The Preliminary Research Of 'Algorithm' Teaching In The New Mathematics Curriculum

Algorithm plays a center role in ancient Chinese mathematics. Along with the quick development of computer technology, algorithmic knowledge and skills are necessary to every modern citizen. The newly issued Standards of High School Mathematics Curriculum in China lists algorithm for the first time as a necessary course. This is the demand that complies with times, but it has also brought a series of problems in the teaching and learning of the new course, such as: What is the instructional function of algorithm? How to divide the goal levels of algorithm teaching? Are there any related experiences in other countries? Which difficulties will students meet? And how to teach and evaluate in a real classroom? etc.. Therefore, this paper tries hard to make some preliminary discussions with eyes both toward theory and practice.This paper divides into two parts. The first part includes literature review and document analyses, which aims to clarify the meaning of algorithm, general requirement of learning, and standard of a good algorithm; to look back the algorithm feature of the Chinese ancient mathematics as well as its influence to teaching and learning; to trace back the development process of algorithm in the past teaching syllabus of our country and the arrangements of algorithm contents in other counties; as well as to analyze the requirements for algorithm in the new high school mathematics courses in our countryThe second part contains two case studies. The first case is on the teaching of ' Approximate calculation of 5^1/2', which tries to distinguish the cognitive levels of algorithmic learning according to van Hiele's five levels of geometric reasoning; The second case comes from a experiment research project on the new high school mathematics curriculum conducted by Teaching and Research Section of Suzhou City, which focuses the following four case questions on algorithm teaching: (l)Are there any requirements of teaching and learning algorithm contents? (2) What kinds of sample problems are helpful to algorithm teaching? (3)How to guide students to investigate algorithm thought? (4) What roles should modern IT play in algorithm teaching? There are only preliminary discussions toward these case questions in this paper. More reflection is needed for teachers during their classroom practice.Based on the above document analyses and case studies, the dissertation is ended by raising some suggestions for the teaching of algorithm and related teachers' training.