【摘要】：數(shù)列在高考中有著非常重要的位置。本文通過文獻研究、問卷調(diào)查、訪談及個案跟蹤等研究方法對高三學(xué)生數(shù)列問題解題狀況進行調(diào)查分析,將波利亞解題數(shù)學(xué)模式運用到高中數(shù)列問題的求解與教學(xué)實踐當(dāng)中,力求能夠改善學(xué)生高中數(shù)列問題求解狀況,在高考中取得好成績。本文主要分為四大部分：(一)對高中學(xué)生進行關(guān)于數(shù)列問題解題狀況調(diào)查,發(fā)現(xiàn)其解題過程不符合波利亞數(shù)學(xué)解題模式。(二)基于波利亞解題模式的研究,提出數(shù)列求解模式的四個步驟：①認真審題,獲悉顯隱性條件②觀察數(shù)列特征,尋求有用的思路③用好數(shù)學(xué)思想方法④解題回顧(三)基于波利亞解題模式進行數(shù)列重點題型的求解實踐,歸納總結(jié)重點題型的解題方法技巧。讓學(xué)生體會解題思維過程和數(shù)學(xué)思想方法。(四)基于波利亞解題模式給出數(shù)列解題教學(xué)建議：①重視并用好概念及性質(zhì)②觀察數(shù)列特征、啟發(fā)引導(dǎo)學(xué)生找解法③用好數(shù)學(xué)思想方法、優(yōu)化解題思維過程④解題回顧。并給出數(shù)列習(xí)題解題課的教學(xué)設(shè)計。本文的研究不僅僅是波利亞解題模式的推廣,也對一線教師的教學(xué)和高中生的解題有著非常重要的指導(dǎo)意義。
[Abstract]:The sequence of numbers plays a very important role in the college entrance examination. Through literature research, questionnaire survey, interview and case tracking, this paper investigates and analyzes the problem solving situation of the series of problems for senior high school students, and applies the mathematical model of Polya problem solving to the solving and teaching practice of the series of problems in senior high school. Strive to improve the high school series of problem-solving situation, in the college entrance examination to achieve good results. This paper is divided into four parts: (1) the high school students are investigated about the problem solving of series of problems, and it is found that the process of solving problems does not accord with Pollya mathematical problem solving model. (2) based on the study of Polya's problem-solving model, four steps of solving the series of problems are put forward: (1) carefully examining the problem and learning that the hidden condition 2 observes the characteristics of the sequence of numbers, Find useful ideas 3 make good use of mathematical thinking method 4 Review of problem solving (3) solve a series of key problem types based on Polya problem solving mode, summarize the key problem solving methods and skills. Let the students experience the thinking process and mathematical thinking method of solving problems. (4) based on Polya problem solving mode, this paper gives some suggestions on how to solve problems in series of numbers: (1) pay attention to and use the concept and nature of 2 to observe the characteristics of series of numbers, enlighten and guide students to find a solution and make good use of mathematical thinking methods, and optimize the thinking process of solving problems. (4) Review of problem solving. The teaching design of the course of solving problems in several series of exercises is given. The research in this paper is not only the promotion of Polya problem-solving model, but also has a very important guiding significance for the teaching of front-line teachers and the problem-solving of senior high school students.
【學(xué)位授予單位】：西北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6

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