中學(xué)數(shù)學(xué)解題中逆向思維的應(yīng)用

1萬多字 24頁

目 錄
摘要 1
第一章 中學(xué)數(shù)學(xué)解題中逆向思維應(yīng)用的研究概況 3
1.1研究的背景 3
1.2國內(nèi)外的研究現(xiàn)狀 3
1.3研究的意義和目的 4
1.4研究方法 4
第二章 逆向思維在證明題中的應(yīng)用 6
2.1反證法 6
2.1.1反證法原理 6
2.1.2反證法的邏輯基礎(chǔ) 7
2.1.3反證法的應(yīng)用解析 8
2.2 分析法 12
2.2.1分析法原理 12
2.2.2分析法應(yīng)用例析 13
第三章 逆向思維在中學(xué)數(shù)學(xué)解答題中的應(yīng)用 16
3.1定義的逆用 16
3.2定理的逆用 17
3.3公式的逆用 18
3.4靈活運用補集的思想 19
3.5互為反函數(shù)法的應(yīng)用 21
結(jié) 論 22
參考文獻 23


摘要 解決數(shù)學(xué)問題是數(shù)學(xué)教育和學(xué)習(xí)的核心，而當(dāng)正面著手解決問題困難重重或工作量大時，逆向思維的運用則能幫助我們另辟蹊徑，解放思想，以新的角度審視問題，打破僵局，化難為易。
基于前人的研究成果，本文主要采用文獻研究法，從逆向思維在中學(xué)數(shù)學(xué)證明題和解答題中的應(yīng)用這兩大方面來探索中學(xué)數(shù)學(xué)解題中逆向思維的應(yīng)用。
在研究逆向思維在中學(xué)數(shù)學(xué)證明題中應(yīng)用時，主要從逆向思維的兩大體現(xiàn)形式—反證法和分析法來研究；而在研究逆向思維在中學(xué)數(shù)學(xué)解答題中應(yīng)用時，主要從定義的逆用、定理的逆用、公式的逆用、補集思想的運用、互為反函數(shù)法的應(yīng)用這五個方面來研究。

關(guān)鍵詞 逆向思維　反證法 分析法


Application of reverse thinking in mathematical problem solving in high school

Abstract Solve mathematical problems is the core of mathematics education and learning, and when the front or difficult to address workload issues, the use of reverse thinking is another way to help us, emancipate the mind, in order to examine the issue of new angles to break the deadlock of Aesthetic Easy.
Based on results of previous studies, this paper uses the literature study, from the reverse thinking proofs answer reconciliation of these two aspects of the application of mathematics in secondary school mathematics problem solving to explore the application of reverse thinking.
     In studying the problem of reverse thinking applied to prove in high school mathematics, mainly from the two reverse thinking embodied in the form of -reduction to absurdity and analysis to study; while studying mathematics at the secondary reverse thinking when you answer questions in the application, mainly from the definition of the inverse with , with inverse theorem, inverse formula used, the use of ideas complement each other applications inverse function method to study these five areas.
Key words reverse thinking　reduction to absurdity analysis method