將數(shù)學建模的思想融入高等數(shù)學的教學

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

2、入高等數(shù)學的教學模式的研究分析與評價,并對教學效果進行分析與評價,促使教師改變教學模式,從而提高學生的課堂學習效率和學生數(shù)學素養(yǎng),進而提高學生的整體綜合素質(zhì)。本文采用問卷調(diào)查、教學實踐研究、建立馬爾科夫教學評價模型分析等方法,結(jié)合高等數(shù)學教學大綱的要求,將數(shù)學建模的思想融入高等數(shù)學教學,并通過課堂教學的實踐,使建模思想和數(shù)學理論有機的結(jié)合。將建模思想融入高等數(shù)學教學,為正在進行的高等學校教育教學改革提供了新的思路和方法,與此同時,本人根據(jù)教學改革的需要,對實施教學改革的班級和對照班進行了相應的教學效果分析和評價。本文共分六個章節(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)學教學模式的基本思路。結(jié)合我校實際提出建模思想融入高等數(shù)學的教學設(shè)計。第三章:建模思想融入高等數(shù)學的教學的教學案例。第四章:建模思想融入高等數(shù)學的教學實踐。第五章:教學效果調(diào)查與評價。第六章:教學反思 【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; 建模思想; 基本思路

13、; 教學設(shè)計; 教學實踐 【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)學課程發(fā)展的歷史沿革 10     

14、    1.2 國內(nèi)外利用數(shù)學建模教學的背景與狀況分析 10-11     2 高等數(shù)學的教學目標 11-13         2.1 高等數(shù)學的總體目標 11         2.2 我校（河北北方學院）高等數(shù)學課程的教學目標 11-13     3 在我校高職高專高等數(shù)學教學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)學教學的必要性 13-14         3.2 建模思想融入高等數(shù)學教學的可行性 14-15     4 相關(guān)研究綜述與現(xiàn)狀 15-19         4.1 對數(shù)學建模理論的研究 15-17         4.2 將數(shù)學建模思想融入數(shù)學主干課程的研究 17-19 第二章 將建模思想融

16、入高等數(shù)學教學的基本思路 19-32     1 實驗目的與研究的問題 19-20     2 數(shù)學建模融入到高等數(shù)學教學中的方法 20-21         2.1 弄清、搞透概念的意義 20         2.2 加深、推廣應用問題 20-21         2.3 高等數(shù)學中數(shù)學模型的案例教學 21  

17、60;  3 在高等數(shù)學中要全方位滲透數(shù)學思想方法 21     4 針對我校高等數(shù)學融入建模思想的教學設(shè)計 21-31         4.1 設(shè)計思想 21-22         4.2 教學設(shè)計的實施 22-31     5 教學實踐 31     6 教學反思 31-32 第三章 在高等數(shù)學教學中融入數(shù)學建模思想的案例 32-47  

18、60;  1 建模思想在概念、定義教學中的融入 32-38         1.1 導數(shù)概念的引入 32-35         1.2 定積分定義的教學 35-38     2 建模思想在定理應用教學中的融入 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 運用建模思想分析解決實際應用問題 41-47         3.1 貸款購房函數(shù)的應用 41-42         3.2 投資費用問題級數(shù)的應用 42-45         3.3 電學問題微分方程的應用 45-47 第四章 建模思想融入高等數(shù)學的教學實踐 47-52 

20、0;   1 教學實踐的實驗設(shè)計 47-49         1.1 實驗目的與假設(shè) 47         1.2 實驗對象的選取 47         1.3 實驗方法 47         1.4 干擾變量控制 47         1.5 實驗內(nèi)容分析分期付款模型 47-49     2 在數(shù)學教學中融入建模思想的主要困難和策略 49-52