【摘要】：概率是數(shù)學(xué)課程中的一個(gè)重要的模塊,它廣泛運(yùn)用于航天、醫(yī)學(xué)、農(nóng)業(yè)等多個(gè)領(lǐng)域,對(duì)社會(huì)的發(fā)展有著不可忽視的作用。學(xué)生對(duì)概率的學(xué)習(xí)很大程度上取決于教師概率知識(shí)系統(tǒng)的完善程度。本文旨在探討數(shù)學(xué)師范生對(duì)高中概率概念的認(rèn)知水平,通過(guò)調(diào)查找出師范生認(rèn)知現(xiàn)狀及存在的主要問(wèn)題,并提出具有針對(duì)性的建議。在大量文獻(xiàn)分析的基礎(chǔ)上確定本文測(cè)試的內(nèi)容為高中概率的三種定義,即:統(tǒng)計(jì)定義、古典概型、幾何概型,并對(duì)相關(guān)概念進(jìn)行了明確的界定。研究的主體部分為以下四步:第一步編制預(yù)測(cè)卷,測(cè)試試卷的可行性;第二步制成正式測(cè)試卷,并對(duì)204名大三的數(shù)學(xué)師范生進(jìn)行測(cè)試;第三步用SOLO分析法對(duì)試卷的回答進(jìn)行水平劃分,并統(tǒng)計(jì)結(jié)果;第四步進(jìn)行個(gè)案研究。測(cè)試對(duì)象是西華師范大學(xué)和樂(lè)山師范學(xué)院的部分大三學(xué)生。測(cè)試結(jié)果分別在第四章、第五章、第六章進(jìn)行分析和總結(jié),在第七章對(duì)幾份具有代表性的測(cè)試卷作個(gè)案研究,并在第八章展示研究結(jié)論。研究表明:針對(duì)于樣本,師范生對(duì)古典概型的總體認(rèn)知水平較高,其次是幾何概型,而對(duì)于統(tǒng)計(jì)定義的認(rèn)知水平則相對(duì)偏低。存在的主要問(wèn)題:對(duì)概率和頻率的理解模糊不清;混淆古典概型與幾何概型;重運(yùn)算,輕理解;對(duì)隨機(jī)事件、基本事件等基本概念的理解還停留在中學(xué)階段;數(shù)形結(jié)合思維能力不足,數(shù)學(xué)知識(shí)板塊之間的聯(lián)系不夠緊密。最后,基于研究結(jié)論提出若干建議,并得出了師范生概率概念認(rèn)知框架。
[Abstract]:Probability is an important module in mathematics curriculum. It is widely used in many fields, such as aerospace, medicine, agriculture and so on. It plays an important role in the development of society. Students' learning of probability depends to a great extent on the perfection of teacher's probabilistic knowledge system. The purpose of this paper is to probe into the cognition level of mathematics normal students to the concept of high school probability, to find out the cognitive status quo and the main problems of the normal school students through the investigation, and to put forward some pertinent suggestions. On the basis of a lot of literature analysis, it is determined that the contents of this paper are three definitions of high school probability, that is, statistical definition, classical probability type, geometric probability type, and the related concepts are clearly defined. The main part of the study consists of the following four steps: the first step is to compile the forecast paper to test the feasibility of the test paper, the second step is to make the formal test paper, and to test 204 math normal students in junior high school. The third step uses the SOLO analysis method to divide the answer level of the test paper and the statistical result; the fourth step carries on the case study. The subjects are some junior students of Xihua normal University and Leshan normal College. The test results are analyzed and summarized in chapter 4, chapter 5 and chapter 6 respectively. In chapter 7, some representative test papers are studied, and the conclusions are shown in chapter 8. The results show that normal students have a higher overall cognitive level of classical probability type, followed by geometric probability type, and relatively low level of cognition about statistical definition. The main problems are: vague understanding of probability and frequency; confusion between classical probability and geometric probability; heavy operation, light understanding; understanding of basic concepts such as random events and basic events are still in the middle school stage; The combination of number and form thinking ability is not enough, mathematical knowledge between the plate is not close enough. Finally, some suggestions are put forward based on the conclusions of the study, and the conceptual cognitive framework of normal school students' probability is obtained.
【學(xué)位授予單位】：西華師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6;G652.4

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