Analysis Of Mathematical Algorithms Research And Teaching

From the combination of algorithm study and the new concepts of mathematical curriculum reform the thesis tries to expound algorithm teaching preliminarily in elementary mathematics especially with the guide of our county's Mathematics Ctirriailar Criterion of Ordinary Senior Middle School. It carries out mainly through studying the correlated documents and data. And its principal work and results are as follows:1. The thesis makes a commentary on mathematics algorithm from the viewpoint of history. Mathematics algorithm is a series of basic operations or orders for solving mathematical problems. It is an old concept. And it has three basic characteristics-limitation, definitude and feasibility. Mathematics algorithm promotes both the development of mathematics and the progress of the whole social culture tremendously. It has a profound and far-reaching significance of methodology.Among it, the thesis tries to divide the history of algorithm into 4 stages: the germination period of original algorithm (Before 600 B.C.), the development period of antiquity algorithm (600 B.C.-16thC), the prosperous period of modern times algorithm (17thC-18thC) and the development period of contemporary ages algorithm (1920s- ). Along the historic track of algorithm, the thesis reveals its vast prospect.2. By analyzing the present conditions of algorithm teaching and its significance, the author tries to establish her understanding of algorithm teaching. Mathematics algorithm is easier to master for its explicit steps and formulas. But in traditional algorithm teaching it was only regarded as a regular drill and its process was ignored. As a result, the students' enthusiasm and creativity were strangled. Their development was blocked. Now, every country in the world has begun to be concerned with mathematics algorithm teaching and has carried out a series of reforms.The author thinks mathematics algorithm teaching consists of three parts. The first part is about the mastery and practice of algorithm. The second is the creative activity to solve problems by the method of algorithm. The last is the mastery of algorithm thought. And the fist part is primary and necessary. It is the basis of the second. But the gist of algorithmteaching is the mastery of algorithm thought. So it should be permeated in the whole teaching process.3. On the standpoints of "constructivism"\, "the distinction of cognitive structure" and "the study of procedural knowledge", the author does research in the theory of algorithm teaching. Constructivism should be the theoretic foundation of algorithm teaching. Teachers must attach much importance to students' self-construction. Meanwhile, the theory of thinking operation can provide a guide to the first part of algorithm teaching. The theory of the distinction of cognitive structure points out there are two kinds of cognitive structure-"characteristic" and "functional". Every student uses his(her) own cognitive structure to learn and solve problems. So teachers should respect their individual characters fully and should adopt flexible models to teach, encouraging and stimulating students to use their own cognitive means to solve algorithm problems. Besides, algorithm belongs to a kind of procedural knowledge. The thesis stresses on how to teach "production" and "rule" with examples in the study of procedural knowledge.4. From the activity of Chinese traditional algorithm the author explores algorithm teaching. Algorithm is the foundation and the impetus of development of Chinese traditional mathematics. Chinese traditional mathematics centered on algorithm research and formed a unique system of algorithm roughly. Its projecting features are "algorithm thought" and "constructive method". Through analyzing some algorithm in Chinese traditional mathematics-"the algorithm of finding out the maximal common divisor" and "the algorithm of dealing with the polynomial of degree n of one indeterminate" the author explains the training for "the method of algorithm" of Chinese traditional m...