Algorithm Research In Mathematics Education

Algorithm is a kind of powerful and intellectual tool for learning and understanding knowledge of other subjects. However the results of the questionnaires and interviews among the teachers and students show that the actuality of our "algorithm" teaching in secondary mathematics education is not so good. Therefore the research on algorithm teaching from a culture angle is essential, which is beneficial to the modernization of mathematics education, the inheriting and development of our mathematics tradition, and also to the improvement of our national intellectual quality. First, conceptualize "algorithm" in mathematics education based on the review of its different concepts. It is a prescrip (rule, procedure, rigorous calculate order) that everyone can know and if that is executed well and truly, any kinds of problems established on it can be solved. In essence, it includes some main characters: certain, sequence, limitedness and universality. Second, analyse the education value of algorithm in detail with the theories of mathematics education, cognition and structure, including fostering good thinking habits, enhancing mathematics thought ability, developing the consiousness of technology and mathematics application, and forming active and favorable emotions. Third, probe the organization and implementation of the algorithm contents for teaching in secondary mathematics education, according to the modern theories of mathematics curriculum, teaching and learning ,and general curriculum, and the survey of the algorithm teaching in other developed countries, and our mathematics culture tradition. Pay much attention to the fundermentality, nationality and conform to the times when choosing contents. We can rebuild the actual teaching materials to realize arithmetization, add ancient Chinese mathematical methods and the introduction to the algorithm combined with computer. Pay much attention to integrality, facing to all students, application, oneness combined with distinguish and present the diversification, problem solving and spire when organizing the contents. As demonstrations, tow sections of our mathematical textbooks are adapts. As for the algorithm teaching, four suggestions are given: teaching both algorithm and the fundamentals of the algorithm, encouraging diversification of the algorithms, emphasizing "doing" with hands and "computing" through computers. Here students might operate by some intuitional learning materials, explore the mathematical disciplinarian through modern information technology such as computer, reflect the algorithm action through written records. In the end, point out some problems for further research on the level of theory and practice, i.e. how can the algorithm get a balance and a harmony between mathematics curriculum and information technology curriculum? is there a special learning mechanism in the algorithm learning? can we equrate a general patten of the algorithm teaching? how should we evaluate the algorithm teaching and learning? In addition, the questionnaire are attached to the paper, too.