本文選題：新定義型問題 + 解題困難�。� 參考：《山東師范大學》2016年碩士論文

【摘要】：新定義型問題是“以能力立意”的問題,它主要考查的是答題者的創(chuàng)新意識和抽象概括能力等多方面的數(shù)學素質(zhì)。新定義型問題的內(nèi)容不同于高中數(shù)學教材的內(nèi)容,它給學生設(shè)置全新的情景,讓學生在一個公平的環(huán)境里現(xiàn)學現(xiàn)用,充分展示學生的學習能力。但在實際教學中,不少學生在解決新定義型問題時困難重重,例如不理解題目給出的新定義或新信息、不能選擇合適的解法以及無法進行必要的運算等。因此,找出學生解決新定義型問題的真正困難,挖掘出產(chǎn)生這些困難的原因具有重要意義。本文通過口語報告法、觀察法與訪談法等研究方法對淄博、濟南和青島的40名解決新定義型問題有明顯困難的學生進行調(diào)查,旨在找出學生解決新定義型問題困難的真正原因,并根據(jù)這些原因找出有針對性的教學策略,幫助學生克服困難,提高他們的數(shù)學學習能力。本文利用口語報告法看出高中生在解決新定義型問題過程中的困難主要在以下幾個方面:快速而正確地理解題目的各種條件,包括示例、算法、公式、符號、概念等;正確提取解題所需的基礎(chǔ)知識,包括公式、概念等;仔細審題和挖掘題目隱含條件;熟練進行解題過程中必要的化簡變形;正確選擇解決新定義型問題的思想方法;形成條理的解答新定義型問題的思路;正確進行解題過程中的數(shù)學運算。其中,理解題目的各種條件是當前學生最大的困難。針對上述困難,進一步結(jié)合觀察法和訪談法得出高中生解決新定義型問題存在困難的主要原因有:學生在閱讀新定義型問題的題干收集信息的時候容易馬虎大意,遺漏關(guān)鍵內(nèi)容;學生在根據(jù)從新定義型問題中收集到的信息里提取解題所需信息的時候容易受到干擾,出現(xiàn)理解偏差;學生在對提取到的解決新定義型問題所需的信息進行整合的過程中,容易受到平時對知識學習情況的影響;學生在分析新定義型問題的時候容易以偏概全,表現(xiàn)出自學能力有待提高;學生在解答新定義型問題的過程中缺少技巧,易受思維定勢的影響。在教學方面,針對高中生解決新定義型問題存在困難的主要原因提出以下教學建議:在講解新定義型問題時,教師需要指導學生從背景文字中收集信息,標記關(guān)鍵信息的同時排除干擾信息;教師引導學生在分析問題的過程中要整體看待題目條件選擇解題方法,從中獲取自學技巧;在講解新定義型問題后,教師應(yīng)對問題進行必要的變式,讓學生體會抓住問題的本質(zhì)的重要性;為了提高學生解決新定義型問題的能力,教師需要傳授給學生正確的豐富的知識,指導他們有計劃地復(fù)習知識,牢固地保持所學知識,并能靈活地加以應(yīng)用;在平時的教學中,教師既要注意訓練學生思維的相對定向,又要訓練其思維的靈活多樣;教師不僅需要訓練學生從多種角度解決問題,提倡一題多解,還需要引導學生注意對同一問題的不同解決方法進行比較,仔細觀察解法的區(qū)別、優(yōu)缺點和合理程度,掌握解法的針對性;教師每天給學生提供一道新定義型問題作為作業(yè),適當訓練,又不增加訓練負擔;教師需要引導學生進行積極的反思。
[Abstract]:The new definition problem is the question of "ability to stand up". It mainly examines the mathematical quality of the respondent's creative consciousness and abstract generalization ability. The content of the new definition type is different from the content of the high school mathematics teaching material. It sets a new scene for the students to make the students learn to use in a fair environment and to make full use of them. But in the actual teaching, many students are difficult to solve the new definition problem, such as not understanding the new definition or new information given by the subject, not choosing the appropriate solution and unable to carry out the necessary operation. Therefore, to find out the real difficulties for the students to solve the new definition problems and excavate this Some of the reasons for the difficulties are of great significance. In this paper, 40 students in Zibo, Ji'nan and Qingdao who have obvious difficulties in solving new definition problems have been investigated by oral reporting, observation and interview. The purpose of this study is to find out the true reasons for students to solve the problems of newly defined problems and to find out the pertinence according to these reasons. Teaching strategies to help students overcome difficulties and improve their ability to learn mathematics. This paper uses oral report to see that the difficulties in solving new definition problems are mainly in the following aspects: fast and correct understanding of the various conditions of the subject, including examples, algorithms, formulas, symbols, concepts and so on; and the correct extraction of problems. The necessary basic knowledge, including the formula, the concept, and so on; careful examination and excavation of the hidden condition of the subject; the necessary simplification of the deformation in the process of solving the problem; the correct choice of the thought and method of solving the newly defined problem; the formation of a rational solution to the new definition of the problem; the correct calculation of the mathematical operation in the process of solving the problem. Among them, the understanding of the subject. Various conditions are the most difficult for the students at present. In view of the above difficulties, the main reasons for the difficulties in solving new definition problems are: the students are easy to be careless and omit the key content when they are reading the new definition problem to collect information; students are in the new definition. When the information collected in the type problem is extracted, it is easy to be disturbed when the information is needed to solve the problem. In the process of integrating the information needed to solve the newly defined problem, the students are easily affected by the usual knowledge learning situation, and the students are apt to be biased when analyzing the newly defined problems. All of them show that self-learning ability needs to be improved; students are lacking in skills in solving new definition problems and are vulnerable to the influence of thinking. In teaching, the following suggestions are put forward for high school students to solve new definition problems: teachers need to guide students from Bei Jingwen when explaining new definition problems. In the word, the information is collected, the key information is marked and the interference information is excluded. The teacher guides the students to choose the problem solving method as a whole in the process of analyzing the problems and obtain the self-study skills from it. After explaining the new definition, the teachers should make the necessary changes in dealing with the problems so that the students can grasp the importance of the essence of the problem. In order to improve students' ability to solve newly defined problems, teachers need to impart correct and rich knowledge to their students, guide them to review knowledge in a planned way, maintain their knowledge firmly, and apply them flexibly. In ordinary teaching, teachers should pay attention to training students' relative orientation of thinking and training their thinking. The teacher not only needs to train the students to solve the problems from a variety of angles, but also needs to guide the students to compare the different solutions of the same problem, carefully observe the difference of the solution, the advantages and disadvantages and the reasonable degree, and grasp the pertinence of the solution; the teachers provide a new definition problem to the students every day. For homework, proper training and no increase of training burden; teachers need to guide students to reflect positively.

【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：G633.6

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