立體幾何解題中數(shù)學(xué)思想方法的相關(guān)研究
發(fā)布時(shí)間：2018-10-15 09:53
【摘要】：一直以來(lái),立體幾何都被公認(rèn)為是高中數(shù)學(xué)的重點(diǎn)內(nèi)容之一。在我國(guó)歷次數(shù)學(xué)課改中,立體幾何在內(nèi)容、體系和結(jié)構(gòu)上都發(fā)生了諸多變化,而其在高中數(shù)學(xué)中的重要地位卻自始至終保持不變。主要原因在于立體幾何確有與眾不同的教育價(jià)值和教育意義,對(duì)于學(xué)生數(shù)學(xué)能力的培養(yǎng)具有巨大作用。因此,全面掌握并深刻理解立體幾何內(nèi)容是高中階段數(shù)學(xué)學(xué)習(xí)中至關(guān)重要的一個(gè)環(huán)節(jié)。而在數(shù)學(xué)學(xué)科中,知識(shí)的掌握和理解很大程度上取決于解題的訓(xùn)練。所以,立體幾何的學(xué)習(xí)必然離不開(kāi)立體幾何問(wèn)題的求解。數(shù)學(xué)思想方法是數(shù)學(xué)的精粹,將其運(yùn)用于立體幾何解題之中顯然是非常重要的一個(gè)思路。在立體幾何解題中合理使用數(shù)學(xué)思想方法可以將問(wèn)題化繁為簡(jiǎn),靈活克服題中的困難與障礙,從而收到事半功倍的成效�？梢哉f(shuō),數(shù)學(xué)思想方法是立體幾何解題之智慧源泉。那么,學(xué)生是否確有必要在立體幾何解題中以數(shù)學(xué)思想方法為指導(dǎo)?教師是否必需于立體幾何教學(xué)中進(jìn)行數(shù)學(xué)思想方法的滲透?是否可以清晰地認(rèn)識(shí)數(shù)學(xué)思想方法在立體幾何解題中的顯著效用,以便學(xué)生規(guī)范立體幾何解題模式,教師優(yōu)化立體幾何教學(xué)結(jié)構(gòu)。有鑒于此,本文將聚焦于闡述數(shù)學(xué)思想方法在立體幾何解題中的顯著性效果。首先,基于調(diào)查設(shè)計(jì)的邏輯性原則、通俗性原則、明確性原則、以及目的性原則等,設(shè)計(jì)了一份關(guān)于影響高中生立體幾何解題效果的相關(guān)因素的調(diào)查問(wèn)卷,并以三所學(xué)校的高中生為對(duì)象發(fā)放問(wèn)卷進(jìn)行調(diào)查。選取有效問(wèn)卷并建立數(shù)據(jù)集。其次,完成所獲數(shù)據(jù)的統(tǒng)計(jì)分析。利用MATLAB軟件對(duì)立體幾何測(cè)評(píng)考試成績(jī)進(jìn)行多元線性回歸分析,同時(shí)繪制數(shù)學(xué)思想方法效用性的數(shù)據(jù)統(tǒng)計(jì)圖。最后,根據(jù)上述統(tǒng)計(jì)結(jié)果可得,相比于其他立體幾何解題影響因子,如知識(shí)儲(chǔ)備量、解題經(jīng)驗(yàn)、心理素質(zhì)水平,數(shù)學(xué)思想方法是影響立體幾何解題效果的最主要因素,而且在提高立體幾何解題效率、準(zhǔn)確率以及降低題目難度等方面發(fā)揮著舉足輕重的作用。
[Abstract]:All along, solid geometry has been recognized as one of the key contents of high school mathematics. In the previous mathematics course reform in our country, many changes have taken place in the content, system and structure of solid geometry, but its important position in senior high school mathematics has remained unchanged from beginning to end. The main reason is that solid geometry has different educational value and educational significance, which plays an important role in the cultivation of students' mathematics ability. Therefore, mastering and deeply understanding the content of solid geometry is a crucial link in mathematics learning in senior high school. In mathematics, the mastery and understanding of knowledge depends largely on the training of problem solving. Therefore, the learning of solid geometry must be inseparable from the solution of solid geometry problems. Mathematical thought method is the essence of mathematics, it is obviously a very important train of thought to apply it to solving solid geometry problems. The rational use of mathematical thought method in solving problems in solid geometry can simplify the problems, overcome the difficulties and obstacles in the problems flexibly, and achieve twice the result with half the effort. It can be said that mathematical thinking method is the source of wisdom for solving solid geometry problems. So, is it really necessary for students to be guided by mathematical thinking methods in solving problems in solid geometry? Is it necessary for teachers to infiltrate mathematical ideas and methods in the teaching of solid geometry? Whether we can clearly understand the remarkable effect of mathematical thought method in solving solid geometry problems, so that students can standardize the model of solid geometry problem solving and teachers can optimize the teaching structure of solid geometry. In view of this, this paper will focus on the remarkable effect of mathematical thinking method in solving solid geometry problems. First of all, based on the logical principle, the general principle, the clear principle and the purpose principle of the investigation design, a questionnaire is designed about the factors that affect the effect of the high school students' three-dimensional geometric problem solving. And take three high school students as the object to issue the questionnaire to carry on the investigation. Select valid questionnaire and establish data set. Secondly, complete the statistical analysis of the obtained data. The multivariate linear regression analysis was carried out by using MATLAB software, and the data statistics of the utility of mathematical ideas and methods were plotted at the same time. Finally, according to the above statistical results, compared with other factors, such as knowledge reserve, problem solving experience, psychological quality level and mathematical thinking method, these factors are the most important factors that affect the effect of three-dimensional geometric problem solving. Moreover, it plays an important role in improving the efficiency and accuracy of solid geometry problem solving and reducing the difficulty of the problem.
【學(xué)位授予單位】：西北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：G633.6
本文編號(hào)：2272165
[Abstract]:All along, solid geometry has been recognized as one of the key contents of high school mathematics. In the previous mathematics course reform in our country, many changes have taken place in the content, system and structure of solid geometry, but its important position in senior high school mathematics has remained unchanged from beginning to end. The main reason is that solid geometry has different educational value and educational significance, which plays an important role in the cultivation of students' mathematics ability. Therefore, mastering and deeply understanding the content of solid geometry is a crucial link in mathematics learning in senior high school. In mathematics, the mastery and understanding of knowledge depends largely on the training of problem solving. Therefore, the learning of solid geometry must be inseparable from the solution of solid geometry problems. Mathematical thought method is the essence of mathematics, it is obviously a very important train of thought to apply it to solving solid geometry problems. The rational use of mathematical thought method in solving problems in solid geometry can simplify the problems, overcome the difficulties and obstacles in the problems flexibly, and achieve twice the result with half the effort. It can be said that mathematical thinking method is the source of wisdom for solving solid geometry problems. So, is it really necessary for students to be guided by mathematical thinking methods in solving problems in solid geometry? Is it necessary for teachers to infiltrate mathematical ideas and methods in the teaching of solid geometry? Whether we can clearly understand the remarkable effect of mathematical thought method in solving solid geometry problems, so that students can standardize the model of solid geometry problem solving and teachers can optimize the teaching structure of solid geometry. In view of this, this paper will focus on the remarkable effect of mathematical thinking method in solving solid geometry problems. First of all, based on the logical principle, the general principle, the clear principle and the purpose principle of the investigation design, a questionnaire is designed about the factors that affect the effect of the high school students' three-dimensional geometric problem solving. And take three high school students as the object to issue the questionnaire to carry on the investigation. Select valid questionnaire and establish data set. Secondly, complete the statistical analysis of the obtained data. The multivariate linear regression analysis was carried out by using MATLAB software, and the data statistics of the utility of mathematical ideas and methods were plotted at the same time. Finally, according to the above statistical results, compared with other factors, such as knowledge reserve, problem solving experience, psychological quality level and mathematical thinking method, these factors are the most important factors that affect the effect of three-dimensional geometric problem solving. Moreover, it plays an important role in improving the efficiency and accuracy of solid geometry problem solving and reducing the difficulty of the problem.
【學(xué)位授予單位】：西北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：G633.6
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