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題 名 | 乘法直式算則的學習探究=Learning Investigation of Algorithm of Multiplication |
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作 者 | 李源順; | 書刊名 | 臺北市立師範學院學報 |
卷 期 | 33 2002.12[民91.12] |
頁 次 | 頁539-562 |
分類號 | 523.42 |
關鍵詞 | 乘法直式算則; 位值概念; 學習負荷; Algorithm of multiplication; Place value; Learning loading; |
語 文 | 中文(Chinese) |
中文摘要 | 九年一頁數學學習領域課程綱要能力指標的訂定有些並沒有做過實徵性的研究,而且教學時數也相對減少。因此,有必要對課程的編排做適當的安排。其中,「嘗試理解乘、除直式算則」明列於第三階段,它是受到八二年課程標準編輯委員的影響。同時一些家長、教師和數學教授們對於八二年版數學課程的反對聲浪中曾以乘、除法計算過程做為批判數學教學的例子。居於上述理由,本文的研究目的在檢視九年一貫數學學習領域能力指標N-3-2「能嘗試理解乘、除直式算則」的編排是否恰當。也就是在探究現行八二年版架構下,學童計算全故乘法算式時的程序性知識學習荷負,以及五年級學童對全數乘法直式算則的理解,進而提出九年一貫數學課程中乘法直式算則學習時機的建議。 研究方法採本文分析,以及問卷調查。文本分析以國立編譯館主編的數學教科書(簡稱國編本)為對象,主要是因為有些修訂八二年版數學課程標準的委員參與國編本教科書的編著,所以國編本教科書最能詮譯八二年課程標準的精神。接受問卷調查的學童也是四年半以來都以國編本為教科用書的102位臺北市學童,他們最能反應八二年課程的學習負荷。 文本分析發現,三年級以前學童幾乎需要使用累加的方式計算問題且需做乘法表徵的轉換,四年級以上的學童計算乘法問題需做「幾千」和「幾個千」兩種形式的位值概念轉換和一種等價關係的轉換,而且需要使用多步驟的算式。問卷調查發現,五年級學童習慣於「幾千」的位值概念乘法,而較不習慣於「幾個千」的位值概念乘法;他們可以以「幾千」的位值概念理解乘法宜式算則,也可以正確使用算則計算乘法問題。文本分析和問卷調查結果發現,使用幾個百幾個十幾個一的幾倍的多步驟計算方式,需要兩種形式的位值概念轉換以及一種等價關係的轉換,對學童的學習負荷量大。 研究者建議,我們應以「幾千」的位值概念轉換做為學童理解乘法直式算則概念過程的主軸,不要以需做「幾千」和「幾個千」兩種形式的位值概念轉換和一種等價關係的轉換方式理解直式算則,以免造成學童的學習負荷。同時,為了減低學童解題過程中的計算程序性知識的負荷,五年級的學童應該、也可以理解乘、除直式算則。也就是說,「能嘗試理解乘、除直式算則」應該提前明列於九年一貫課程第二階段或者不列入能力指標。 |
英文摘要 | Some parents, teachers, and mathematician question performance of '93 mathematics curriculum, their examples are about students learning of algorithm of multiplication and division. Now, The Mathematics Scenario of Nine-Year Curriculum Integration, in N-3-2 (sixth and seventh grades) Say: Try to comprehend algorithm of multiplication and division. Hence we want to investigation students' learning loading, and students' comprehension about algorithm of multiplication and division, then give some suggest of learning about algorithm of multiplication and division. Research methods are text analysis and questionnaire. The textbooks of text analysis are National Institute for Compilation and Translation published. The students be surveyed that had used those textbooks four and a half years. Text analysis found that students needs to use addition to calculate multiplication questions, and needs to transform to multiple representations in first three grades. After fourth grade, when students calculated multiplication question, they needs to transform digits into two different place values, and use multiple steps method. Questionnaire survey found that fifth grade students are used to calculation by 20x700, don't used to calculation by ten of five multiple hundred of three. Fifth grade students can comprehend concepts of multiplication algorithm that used place value concept of "how thousand", and can correct calculation multiplication question. Text analysis and questionnaire survey found that students had much burden, when they calculate multiplication question with multiple steps method. Researcher suggests that if we want reduce learning loading of students, we can teach the concepts of multiplication algorithm with transformation method of place value of "how thousand". If we want reduce learning loading of the processing knowledge of problem solving of students, fifth grade students will and can learning multiplication algorithm. |
本系統中英文摘要資訊取自各篇刊載內容。