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  • 學位論文

高中數學中的函數主題之問題導引式教材的研究

The Research of High School Mathematic Teaching in The Topic of Functions with The Problem Based Learning

指導教授 : 王牧民

摘要


本研究目的旨在探討數學教學相關的理論,應用其原理,設計問題導引式教材,藉由問題引導及多元表徵的呈現,幫助學生函數相關概念的學習。另外探討函數學習相關文獻,了解學生有哪些迷失概念,進而進行教科書轉化,以協助學生建立正確函數概念。 本研究編製完成之實驗教材,採比較法及專家審查的方式進行評審,具有下列幾項優點,提供教學現場之教育工作者參考: 1. 能以問題導引學生思考,並藉由生活經驗中的實例,建立學生的函數基模,而後再導入抽象的函數定義,如此循序漸近,學生較易形成正確的函數概念。 2. 提供了多種函數圖形的正例與非例,讓學生歸納出這些圖形的屬性,進而修正原本存在的的迷思概念。 3. 教材提供了多元的函數表徵(文氏圖、表格、文字敘述、圖形)的轉換,有助於學生理解函數定義的概念。 4. 以圖形、動畫表徵輔助說明函數的相關概念,學生較容易理解。例如:(1)各種函數圖形的特徵及其平移、伸縮的概念;(2)函數極限及函數連續的概念;(3)函數的夾擠原理。 5. 提供「無窮」、「極限」、「連續」的概念說明,可增進學生的基本推論能力,並了解這些概念的發展過程。 各種教學模式皆有其優點,教師可依學生程度及教學目標來選擇合適有效的教學模式。當教師進行函數教學時,應循序漸近,先以問題及生活經驗的例子,導引學生思考,然後再引入函數的定義;教師可嘗試以多元表徵的方式做呈現,修正學生函數迷失概念,幫助學生函數概念的學習。

並列摘要


This research aims to investigate how to use the problem based learning and multiple representations to help students understand function related concepts. To assist students to build correct function concepts, this research also inspects the past researches related to function learning to realize the misconcepted parts of student the and establish an appropriate math instruction by text transformation. The experimental math instruction was evaluated by comparative method and expert examination in this study. There are five advantages in this instruction: 1. It is easier to form correct function concepts gradually by using problem based learning and living examples first, then adding abstract function definitions. 2. This instruction supplies many function graphs in positive examples and wrong cases to lead students modify their misconceptions by induction. 3. This instruction provides multiple function representations, including venn diagram,form, description, and graph. These representations are helpful for learning function definitions. 4. It is easier to comprehend the text by graphs and animations. For example, the translation and stretch of functions, the limits of functions, and squeezing principle of functions. 5. This instruction can improve basic inference abilities by offering the cocepts and development process of “Infinite” ,“Limit” and “Continty. Every teaching model has its advantages.Teachers can choose their effective models depend on students’ level and teaching objectives. When teaching function concept, we can try to use questions and living experiences to be examples to lead thinking at first, and then add abstract definitions. Besides,teachers can attempt to use multiple representations to modify the misconceptions of students and to help teaching.

參考文獻


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