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| 題 名 | 我國國小學生估算概念之研究=A Study on Computational Estimation of R.O.C. Students at Elementary School Level |
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| 作 者 | 支毅君; | 書刊名 | 臺東師院學報 |
| 卷 期 | 7 1996.06[民85.06] |
| 頁 次 | 頁1-51 |
| 分類號 | 523.32 |
| 關鍵詞 | 估算; 概算; 概數; 數感; 數學解題; Computational estimation; Estimate; Number sense; Problem solving; |
| 語 文 | 中文(Chinese) |
| 中文摘要 | 本研究的主要目的是探討我國國小學童的估算概念之發展及估算教學。為了完成 預定的研究目標,本研究以三年時間進行國小學生估算概念及態度之收集、估算教學之實 驗。第一年度除對學生進行個別訪談外,亦收集教師對估算的態度及平日使用估算的經驗, 以了解學習估算的環境及可能性。第一年度研究之對象為國小三至六年級中上程度小朋友。 第二年度之研究範圍有兩部份,第一部份是延續第一年之個別追蹤訪談,第二部份則是 設計估算實驗教材並實施。第三年度之研究範圍有兩部份,一為繼續個別追蹤訪談,一為國 小四年級的概數教學觀察。 根據所得之資料,國小及國中生幾乎都沒有使用「大約」值的經驗,少數的經驗是驗算 作業;考試時是「再算一遍」來驗算;使用電子計算機時,是「再按一遍」或「反著算」來 驗算,均不是使用估算。受訪學生均知道「大概」、「大約」的意義,同時也能舉出同義字 「差不多」、「接近」、「可能」、「近似」、「或許」等。唯一困擾的名詞是「合理」; 許多國小學生認為「合理」就是「正確答案」,這種想法低年級尤多。成人估算的經驗似乎 與量的經驗有關。研究中發現即使沒有時間的壓力,估算仍然可能發生。使用估算的意願, 似乎與習慣有關。受訪者的估算方法隨著題型改變。大部分的受訪者所使用的方法與文獻中 所提到的一樣或類似。估算能力似乎可以分成下列層次:瞭解「估算」的意義及名詞、知道 何時可以使用估算來解題、能夠得到合理的估算值、使用適當的估算方法、能夠視數值的特 色使用不同的估算方法能判斷何者是最好的估算方法。 本研究發現大部分國小教師聽過「估算」一詞,其場合多半與商業有關。四捨五入法為 教師在連加時最普遍使用的方法,但在可以適用集中法(Clustering)時,亦有半數人願意 使用集中法。在經過估算的討論之後,所有的教師均承認其數學教學會改變,其中一半會視 教材而定,另有近於一半的教師會把估算介紹給學生。有超過五分之四的教師認為估算在日 常生活中很重要;認為小學課程中應加上估算的也有五分之四;這些顯示教師對估算的肯 定。 本研究之實驗教材共有六個單元,每單元約廿五分鐘,藉由教師及學生的反應來檢討其 教學及教材。學生對估算教學很有興趣,但是課外活動方式的教學效果不能持久,學生會忘 記學習的內容重點。經常性、課堂上由授課教師在不同的單元中加入估算,可能是較有效的 辦法。 追蹤訪談的對象有十七位,所收集的學生資料初步顯示出個人估算的習慣因年齡增長而 成熟的程度不多。概數教學的觀察結果顯示,多數學生不瞭解為何用概數、何時用它、及用 到甚麼程度。 |
| 英文摘要 | This three-year's study explores the conceptual development and competency of computational estimation of Chinese students at the elementary school level. In order to achieve the objective, individual interviews were conducted and small groups' activities concerning estimation were observed in the first year. The attitude towards estimation and experience in using estimation of in-service teachers were also collected to reflect the possibility of including estimation in the curriculum. Fifty-eight teachers and thirty students from 3rd-through 8th-grade participated in the first year's work. The second year's work includes two parts. The first part is to interview students from 4th-grade to 6th-grade on estimation, and the second part is to develop and experiment the teaching material on estimation. Twenty-one students were interviewed and six units of material on estimation were developed in this year. The third year's work includes follow-up interviews with seventeen students and observations in an estimation class of 4th graders. Collected data were analyzed to draw conclusions about attitude of students towards computational estimation. More than half of the teachers consider estimation an important topic and would discuss such topic to their classes. Most students in this study never use estimation to check their answers on exams nor on calculators. "Reasonable answer" confuses many students with "Correct answer." A model of six phases of competency of estimation is proposed in this study. The phases are (i) understanding definition and terms (ii) using estimation to solve problems (iii) inquiring a reasonable estimate (iv) using a proper estimation strategy (v) using different strategy according the situation (vi) evaluation the best strategy. Students were found lacking of number sense and too much rely on their computation skill in many cases. Most students were uncomfortable with estimation and reluctant to use it as an alternative way to solve problems. Many students confused how and when to use estimation. This study suggests that estimation should be included in the curriculum and be taught in classroom activities on a regular basis. The interview shows that the competency on estimation does not improve as the students get older. Students need teacher's encouragement and guidance to develop a positive attitude toward estimation. The observation in math class shows that many students do not know when, why and how to use estimation to solve problems. |
本系統中英文摘要資訊取自各篇刊載內容。