault of understanding and doing in practice, administration disturbance and emotional inclination. 2. Backward traditional mathematics teaching in gifted children in China. It included lower teaching starting point, slower teaching planned speed, simpler teaching contents and so on. The paper analyzed the problems, and made enlightenment for gifted children's mathematical teaching strategies: raising starting point of contents; emphasizing essential principles and skills; using flexible teaching methods; encouraging discover and creativity and developing harmoniously psychological level and mathematical ability. As to these strategies, some detail measures were offered as well.

In this increasingly technological world, the creativity development has been highlighted much in many countries. In this paper, two mathematical activities with Chinese characteristics are presented to illustrate how to integrate algorithmic teaching into mathematical activities to develop students' creativity. Case studies show that the learning of algorithm can be transferred into creative learning when students construct their own algorithms in Logo environment rather than being indoctrinated the existing algorithms. Creativity development in different stages of mathematical activities and creativity development in programming are also discussed.