發(fā)布時(shí)間：2018-05-09 15:08

  本文選題：初中生 + 幾何證明��； 參考：《山東師范大學(xué)》2017年碩士論文

【摘要】：美國(guó)數(shù)學(xué)教師協(xié)會(huì)在《數(shù)學(xué)課程標(biāo)準(zhǔn)(2000年)》中首次提出了數(shù)學(xué)聯(lián)結(jié)能力,其“中介”的特質(zhì)可以很好地將學(xué)生頭腦中儲(chǔ)備的相關(guān)信息調(diào)配運(yùn)用起來。而目標(biāo)選擇性聯(lián)結(jié)能力是基于數(shù)學(xué)聯(lián)結(jié)的多向性和復(fù)雜性提出的,重在以問題目標(biāo)為導(dǎo)向進(jìn)行選擇性聯(lián)結(jié)。本文通過對(duì)數(shù)學(xué)聯(lián)結(jié)能力以及目標(biāo)選擇性聯(lián)結(jié)相關(guān)文獻(xiàn)的分析,在聯(lián)結(jié)主義、認(rèn)知主義以及相關(guān)數(shù)學(xué)教育心理學(xué)的基礎(chǔ)上,結(jié)合幾何證明的特點(diǎn),提出初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的概念,即初中生能以問題目標(biāo)為導(dǎo)向,聯(lián)結(jié)到數(shù)學(xué)學(xué)習(xí)中的相關(guān)的概念、命題、方法等,并積極主動(dòng)地作出正確、合理的篩選和加工,能監(jiān)控自己的選擇性聯(lián)結(jié)對(duì)證明過程產(chǎn)生的影響,并能對(duì)自己選擇性聯(lián)結(jié)行為進(jìn)行調(diào)節(jié)的一種個(gè)性心理特征。它是一種以解決幾何證明問題為特定任務(wù)的數(shù)學(xué)解題能力,既包括對(duì)幾何模塊學(xué)習(xí)中的知識(shí)進(jìn)行選擇聯(lián)結(jié)、重組加工等認(rèn)知成分,也包括對(duì)自己的目標(biāo)選擇性聯(lián)結(jié)的過程進(jìn)行計(jì)劃、監(jiān)控、調(diào)節(jié)等元認(rèn)知成分。本文通過對(duì)初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力進(jìn)行調(diào)查,了解初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力水平,以及目標(biāo)選擇性聯(lián)結(jié)對(duì)初中生幾何證明的影響,并據(jù)此提出培養(yǎng)初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的對(duì)策。本文的研究順序主要有以下幾點(diǎn):第一,確定研究方向。首先對(duì)目標(biāo)選擇性聯(lián)結(jié)等相關(guān)文獻(xiàn)進(jìn)行分析,得出相關(guān)研究成果,并確定研究的內(nèi)容。第二,建構(gòu)相關(guān)理論。根據(jù)相關(guān)心理學(xué)和數(shù)學(xué)教育心理學(xué)的理論建構(gòu)了幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的理論基礎(chǔ),并對(duì)其內(nèi)涵以及能力成分進(jìn)行界定。第三,設(shè)計(jì)調(diào)查并實(shí)施。本次調(diào)查以調(diào)查問卷和幾何證明測(cè)試題相結(jié)合的形式進(jìn)行調(diào)查。第四,得出調(diào)查結(jié)論。根據(jù)調(diào)查統(tǒng)計(jì)結(jié)果,得出初中生在幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的現(xiàn)狀和水平,以及對(duì)解決幾何證明問題的影響,并做出反思,提出培養(yǎng)幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的必要性。第五,提出培養(yǎng)策略。本文研究的結(jié)論主要有以下幾點(diǎn):第一,初中生在幾何證明中目標(biāo)選擇性聯(lián)結(jié)意識(shí)表現(xiàn)中等,兩級(jí)差異大。第二,在目標(biāo)選擇性聯(lián)結(jié)能力中,在聯(lián)結(jié)和目標(biāo)轉(zhuǎn)化中性別差異顯著,主要表現(xiàn)在女生比男生更盡可能地解讀題目已知信息和思考相關(guān)證明思路。另外,女生比男生更有目標(biāo)導(dǎo)向意識(shí)。第三,在解決幾何證明題的具體解題過程中,初中生目標(biāo)導(dǎo)向能力不足。主要體現(xiàn)在不能很好的以待證明的結(jié)論為導(dǎo)向,將待求證的結(jié)論轉(zhuǎn)化成結(jié)論等價(jià)鏈,縮小問題空間。同時(shí),初中生在幾何證明中目標(biāo)轉(zhuǎn)化的小步性和反思性方面表現(xiàn)欠佳,未能結(jié)合已知信息將結(jié)論等價(jià)鏈進(jìn)行小步論證,同時(shí)推理過程不嚴(yán)謹(jǐn),不能對(duì)證明過程合理驗(yàn)證。另外,不能及時(shí)對(duì)目標(biāo)轉(zhuǎn)化的方向進(jìn)行修正。第四,初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力對(duì)初中生在幾何證明測(cè)試題中的成績(jī)有顯著影響,尤其是對(duì)于難度越大的幾何證明題,初中生的目標(biāo)選擇性聯(lián)結(jié)能力越高,其在幾何證明測(cè)試題中的表現(xiàn)越好。最后,為加強(qiáng)初中生幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力,從幾何證明中目標(biāo)選擇性聯(lián)結(jié)能力的構(gòu)成成分角度提出相關(guān)培養(yǎng)對(duì)策。在知識(shí)聯(lián)結(jié)方面,構(gòu)建知識(shí)網(wǎng)絡(luò),夯實(shí)基礎(chǔ)知識(shí);積累基本解題經(jīng)驗(yàn),促進(jìn)知識(shí)遷移。在目標(biāo)轉(zhuǎn)化方面,培養(yǎng)目標(biāo)導(dǎo)向意識(shí),促進(jìn)逆推分析能力;構(gòu)建等價(jià)或半等價(jià)命題體系,促進(jìn)目標(biāo)轉(zhuǎn)化。在解題監(jiān)控方面,增強(qiáng)反思意識(shí),養(yǎng)成“推理有據(jù)”的習(xí)慣;加強(qiáng)解題監(jiān)控訓(xùn)練,提高解題監(jiān)控水平。
[Abstract]:The American Association for mathematics teachers first put forward the ability to connect mathematics in the mathematics curriculum standard (2000). Its "intermediary" characteristics can well apply the related information stored in the students' minds. The ability of the target selection is based on the multi nature and complexity of the mathematical connection, and the emphasis is on the goal of the problem. Based on the analysis of mathematical connectionism and the related literature of target selection, this paper, based on connectionism, cognition and related mathematical education psychology, combines the characteristics of geometric proof, and puts forward the concept of selective binding ability of junior middle school students' geometric proof, that is, junior high school students can The problem goal is oriented, connects to the relevant concepts, propositions, methods, etc. in mathematics learning, and actively and actively make the correct and reasonable selection and processing, can monitor the influence of their selective connection to the process of proof, and can adjust the behavior of their selective connection. It is a kind of solution. The problem of geometric proof is a mathematical problem solving ability for a specific task, which includes the selection of knowledge in the learning of the geometric modules, the cognitive components of the reorganization process, and the process of planning, monitoring and adjusting the metacognitive components of the process of the selection of their own targets. In order to understand the level of target selection in junior middle school students' geometric proof and the effect of target selection on the geometric proof of junior high school students, the paper puts forward the countermeasures to cultivate the ability of target selection in junior middle school students' geometric proof. First, the relevant literature of the target selection is analyzed, the relevant research results are obtained, and the content of the research is determined. Second, the relevant theory is constructed. Based on the theory of related psychology and mathematics educational psychology, the theoretical basis of the objective selective connection in the geometric proof is constructed, and its connotation and ability components are bound. Third, design investigation and implementation. This survey is conducted in the form of a combination of questionnaires and geometric proof tests. Fourth, draw the conclusion of the investigation. According to the results of the survey, the status and level of the junior middle school students' ability to join the geometric proof in the geometric proof are obtained, and the influence on the problem of solving the geometric proof is made and made. Fifth, put forward the training strategy. The main conclusions of this study are as follows: first, the junior middle school students are medium in the geometric proof, and the two level difference is large. Second, in the ability of the target selection, the combination and the goal transformation are in the target selection. The difference of neutral difference is significant, which mainly shows that girls are more likely to interpret the known information of the topic and think about the related ideas. In addition, the female students have more goal oriented consciousness than the boys. Third, in the process of solving the problem of geometric proof, the junior middle school students' goal orientation is insufficient. The main manifestation is that it is not good to be proved. At the same time, the junior middle school students are not good at the small step and reflective aspects of the target transformation in the geometric proof, and fail to demonstrate the equivalent chain of the conclusion in combination with the known information. At the same time, the process is not rigorous, and the process of proof can not be properly verified. In addition, the direction of the target transformation can not be corrected in time. Fourth, the goal selective connection ability of junior high school students has a significant influence on the achievement of junior high school students in the geometric proof test questions, especially for the more difficult geometric proof questions, the higher the ability of the junior middle school students to join in the selection of the target, the higher the ability of the junior middle school students' goal selection. The better the performance is. Finally, in order to strengthen the goal selective connection ability of the junior high school students' geometric proof, the relevant training countermeasures are put forward from the angle of the composition of the target selection ability of the geometric proof. In the knowledge connection, the knowledge network is constructed, the basic knowledge is rammed, the basic knowledge solving experience is accumulated and the knowledge transfer is promoted. Face, train target oriented consciousness, promote the ability to push back analysis, build an equivalent or semi equivalent proposition system, promote target transformation, strengthen the consciousness of reflection, develop the habit of "reasoning with evidence", strengthen the training of problem solving monitoring and improve the level of problem solving and monitoring.

【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

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本文編號(hào)：1866494