本文關鍵詞： 范希爾幾何思維水平 SOLO分類理論 幾何證明 九年級學生　出處：《廣州大學》2016年碩士論文　論文類型：學位論文

【摘要】：在新課程改革的背景下,幾何課程在編排與設置上發(fā)生了許多變化,但幾何教學問題并沒有因為幾何課程的改革而減少,不少數(shù)學教師在教學中發(fā)現(xiàn),有些學生對幾何知識點的理解不存在認知障礙,但在解答證明題時卻無法準確作答,這反映出學生的幾何認知結構向思維結構的轉化出現(xiàn)障礙,即學生的幾何思維水平與其證明水平并不匹配。本研究采用了以定量為主的研究方法,以范希爾理論和SOLO分類理論為基礎,首次提出幾何證明水平層次可分為:水平1-直觀證明,水平2-描述證明,水平3-關聯(lián)證明,水平4-邏輯證明,水平5-優(yōu)化證明,然后結合初中教材與《課程標準(2011版)》編制了幾何證明水平測試卷,制定了相應的評價指標,并選取廣州市某中學191名九年級學生作為研究樣本,通過對相關測試的數(shù)據(jù)統(tǒng)計分析,不僅探討了九年級學生在幾何思維水平、幾何證明水平的分布情形,而且也探究九年級學生的幾何思維水平與證明水平的相關性、幾何證明水平與學業(yè)成績的關聯(lián)性。主要結論有:1.12%的學生的幾何思維處于水平三以下,80%以上的學生的幾何思維達到了水平三甚至更高,整體的分布并不均勻,水平一至水平四分別為3.8%、8.2%、66.5%、14.3%,有7.1%的學生是違反范希爾理論的。另外,男女生在幾何思維水平的發(fā)展上沒有顯著差異。2.16%的學生仍停留在低幾何證明水平階段,32%的學生處于中幾何證明水平階段,超過50%的學生達到高幾何證明水平階段,整體的分布不均勻,層次一至層次五分別為3.3%、12.64%、32.42%、42.86%、8.79%。另外,男女生在幾何證明水平的發(fā)展上沒有顯著差異。3.在幾何思維水平與幾何證明水平的關聯(lián)對比上,兩者具有一定的相關性,不同的范希爾幾何思維水平對應著若干個不同的幾何證明水平,并可按一定的比例轉換成相應的幾何證明水平層次。4.幾何思維水平與幾何證明水平有強正相關性,兩者之間的Spearman相關系數(shù)為0.822,幾何證明水平與“一模成績”、中考成績有強正相關性,它們之間的Spearman兩兩相關系數(shù)分別為0.937、0.956。以此研究結論為基礎,筆者通過對不同幾何證明水平的學生進行認知分析,提出幾何證明水平的層級結構與相應特點,并對不同幾何證明水平的學生提出相應的教學建議如下:1.低幾何證明水平學生應加強閱讀與識圖訓練,教師在課堂上應有詳細板書,讓學生模仿學習;2.中幾何證明水平學生可采用思維導圖的方式,讓學生寫證明的思路分析,從而將知識加工成有聯(lián)系的結構網(wǎng);3.高幾何證明水平學生要注意幾何學習方法的歸納與總結,教師應進行針對性指導,并鼓勵在解決原問題后提出新問題。本課題旨在為幾何課程的改革、教材的編寫和教師的教學提供有價值的參考依據(jù),促使廣大教師在教學實踐中,能更加科學、有效地運用現(xiàn)代教育理念,組織并完善課堂教學。
[Abstract]:Under the background of the new curriculum reform, many changes have taken place in the arrangement and setting of the geometry curriculum, but the problems in geometry teaching have not been reduced because of the reform of the geometry curriculum. Many mathematics teachers have found out in the course of teaching. Some students do not have cognitive barriers to the understanding of geometric knowledge points, but they can not answer the proof questions accurately, which reflects the obstacles in the transformation of students' geometry cognitive structure to thinking structure. That is, the level of students' geometric thinking does not match their level of proof. This study adopts a quantitative approach, based on Van Hell's theory and SOLO's classification theory. For the first time, the level level of geometric proof can be divided into: level 1-visual proof, horizontal 2-description proof, horizontal 3-correlation proof, horizontal 4-logic proof, horizontal 5-optimization proof. Then combined with the junior high school textbooks and "Curriculum Standards 2011 Edition)" compiled a geometric proof level test paper, and formulated the corresponding evaluation indicators. With 191 ninth grade students in a middle school in Guangzhou as the research sample, the distribution of geometric thinking level and geometric proof level of ninth grade students is not only discussed by statistical analysis of relevant test data. It also explores the correlation between the level of geometric thinking and the level of proof and the correlation between the level of geometric proof and academic achievement. The main conclusion is that 1.12% of the students are below the level of three levels of geometric thinking. The geometric thinking of more than 80% students reached the level of three or more, the overall distribution is not even, the level of one to level four is 3.88.2or 66.5%. In addition, there is no significant difference between boys and girls in the development of geometric thinking level. 2.16% of the students are still at the stage of low geometric proof level. 32% of the students were in the level of middle geometric proof, and more than 50% of the students had reached the stage of high geometric proof, and the distribution of the whole was not even. 32.42 / 42.86 / 8.79. in addition, there is no significant difference in the development of the level of geometric proof between male and female students. (3) there is no significant difference between the level of geometric thinking and the level of geometric proof. There is a certain correlation between them. Different levels of van hill's geometric thinking correspond to several different levels of geometric proof. The geometric thinking level has strong positive correlation with geometric proof level, and the Spearman correlation coefficient between them is 0.822. There is a strong positive correlation between the level of geometric proof and the "score of one mode", and the correlation coefficient of Spearman between them is 0.937 / 0.956 respectively, which is based on the conclusion of the study. Through the cognitive analysis of students with different levels of geometric proof, the author puts forward the hierarchical structure and corresponding characteristics of the level of geometric proof. The teaching suggestions for students with different levels of geometric proof are as follows: 1.The students with low level of geometric proof should strengthen the training of reading and reading map, and teachers should have detailed blackboard writing in class to allow students to imitate learning; 2. The students can use the way of thinking map to write the thought analysis of proof, so that the knowledge can be processed into a network of related structures. 3. Students with high level of geometric proof should pay attention to the induction and summary of geometric learning methods, and teachers should give targeted guidance and encourage them to raise new problems after solving the original problems. The purpose of this project is to reform the geometry curriculum. The compilation of teaching materials and the teaching of teachers can provide valuable reference for teachers to be more scientific and effective in their teaching practice and to organize and perfect classroom teaching.
【學位授予單位】：廣州大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：G633.6

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