本文關(guān)鍵詞： 范希爾幾何思維水平 SOLO分類(lèi)理論 幾何證明 九年級(jí)學(xué)生　出處：《廣州大學(xué)》2016年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：在新課程改革的背景下,幾何課程在編排與設(shè)置上發(fā)生了許多變化,但幾何教學(xué)問(wèn)題并沒(méi)有因?yàn)閹缀握n程的改革而減少,不少數(shù)學(xué)教師在教學(xué)中發(fā)現(xiàn),有些學(xué)生對(duì)幾何知識(shí)點(diǎn)的理解不存在認(rèn)知障礙,但在解答證明題時(shí)卻無(wú)法準(zhǔn)確作答,這反映出學(xué)生的幾何認(rèn)知結(jié)構(gòu)向思維結(jié)構(gòu)的轉(zhuǎn)化出現(xiàn)障礙,即學(xué)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(lèi)理論為基礎(chǔ),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(guān)聯(lián)證明,水平4-邏輯證明,水平5-優(yōu)化證明,然后結(jié)合初中教材與《課程標(biāo)準(zhǔn)(2011版)》編制了幾何證明水平測(cè)試卷,制定了相應(yīng)的評(píng)價(jià)指標(biāo),并選取廣州市某中學(xué)191名九年級(jí)學(xué)生作為研究樣本,通過(guò)對(duì)相關(guān)測(cè)試的數(shù)據(jù)統(tǒng)計(jì)分析,不僅探討了九年級(jí)學(xué)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(jí)學(xué)生的幾何思維水平與證明水平的相關(guān)性、幾何證明水平與學(xué)業(yè)成績(jī)的關(guān)聯(lián)性。主要結(jié)論有:1.12%的學(xué)生的幾何思維處于水平三以下,80%以上的學(xué)生的幾何思維達(dá)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(xué)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(méi)有顯著差異。2.16%的學(xué)生仍停留在低幾何證明水平階段,32%的學(xué)生處于中幾何證明水平階段,超過(guò)50%的學(xué)生達(dá)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(méi)有顯著差異。3.在幾何思維水平與幾何證明水平的關(guān)聯(lián)對(duì)比上,兩者具有一定的相關(guān)性,不同的范希爾幾何思維水平對(duì)應(yīng)著若干個(gè)不同的幾何證明水平,并可按一定的比例轉(zhuǎn)換成相應(yīng)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(qiáng)正相關(guān)性,兩者之間的Spearman相關(guān)系數(shù)為0.822,幾何證明水平與“一模成績(jī)”、中考成績(jī)有強(qiáng)正相關(guān)性,它們之間的Spearman兩兩相關(guān)系數(shù)分別為0.937、0.956。以此研究結(jié)論為基礎(chǔ),筆者通過(guò)對(duì)不同幾何證明水平的學(xué)生進(jìn)行認(rèn)知分析,提出幾何證明水平的層級(jí)結(jié)構(gòu)與相應(yīng)特點(diǎn),并對(duì)不同幾何證明水平的學(xué)生提出相應(yīng)的教學(xué)建議如下:1.低幾何證明水平學(xué)生應(yīng)加強(qiáng)閱讀與識(shí)圖訓(xùn)練,教師在課堂上應(yīng)有詳細(xì)板書(shū),讓學(xué)生模仿學(xué)習(xí);2.中幾何證明水平學(xué)生可采用思維導(dǎo)圖的方式,讓學(xué)生寫(xiě)證明的思路分析,從而將知識(shí)加工成有聯(lián)系的結(jié)構(gòu)網(wǎng);3.高幾何證明水平學(xué)生要注意幾何學(xué)習(xí)方法的歸納與總結(jié),教師應(yīng)進(jìn)行針對(duì)性指導(dǎo),并鼓勵(lì)在解決原問(wèn)題后提出新問(wèn)題。本課題旨在為幾何課程的改革、教材的編寫(xiě)和教師的教學(xué)提供有價(jià)值的參考依據(jù),促使廣大教師在教學(xué)實(shí)踐中,能更加科學(xué)、有效地運(yùn)用現(xiàn)代教育理念,組織并完善課堂教學(xué)。
[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(xué)位授予單位】：廣州大學(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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