【摘要】：算理知識是在解決數(shù)學(xué)問題的過程中,技能操作的程序和步驟背后的原理與依據(jù)。義務(wù)教育數(shù)學(xué)課程標準(2011年版)明確提出:課程內(nèi)容不僅包括數(shù)學(xué)結(jié)果,也包括數(shù)學(xué)結(jié)果的形成過程和蘊含的數(shù)學(xué)思想方法,它的選擇要有利于學(xué)生體驗與理解、思考與探索,從而培養(yǎng)學(xué)生問題解決的能力。研究主要從兩方面進行:首先,利用文本分析法對新課標小學(xué)數(shù)學(xué)教科書(2012年版)中的算理知識進行系統(tǒng)化分析;其次,以小學(xué)數(shù)學(xué)教師為研究對象,通過實證研究的方法調(diào)查其對算理知識掌握程度,同時對影響小學(xué)數(shù)學(xué)教師算理知識掌握程度的因素進行分析。根據(jù)研究,將小學(xué)數(shù)學(xué)教科書中的算理知識按呈現(xiàn)方式及呈現(xiàn)層次分類。呈現(xiàn)方式分別為教科書正文呈現(xiàn)、閱讀材料呈現(xiàn)與習題呈現(xiàn)三類,呈現(xiàn)層次分別為教科書中全部呈現(xiàn)、部分呈現(xiàn)與未呈現(xiàn)三類,分別對每一類進行具體分析。依照此分類及各維度知識的比例編寫測試卷,對新疆烏魯木齊市47名小學(xué)數(shù)學(xué)教師進行測試,對教師的掌握程度及影響因素進行分析。研究的主要結(jié)果為以下幾點。(1)對教科書中的算理知識進行梳理分類,用圖片的形式呈現(xiàn)教科書中的內(nèi)容,分析教科書中對算理的呈現(xiàn)形式。按照呈現(xiàn)層次對每類算理知識進行具體分析,得出算理的由來。(2)根據(jù)測試結(jié)果的統(tǒng)計,小學(xué)數(shù)學(xué)教師對算理知識的掌握程度并不理想,測試卷總平均分為55.57。按呈現(xiàn)方式分類時,在教科書閱讀材料中呈現(xiàn)的算理知識掌握程度最弱,在習題中呈現(xiàn)的算理知識掌握程度較好;按呈現(xiàn)層次分類時,教科書中部分呈現(xiàn)的算理知識掌握程度最弱,全部呈現(xiàn)及未呈現(xiàn)的算理知識掌握程度較好。(3)根據(jù)測試結(jié)果與個案分析,發(fā)現(xiàn)對小學(xué)數(shù)學(xué)教師算理知識掌握的影響因素分別為教科書中算理知識呈現(xiàn)形式、教師學(xué)歷、教齡、職稱及任教年級等。(4)教科書中算理知識呈現(xiàn)形式是影響教師算理知識掌握程度的主要因素。在教師學(xué)歷方面,大專學(xué)歷教師各部分算理知識平均得分均低于本科學(xué)歷教師。在教師教齡與職稱方面,隨著教齡與職稱的增長,測試卷平均分大體呈遞增趨勢。在任教年級方面,任教高年級段的教師得分明顯高于于其他教師。
[Abstract]:The knowledge of calculation is the principle and basis behind the procedures and steps of skill operation in the process of solving mathematical problems. The mathematics curriculum standard of compulsory education (2011 edition) clearly points out that the curriculum content includes not only the mathematics result, but also the forming process of the mathematics result and the mathematics thought method contained therein. The choice of the curriculum should be beneficial to the students' experience and understanding, thinking and exploration. So as to cultivate students' ability to solve problems. The research is mainly carried out from two aspects: first, the text analysis method is used to systematize the knowledge of calculation in the new curriculum standard primary school mathematics textbook (2012 edition); secondly, the primary school mathematics teachers are taken as the research objects. Through the method of empirical research, the author investigates the degree of mastery of mathematical knowledge, and analyzes the factors that affect the degree of mastery of mathematical knowledge of primary school mathematics teachers. According to the research, the mathematical knowledge in primary school mathematics textbooks is classified according to presentation mode and presentation level. The presentation methods are textbook text presentation, reading material presentation and exercise presentation, presentation levels are all presented in the textbook, partial presentation and non-presentation of three types, respectively, for each type of specific analysis. According to this classification and the proportion of knowledge in each dimension, 47 primary school mathematics teachers in Urumqi, Xinjiang were tested, and their mastering degree and influencing factors were analyzed. The main results are as follows: (1) sorting out and classifying the knowledge of calculation in textbooks, presenting the contents of textbooks in the form of pictures, and analyzing the forms of presentation of reasoning in textbooks. According to the level of presentation of each kind of knowledge of calculation specific analysis, the origin of reasoning. (2) according to the results of the test statistics, primary school mathematics teachers to master the degree of knowledge of calculation is not ideal, the average test paper is divided into 55.57. When classifying according to presentation, the degree of mastery of mathematical knowledge presented in textbook reading materials is the weakest, and the degree of mastery of mathematical knowledge presented in exercises is better; when classifying according to presentation level, Part of the textbook presents the weakest degree of knowledge in the knowledge of calculation, all presented and not presented, the degree of mastery of the knowledge of calculation is better. (3) according to the test results and case analysis, It is found that the factors influencing the mastery of mathematical knowledge in primary school mathematics teachers are the presentation form of mathematical knowledge in textbooks, teachers' educational background and teaching age. Professional title and teaching grade. (4) the form of knowledge presentation is the main factor that affects teachers' knowledge of calculation. In terms of teachers' qualifications, the average scores of each part of the teachers with junior college qualifications are lower than that of teachers with undergraduate degrees. In terms of teachers' teaching age and professional title, the average score of test paper increases with the increase of teaching age and professional title. In terms of teaching grade, the score of teachers in senior grades was significantly higher than that of other teachers.
【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G623.5

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