將數(shù)學(xué)建模的思想融入高等數(shù)學(xué)的教學(xué)

1、將數(shù)學(xué)建模的思想融入高等數(shù)學(xué)的教學(xué)    將數(shù)學(xué)建模的思想融入高等數(shù)學(xué)的教學(xué) 【中文摘要】 隨著我國高等院校大范圍的擴(kuò)大招生,學(xué)生的個(gè)體差異和數(shù)學(xué)基礎(chǔ)的差別越來越大,而作為高等學(xué)校的重要基礎(chǔ)課程的高等數(shù)學(xué)的教學(xué)改革也正在進(jìn)行研究和探討之中,許多教育同行都深深的感到,如今的高等數(shù)學(xué)教學(xué)不能還是同一個(gè)模式、同一個(gè)要求。在終身學(xué)習(xí)這種思想的指導(dǎo)下,高等數(shù)學(xué)的教育方式和教學(xué)模式也正在經(jīng)歷一次一次的變革。本文從高等學(xué)校中高職高專學(xué)生的學(xué)習(xí)特征和規(guī)律出發(fā),以問題研究為手段,以全面掌握和熟練運(yùn)用所學(xué)知識解決實(shí)際問題為目標(biāo),結(jié)合高等數(shù)學(xué)的學(xué)科特點(diǎn),進(jìn)行基于數(shù)學(xué)建模思想融

2、入高等數(shù)學(xué)的教學(xué)模式的研究分析與評價(jià),并對教學(xué)效果進(jìn)行分析與評價(jià),促使教師改變教學(xué)模式,從而提高學(xué)生的課堂學(xué)習(xí)效率和學(xué)生數(shù)學(xué)素養(yǎng),進(jìn)而提高學(xué)生的整體綜合素質(zhì)。本文采用問卷調(diào)查、教學(xué)實(shí)踐研究、建立馬爾科夫教學(xué)評價(jià)模型分析等方法,結(jié)合高等數(shù)學(xué)教學(xué)大綱的要求,將數(shù)學(xué)建模的思想融入高等數(shù)學(xué)教學(xué),并通過課堂教學(xué)的實(shí)踐,使建模思想和數(shù)學(xué)理論有機(jī)的結(jié)合。將建模思想融入高等數(shù)學(xué)教學(xué),為正在進(jìn)行的高等學(xué)校教育教學(xué)改革提供了新的思路和方法,與此同時(shí),本人根據(jù)教學(xué)改革的需要,對實(shí)施教學(xué)改革的班級和對照班進(jìn)行了相應(yīng)的教學(xué)效果分析和評價(jià)。本文共分六個(gè)章節(jié),其主要內(nèi)容如下:第一章:研究背景。通過對宏觀背景的研究,提出問題

3、。第二章:建模思想融入高等數(shù)學(xué)教學(xué)模式的基本思路。結(jié)合我校實(shí)際提出建模思想融入高等數(shù)學(xué)的教學(xué)設(shè)計(jì)。第三章:建模思想融入高等數(shù)學(xué)的教學(xué)的教學(xué)案例。第四章:建模思想融入高等數(shù)學(xué)的教學(xué)實(shí)踐。第五章:教學(xué)效果調(diào)查與評價(jià)。第六章:教學(xué)反思 【英文摘要】 As the institutions of higher education of our country expand the enrollment broadly, students' individual differences and the differences on mathematics foundation are great

4、er and greater. The reform in education of“higher mathematics”is carrying on research and discussion, which is the important basic course of the institution of higher education. A lot of college teachers consider that teaching of“higher mathematics”of today can't be still in the same mode and th

5、e same requirement. Under the guidance of this kind of thought studying all the life, the education way and teaching mode of“higher mathematics”are changing again and again. The author of this paper proceeds from study characteristic and law of the students of the high commissioner of the professors

6、hip in the institution of higher education, regards studying problems as the means, regards grasping the goal in an all-round way and using it to solve the practical problem, combines the discipline characteristic of“higher mathematics”, carries on researching and analyzing and appraisal of the teac

7、hing mode based on that the modeling thought of mathematics incorporates higher mathematics, and analyzes and appraises the teaching result, thereby impelling teachers to change the teaching mode, thus improving students' classroom learning efficiency and student's mathematics accomplishment

8、, and then improving students' whole overall qualities.The author of this paper takes the methods of analyzing that appraising models by questionnaire investigation, teaching practice, the establishment of teaching evaluation Markov model analysis, combines the requirement for“higher mathematics

9、”syllabus, integrates the idea of mathematical modeling into the higher mathematics teaching. And through practice of classroom teaching, combines modeling thought with mathematics theory. It has offered new thinking and method for ongoing reform in education of higher school education that incorpor

10、ating teaching of“higher mathematics”of the modeling thought. Meanwhile, according to the needs of reform in education, the author contrasts the class and analyzes the corresponding teaching result to the class. This paper divides into six chapters, its main content is as follows:Chapter: Study of t

11、he background. Through the study of macroscopically background put forward the question.Chapter: The modeling thought incorporates the basic thinking of the teaching mode of“higher mathematics”. The author made light of the actual modeling school thinking into the design of higher mathematics teachi

12、ng. Chapter: The modeling thought incorporates the teaching of higher mathematics to teaching cases.Chapter: The modeling thought incorporates the teaching of higher mathematics to practice.Chapter: The teaching result is investigated and appraised.Chapter: Teaching reviews. 【中文關(guān)鍵詞】 高等數(shù)學(xué); 建模思想; 基本思路

13、; 教學(xué)設(shè)計(jì); 教學(xué)實(shí)踐 【英文關(guān)鍵詞】 Advanced Mathematics; The idea of mathematical modeling; Basic thinking; Instructional design; Teaching practice 【畢業(yè)論文目錄】中文摘要 4-5 Abstract 5-6 第一章 問題的提出 10-19     1 研究背景 10-11         1.1 高等數(shù)學(xué)課程發(fā)展的歷史沿革 10     

14、    1.2 國內(nèi)外利用數(shù)學(xué)建模教學(xué)的背景與狀況分析 10-11     2 高等數(shù)學(xué)的教學(xué)目標(biāo) 11-13         2.1 高等數(shù)學(xué)的總體目標(biāo) 11         2.2 我校（河北北方學(xué)院）高等數(shù)學(xué)課程的教學(xué)目標(biāo) 11-13     3 在我校高職高專高等數(shù)學(xué)教學(xué)中融入建模思想的必要性與可行性 13-15     

15、;    3.1 建模思想融入高等數(shù)學(xué)教學(xué)的必要性 13-14         3.2 建模思想融入高等數(shù)學(xué)教學(xué)的可行性 14-15     4 相關(guān)研究綜述與現(xiàn)狀 15-19         4.1 對數(shù)學(xué)建模理論的研究 15-17         4.2 將數(shù)學(xué)建模思想融入數(shù)學(xué)主干課程的研究 17-19 第二章 將建模思想融

16、入高等數(shù)學(xué)教學(xué)的基本思路 19-32     1 實(shí)驗(yàn)?zāi)康呐c研究的問題 19-20     2 數(shù)學(xué)建模融入到高等數(shù)學(xué)教學(xué)中的方法 20-21         2.1 弄清、搞透概念的意義 20         2.2 加深、推廣應(yīng)用問題 20-21         2.3 高等數(shù)學(xué)中數(shù)學(xué)模型的案例教學(xué) 21  

17、60;  3 在高等數(shù)學(xué)中要全方位滲透數(shù)學(xué)思想方法 21     4 針對我校高等數(shù)學(xué)融入建模思想的教學(xué)設(shè)計(jì) 21-31         4.1 設(shè)計(jì)思想 21-22         4.2 教學(xué)設(shè)計(jì)的實(shí)施 22-31     5 教學(xué)實(shí)踐 31     6 教學(xué)反思 31-32 第三章 在高等數(shù)學(xué)教學(xué)中融入數(shù)學(xué)建模思想的案例 32-47  

18、60;  1 建模思想在概念、定義教學(xué)中的融入 32-38         1.1 導(dǎo)數(shù)概念的引入 32-35         1.2 定積分定義的教學(xué) 35-38     2 建模思想在定理應(yīng)用教學(xué)中的融入 38-41         2.1 連續(xù)函數(shù)的根的存在定理 38-39      

19、0;  2.2 建模思想融入極大極小化問題 39-41     3 運(yùn)用建模思想分析解決實(shí)際應(yīng)用問題 41-47         3.1 貸款購房函數(shù)的應(yīng)用 41-42         3.2 投資費(fèi)用問題級數(shù)的應(yīng)用 42-45         3.3 電學(xué)問題微分方程的應(yīng)用 45-47 第四章 建模思想融入高等數(shù)學(xué)的教學(xué)實(shí)踐 47-52 

20、0;   1 教學(xué)實(shí)踐的實(shí)驗(yàn)設(shè)計(jì) 47-49         1.1 實(shí)驗(yàn)?zāi)康呐c假設(shè) 47         1.2 實(shí)驗(yàn)對象的選取 47         1.3 實(shí)驗(yàn)方法 47         1.4 干擾變量控制 47         1.5 實(shí)驗(yàn)內(nèi)容分析分期付款模型 47-49     2 在數(shù)學(xué)教學(xué)中融入建模思想的主要困難和策略 49-52