Teaching Number Sequences From The HPM Perspective:an Action Research

Number sequences, which occupy an entire chapter in the textbook of middle school and is a very important knowledge, reflect its importance in many respects. And it is connected with other knowledge closely, such as function. Number sequence is the basis of discrete mathematics, and is an important bridge contact primary education and higher education. In addition, many natural phenomena are closely connected with number sequences, and we usually need some knowledge of number sequences in our daily life.The new curriculum standards begin to put mathematical culture in an important position, it require mathematics teachers integrate more mathematical culture in teaching, and improve students’cultural literacy. The chapter "number sequences" in the current textbooks already contains a few materials of mathematical history, but the educational value of these materials played is very limited. In the background of new curriculum reform and textbook revision, our study attempt to design some cases of integrating mathematical history, and to explore a method that can improve the teaching of number sequences. With the hope that helping studengts learn number sequences better, getting a positive emotional experience and establishing a correct conception of mathematics.There are many cases that integrating history into a single knowledge of number sequences. This study, with the exception that, making the teaching design on the whole chapter and integrate the history. And action research method is adoppted, wahich is one method aims to provide effective teaching through combining teaching theory and teaching practice, it also an effective way to promate the curriculum reform and teacher development.Five cases is developed in Shanghai and Zhejiang, they are "The concept of number sequences", "Recurrence sequence", "Summation of arithmetic sequence", "The concept of geometric sequence", "Summation of geometric sequence"Based on the analysis of classroom videos, questionnaires and interviews results, we draw the following conclusions:(1) Impact on students mainly reflect in the following aspects:Integrating history into mathematics teaching can promote students’understanding of number sequences and relevant mathematical thinking; Mathematical history play a certain role on the formation of proper view of mathematics; Mathematical history make a positive effect on students’mathematics learning emotions and beliefs, it can enhance their interest in learning mathematics and triggering motivation; Mathematical history has some moral education value, to cultivate students’pragmatic quality and rational spirit, etc; Mathematical history also lead students learn to appreciate the beauty of mathematics, perception of the aesthetic value of mathematics.(2)Integrating history into the mathematics classroom can enhance the professionalism of teachers. Whether teachers’exploring ability innovative ability on the new teaching mode, or teachers’cultural enrichment of mathematics and understanding of mathematics and so on have a certain promotion.(3) Moon phase table, Fibonacci aequence and spiral, Joseph game, Tom and Jerry problem, Hanoi tower game, story of rich man and stranger, the discovered story of asteroid and so on, these mathematical hiatory materials are suitable for number sequences teaching.Thus, the history of mathematics is an effective way to improve the number sequences teaching, and is worth for middle school teachers to reference.