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  • 學位論文

國中資優數學之三角形的創題思解

The Study of Triangle Problem by Creative thinking for The Gifted Students in Junior High School

指導教授 : 王牧民
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摘要


本研究的目地在於瞭解國中學生學習三角形之相關幾何圖形教材之迷思,以及探究國中相關三角形資優課程適用之幾何題型教材。故以國中數學領域之三角形相關課綱範圍為基礎,編寫國中資優三角形之數學題型,讓教師能藉由本使對此類型有興趣的學生能體會到三角形題型的本質,並提供其多樣化的參考解題方法,增加學生在三角形題型中的解題能力,並增廣其思考方式,進而提升學習興趣。 大綱如下: 一、國中三角形資優數學教育之教材,能讓學生增加接觸更廣更深的解題策略,在解答答案的過程中,培養其分析與多元思考的能力。 二、研究者將題型分成「三角形全等、三角形相似、畢氏定理、特殊三角形應用及技法統整」來做創題思解。 三、幾何解題技巧如下: (一)在解三角形相關題型時,在圖形中增加合適的輔助線有助於邏輯思考與分析圖形的能力。 (二)線段延伸與分隔角度以製造直角三角形,有助於解題。 (三)當原圖形不易分析與或增加補助線無效時,則割補成特殊的、簡單的或完整的新圖形,即能新增條件或搭起解題橋梁。 (四)計算三角形面積時,可使用旋轉,旋轉是利用平面圖形繞定點旋轉某個角度後,重新組成新的幾何圖形。 提出以下幾點建議參考: 1.培養相關課程師資專業能力,在教學上注重思考、解題的多元性與重視實作 2.可善用動態幾何軟體或數學構圖軟體模擬,觀察圖形變換,實證所學之幾何概念 3.充實教材內容,並輔以三角形相關幾何題型強化其思考推演與教材深度,以增加學生對於此教材的熟悉度。

並列摘要


The purpose of this research is to understanding the myth of geometry teaching materials related to the country's high school students learning triangle, and explore the country in the relevant applicable triangular geometry questions gifted curriculum materials. Therefore triangle States mathematics lesson outline the relevant range, based on the preparation of mathematics questions States gifted a triangle, so that teachers can be present so that students are interested in this type of triangle can understand the nature of the kinds of questions, and to provide its diverse the reference method of problem-solving to enhance students' ability to solve problems in the triangle of the kinds of questions, and augmented their way of thinking, and thus enhance interest in learning. The following outline: 一、 The teaching of mathematics States triangle gifted education allows students to increase contact with a broader and deeper problem solving strategies in solution. The answer in the process, develop their ability to analyze and pluralistic thinking. 二、The researchers divided the questions "congruent triangles, similar triangles, the Pythagorean theorem, special applications and technology triangle.Method Integration "do create problems thinking solution. 三、 The geometric problem-solving skills as follows: (一) In solving the triangle related questions, suitable guides help increase the ability to think logically and analyze patterns in the graph. (二) Segment extending partition angle to produce a right triangle to help solve problems. (三) When the original graphics and easy analysis or increase the auxiliary line is invalid, then cut up into a special, simpleor a completely new graphics, which can add a condition or problem solving bridge erected. (四)When calculating the area of a triangle can be used, the rotation is the use of a plane figure around a fixed rotation angle,re-formation of a new geometry. To propose the following reference: 1. Training courses professional competence of teachers, focus on teaching thinking, problem solving and attention to the diversity of implementation. 2. Can make good use of geometric or mathematical concept of dynamic geometry software composition software simulation, graphics transformation observed, learned of the positive. 3. Enrich teaching materials, supplemented by a triangular geometry questions related deduction an Textbook Thinking strengthen its depth,this textbook for students in order to increase familiarity.

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