【摘要】：幾何課程改革是數(shù)學(xué)課程改革中重要的一部分,也是歷來數(shù)學(xué)課程改革的焦點。在有關(guān)學(xué)生幾何概念的發(fā)展與學(xué)習(xí)的研究中,范希爾理論是最有影響力的理論之一。該理論的核心內(nèi)容有兩個:一是幾何思維水平的五個層次,二是與之相對應(yīng)的五個教學(xué)階段。該理論指出教學(xué)的組織和方法以及教材的選擇和使用都會影響學(xué)生的幾何思維水平發(fā)展。所以本研究從該理論出發(fā),結(jié)合新課程標(biāo)準(zhǔn),主要討論以下三個問題:一、參考新課程標(biāo)準(zhǔn),對湘教版幾何教材和新課標(biāo)就教材內(nèi)容進(jìn)行分析;二、結(jié)合范希爾幾何思維水平理論以及其他學(xué)者編制的類目分析表,制定了一份幾何教材類目分析表,對七、八、九年級的湘教版幾何教材的教材內(nèi)容進(jìn)行分析;三、在上述研究的基礎(chǔ)上,結(jié)合自己的教學(xué)實踐,就如何恰當(dāng)使用幾何教材能更好地促進(jìn)學(xué)生幾何思維的發(fā)展提出自己的思考;通過內(nèi)容分析和對比研究的研究方法,發(fā)現(xiàn)以下幾個結(jié)論:一、在對湘教版初中幾何教材和新課標(biāo)進(jìn)行吻合度分析時,在學(xué)習(xí)內(nèi)容方面,兩者所包含的知識模塊和要求掌握的知識點都基本相同;在學(xué)習(xí)目標(biāo)方面,數(shù)據(jù)分析顯示,兩者的要求基本相同,換句話說,湘教版幾何教材基本符合新課標(biāo)的要求。二、基于范希爾理論對湘教版幾何教材進(jìn)行分析時,數(shù)據(jù)分析顯示:首先,七、八、九年級的教材對學(xué)生思維的培訓(xùn)水平要求不同,七年級側(cè)重分析和非形式化演繹的培訓(xùn),占總體比重的80%左右;八年級則側(cè)重對分析、非形式化演繹以及形式化演繹的培訓(xùn),并且每個思維所占比重基本相同,各占30%;相反,由于教學(xué)目標(biāo)的要求,九年級側(cè)重了對分析的培訓(xùn),所占比重達(dá)59%,而對演繹思維的培訓(xùn)則相對較少;三、結(jié)合上述研究結(jié)果,筆者認(rèn)為,在教材使用過程中,應(yīng)該以培養(yǎng)學(xué)生的思維發(fā)展為主進(jìn)行教學(xué),具體過程包括:首先,立足課本,以核心概念和思想為主設(shè)計教學(xué);其次,研讀課本,以培養(yǎng)學(xué)生幾何思維展開教學(xué);最后,總結(jié)課本,以學(xué)生思維的發(fā)展為主評價教學(xué)。
[Abstract]:Geometry curriculum reform is an important part of mathematics curriculum reform, and has always been the focus of mathematics curriculum reform. Van hill theory is one of the most influential theories in the development and study of students' geometric concepts. There are two core contents of the theory: one is the five levels of geometric thinking level, the other is the corresponding five teaching stages. The theory points out that the organization and method of teaching as well as the choice and use of teaching materials will affect the development of students' level of geometric thinking. So this research starts from the theory, combines the new curriculum standard, mainly discusses the following three questions: first, referring to the new curriculum standard, the article analyzes the content of the teaching material of the Hunan edition geometry textbook and the new curriculum standard; Secondly, based on van hill's theory of geometric thinking level and the category analysis table compiled by other scholars, a category analysis table of geometric textbooks is made to analyze the contents of the teaching materials of the seventh, eighth and ninth grades of Hunan textbooks. Third, on the basis of the above research, combined with their own teaching practice, how to properly use the geometry teaching materials can better promote the development of students' geometric thinking. Through the research methods of content analysis and comparative study, the following conclusions are found: first, when analyzing the degree of coincidence between the geometry textbooks and the new curriculum standard of Hunan Education Edition, the contents of the study are analyzed. Both of them contain the same knowledge modules and the same knowledge points as required; In terms of learning objectives, the data analysis shows that the requirements of the two are basically the same, in other words, the geometry textbooks of the Xiang teaching edition basically meet the requirements of the new curriculum standard. Secondly, when analyzing the geometry teaching materials of Hunan Education Edition based on Van Hill's theory, the data analysis shows that: first, the training level of the seventh, eighth and ninth grades for students' thinking is different, and the seventh grade focuses on analysis and informal deductive training. Accounting for about 80% of the total; The eighth grade focuses on the training of analysis, non-formal deduction and formal deduction, and the proportion of each thought is basically the same, which accounts for 30000. On the contrary, due to the requirements of teaching objectives, Grade 9 focuses on the training of analysis, which accounts for 59%, while the training of deductive thinking is relatively less; Thirdly, combined with the above research results, the author thinks that in the course of using the textbook, we should train students' thinking development as the main teaching process, the concrete process includes: first, based on the textbook, design the teaching with the core concept and thought as the main; Secondly, we should study the textbooks to cultivate students' geometric thinking, and finally, summarize the textbooks and evaluate the teaching mainly by the development of students' thinking.
【學(xué)位授予單位】：湖南科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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