This work is supported in part by Vietnam's National Foundation for Science and Technology Development – NAFOSTED under Project Code VI2.2-2010.11. Experiment school mathematics in constructing knowledge of infinitesimal small quantities Nguyen Dang Minh Phuc Pham Sy Nam College of Education Phan Boi Chau Gifted High school Hue University, Vietnam Nghe An Province, Vietnam phucsp@gmail.com phamsynampbc@gmail.com Abstract Experiment school mathematics requires mastering the use of dynamic manipulations on dynamic mathematics models. In the analysis subject, the design of models containing infinitesimal small quantities so that they are displayed visually is not easy. In this paper, we designed two basic mathematical tasks to supports students constructing some knowledge of limit of sequence of numbers and functions. The research results show that experimentation using dynamic manipulations enable students easier in forming hypotheses, verifying them, rejecting the wrong ones and constructing knowledge of infinitesimal small quantities. Keywords: experiment, school mathematics, analysis, infinitesimal small quantities. Introduction Finzer & Nick (1998) studied manipulations on dynamic mathematics models have shown the characteristics of these operations and claimed their roles in supporting students construct mathematical knowledge. The models, designed on the dynamic geometry softwares (DGS) and dynamic manipulations created a new approach in teaching and learning mathematics in school. Followed their works, we designed dynamic mathematics models in E-textbooks for mathematics teachers to use at 4 levels: Use models right way for activity; add, remove or edit objects before using; create a complete lesson plan and create new models (Phuc, 2011a). We also designed models that good support for students forming abductive inferences and improving abductive processes (Phuc, 2011b). We called those activities took place between students using manipulations on dynamic mathematics models as school mathematical experiment activities (SMEA). Analysis subject in mathematics curriculum books at high school in Vietnam related more to the infinitesimal quantities. These knowledge are always hard for students to understand. Teachers often have difficulty to: • describe infinitesimal small and large quantities. Students found hard to understand some terms such as “ ε is positive real number and arbitrarily small”, “n approaches infinity”, “x is very close to x 0 ”, etc.; • show the convergences of numbers, value of functions. Teachers often use more lingual and symbolic representations to describe these processes than others. • display infinitesimal small quantities in motions. For example, with sequence u n = 1 n and n belongs to the set of natural numbers, teachers usually said “if n approaches