【摘要】：發(fā)展學生的六大核心素養(yǎng)與數(shù)學核心素養(yǎng)對學生理解性學習提出了更高的要求.對數(shù)作為高中數(shù)學課程的基本概念,是進一步學習數(shù)學的基礎,其難度不大,卻是學生頻繁出現(xiàn)問題的地方.本文主要的研究問題是刻畫高一學生關于對數(shù)及對數(shù)運算的理解水平,主要進行了三個方面的工作.一是通過文獻分析法構建了高一學生關于對數(shù)及其運算的理解模型:高一學生關于對數(shù)及其運算的理解可分為知其然理解、所以然理解和本然性理解.知其然理解分為知定義性質(zhì)、知運算性質(zhì)、知換底公式,所以然理解分為解釋定義、性質(zhì)公式證明、性質(zhì)公式推廣,本然性理解分為發(fā)明本質(zhì)和數(shù)學思想.其中知定義性質(zhì)與發(fā)明本質(zhì)不相關,其他理解類別之間均為正相關.二是根據(jù)構建的理解模型制作調(diào)查問卷,對蕪湖市第十二中學高一年級學生進行調(diào)查,運用SPSS20.0分析調(diào)查數(shù)據(jù),發(fā)現(xiàn)問卷內(nèi)部一致性系數(shù)為0.806,Spearman-Brown分半信度為0.813,說明問卷具有良好的信度.三是通過問卷調(diào)查法和個案訪談法比較不同性別、不同數(shù)學成績的學生關于對數(shù)及其運算理解水平的差異性.發(fā)現(xiàn)男女生在知其然理解和本然性理解上沒有差異,在所以然理解上男生優(yōu)于女生,具體的,男生在性質(zhì)公式證明與推廣及數(shù)學思想領悟上比女生強,在解釋定義上比女生弱;尖子生、中等生和學困生在不同理解維度上均有顯著差異,且成績越好理解水平越好,但中等生和學困生在“知運算性質(zhì)”上無差異,尖子生和中等生在“知換底公式”上無差異,說明不同數(shù)學成績的學生都存在一定程度的機械記憶現(xiàn)象.
[Abstract]:The development of students' six core qualities and mathematics core qualities puts forward higher requirements for students'understanding learning. Logarithm, as the basic concept of mathematics curriculum in senior high school, is the basis of further learning mathematics. The main research problem of this paper is to describe the level of understanding of logarithmic and logarithmic operations in Senior one students. The first is to construct the understanding model of logarithm and its operation by literature analysis. The understanding of logarithm and its operation can be divided into three parts: the understanding of knowledge, the understanding of reason and the understanding of nature. The understanding of knowing is divided into the nature of knowledge definition, the property of knowing operation, the formula of knowing changing the background, the interpretation definition, the proof of nature formula, the generalization of nature formula, and the understanding of nature is divided into the essence of invention and the thought of mathematics. Among them, the nature of definition is not related to the nature of invention, and the other understanding categories are all positively related. Secondly, according to the constructed understanding model, the questionnaire is made to the first grade students of Wuhu No. 12 Middle School, and the data of the survey are analyzed by SPSS20.0. It is found that the internal consistency coefficient of the questionnaire is 0.806 Spearman-Brown split-half reliability is 0.813, which indicates that the questionnaire has good reliability. The third is to compare the difference of students' understanding of logarithm and operation among different genders and different mathematics achievement by questionnaire and case interview. It is found that there is no difference between male and female students in their understanding of nature and nature, and that boys are better than girls in terms of understanding and understanding. Specifically, boys are stronger than girls in proving and popularizing their nature formulas and understanding mathematical ideas, and in terms of interpretation and definition, they are weaker than girls. There were significant differences among top students, middle students and students with learning difficulties in different understanding dimensions, and the better the achievement, the better the understanding level, but there was no difference between the middle students and the students with learning difficulties in the nature of knowledge and operation. There is no difference between the top students and the middle students in the formula of "knowing and changing the bottom", which indicates that the students with different mathematics scores all have some mechanical memory phenomenon.
【學位授予單位】：安徽師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：G633.6

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