【摘要】：現(xiàn)代學校教育是通過各個學科的教學來實現(xiàn)對整體人的培養(yǎng)的,每個學科都有自己的核心任務。數(shù)學教育的職責使命是培養(yǎng)和造就有探索能力的人才。探索能力不僅包括分析問題和解決問題的能力,也包括發(fā)現(xiàn)問題的能力,而發(fā)現(xiàn)問題的能力是探索能力的最關鍵要素。歸納、類比等歸納邏輯推理思維都是發(fā)現(xiàn)問題的基本手段,這種數(shù)學核心素養(yǎng)強調(diào)數(shù)學教育不再僅僅是灌輸、傳承,而是更加側(cè)重于啟發(fā)以及對數(shù)學思想方法的理解。在過去很長的一段時間里,中國基礎教育階段的數(shù)學教育重視演繹推理,教授訓練學生驗證掌握已有的完善的數(shù)學結(jié)論,而同時卻忽略了歸納推理(1),數(shù)學教育的偏失和不完善,其結(jié)果必然弱化數(shù)學學科的育人價值,影響學生創(chuàng)造力的發(fā)展。本文圍繞初中數(shù)學中歸納推理實證研究這個核心,具體研究如下問題:第一,采用文本分析法,借助文獻梳理演繹推理與歸納推理的關系,同時梳理歸納推理國內(nèi)外研究的現(xiàn)狀,在分析國內(nèi)小學和高中數(shù)學中歸納推理研究結(jié)論的基礎上,探索初中數(shù)學中的歸納推理和演繹推理的關系。第二,通過文本分析的方法,對初中教學大綱和數(shù)學課程標準中歸納推理內(nèi)容以及北師大版與人教版教材歸納推理內(nèi)容呈現(xiàn)分別進行量化比較研究。第三,對師生的歸納推理能力以及師生對歸納推理的認同感和課堂教學現(xiàn)狀進行調(diào)查研究,第四,對調(diào)查研究結(jié)果進行歸因分析。通過研究,主要有以下發(fā)現(xiàn):第一,初中數(shù)學中的歸納推理和演繹推理應該是雙螺旋式發(fā)展。第二,通過對兩個版本數(shù)學教材中與歸納推理能力培養(yǎng)的相關內(nèi)容呈現(xiàn)的量化對比研究,并結(jié)合教學實踐發(fā)現(xiàn)兩個版本教材關于歸納推理呈現(xiàn)沒有達到《義務教育課程標準(2011年版)》(以下簡稱《標準(2011年版)》)的要求。第三,選取北京市、黑龍江省十所學校初中階段學生1446人和在職初中數(shù)學教師212人,運用了試題測試法和問卷調(diào)查法。通過對初中數(shù)學教師和學生完成的調(diào)查問卷、測試題進行的統(tǒng)計分析結(jié)果看,師生對歸納推理的理解不清晰,對《標準(2011年版)》的要求模糊。部分老師和學生的歸納推理能力比較薄弱,亟待提高。第四,通過聚焦訪談,87%初中數(shù)學老師雖然認同歸納推理的重要價值,但是在教學中不知道如何操作,導致在初中課堂教與學過程中目標不明確效果不好。綜合上述情況,呼吁教材編寫部門再修改教材時嚴格按著《標準(2011年版)》對歸納推理的要求,并能提供更多更鮮活的案例供老師們學習參考。也建議教育行政部門和學校真正重視初中階段學生歸納推理能力的培養(yǎng)。本文對調(diào)查研究結(jié)果進行了歸因分析,也從多個角度提供了一些案例,希望引起更多的討論和研究。
[Abstract]:Modern school education realizes the cultivation of the whole person through the teaching of each subject, and each subject has its own core task. The duty mission of mathematics education is to cultivate and bring up people with the ability to explore. The ability to explore includes not only the ability to analyze and solve problems, but also the ability to find problems, and the ability to discover problems is the most important element of the ability to explore. Induction, analogy and other inductive logical reasoning thinking are the basic means to find problems. This kind of mathematics core accomplishment emphasizes that mathematics education is no longer just indoctrination, inheritance, but more emphasis on inspiration and understanding of mathematical thinking methods. For a long time in the past, mathematics education in basic education in China attached importance to deductive reasoning, and the professors trained students to verify and master the existing mathematical conclusions, while neglecting inductive reasoning (1). The deviation and imperfection of mathematics education will inevitably weaken the educational value of mathematics subject and affect the development of students' creativity. This paper focuses on the core of the empirical research on inductive reasoning in junior high school mathematics, and studies the following problems: first, using text analysis, combing the relationship between deductive reasoning and inductive reasoning with the help of literature. At the same time, combing the current situation of inductive reasoning at home and abroad, on the basis of analyzing the research conclusions of inductive reasoning in primary and high school mathematics in China, this paper explores the relationship between inductive reasoning and deductive reasoning in junior high school mathematics. Secondly, through the method of text analysis, the contents of inductive reasoning in middle school syllabus and mathematics curriculum standard, and the presentation of inductive reasoning content in Peking normal University edition and human education edition are studied respectively. Thirdly, the author investigates the ability of inductive reasoning of teachers and students, the identity of teachers and students to inductive reasoning and the present situation of classroom teaching. Fourthly, the attribution analysis of the investigation results is carried out. The main findings are as follows: first, inductive reasoning and deductive reasoning in junior high school mathematics should be double spiral development. Second, through the quantitative comparative study of the two versions of mathematics textbooks and the related contents of the training of inductive reasoning ability, Combined with teaching practice, it is found that the presentation of inductive reasoning does not meet the requirements of "compulsory Education Curriculum Standard (2011 Edition) > (hereinafter referred to as" Standard (2011 Edition) >). Thirdly, 1446 junior middle school students and 212 in-service junior high school mathematics teachers in Beijing, Heilongjiang Province, were selected, and the methods of test and questionnaire survey were used. Through the questionnaire of mathematics teachers and students in junior high school and the statistical analysis of the test questions, we can see that the teachers and students do not have a clear understanding of inductive reasoning, and the requirements of < Standard (2011) > are vague. The inductive reasoning ability of some teachers and students is weak and needs to be improved. Fourth, through focused interviews, 87% of junior high school mathematics teachers agree with the important value of inductive reasoning, but do not know how to operate in the teaching, resulting in the middle school classroom teaching and learning process is not clear effect. In the light of the above situation, the author calls upon the textbook compiling department to strictly follow the requirements of inductive reasoning when revising the textbook according to the Standard (2011 Edition), and can provide more and more vivid cases for teachers to learn for reference. It is also suggested that the educational administration and schools should really pay attention to the cultivation of students' inductive reasoning ability in junior middle school. In this paper, the attribution analysis of the research results is made, and some cases are provided from many angles, hoping to arouse more discussion and research.
【學位授予單位】：東北師范大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：G633.6
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本文編號：2297276