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題名 | 臺灣中部地區國小教師與高年級學生對質數概念之調查研究=An Investigation on the Understanding of the Concepts of Prime Number of Elementary School Teachers and Older Students in Central Taiwan |
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作者 | 吳德邦; 馬秀蘭; 洪聰明; Wu, Der-bang; Ma, Hsiu-lan; Horng, Tsong-ming; |
期刊 | 臺中師院學報 |
出版日期 | 19980600 |
卷期 | 12 1998.06[民87.06] |
頁次 | 頁419-454 |
分類號 | 523.3431 |
語文 | chi |
關鍵詞 | 臺灣; 中部地區; 國小教師; 高年級學生; 質數; Mathematics education; Concept; The prime number; The composite number; Greatest common factor; GCF; Least common multiple; LCM; Older elementary school student; In-service teacher; |
中文摘要 | 本研究主要之目的是在探討臺灣中部地區國小教師, 以及高年級學生對質數認知 與應用的情形;並探討他們在找出 1 ∼ 200 間質數的情形。研究樣本是隨機抽取臺灣省中 部地區教師 154 名,以及國小高年級學生 224 名。本研究之研究工具是由研究群自製的有 關質數概念的問卷。 在分別回收 78 份、146 份、以及 154 份教師,五年級學生、以及六 年級學生的問卷, 經資分析後,研究群發現以下的結論:(一)對質數的認知方面: 1 . 教師部份在各種質數的認知答對率均遠超過學生的答對率。教師在此方面有很優異的表現。 其中,在各題的表現方面校長級的答對率大都高於主任級的,主任級的答對率又高於老師級 的。 2. 對於「質數」與「合數」的定義,大部份五、六年級學生都能了解,對於「最大公 因數」與「最小公倍數」,則有較多學生不了解。 3. 把一個整數分解成質因數的乘積,學 生做起來並不困難,但偶而發現有學生把「合數」當作質因數來用。 4. 自然數 1 常被誤 為是質數, 因為它除了自己沒有別的因數。 5. 大部份學生認為質數的數量有無限多個。 6. 質數按文獻記述,到目前為止,無法找到一個公式來求出所有質數, 但五、六年級學生 卻大部分以為有規則性,可能因為質數除了 2 以外,都是奇數的關係。 亦有不少學生認為 奇數就是質數。(二)對於質數的應用方面:國小高年級學生對質數的計算與應用相當熟練 ,而對於找出 1 ∼ 200 之間的質數,卻有極大的困難。 |
英文摘要 | This research was undertaken to investigate the understanding of the concepts of prime number of elementary school teachers and older students in central Taiwan. The subject of the study consisted of 154 in-service elementary school teachers, 78 fifth-grade, as well as 146 sixth-grade elementary school students in Central Taiwan. Based on the definition of the prime number and the concepts drown from the mathematics textbooks of elementary school, the "Questionnaire of the Concepts of Prime Number (QCPN)" were developed and used by the researchers. The conclusions were drawn as follows: 1.When compared with the elementary school students, the elementary school teachers showed superior understanding of the concepts of prime number. 2.Most of the in-service teachers have a through understanding of the definitions of the "prime number", "composite number", "greatest common factor (GCF)", and "least common multiple (LCM)". Although most of the students have a through understanding of the definitions of the "prime number" and "composite number", they confused the definitions of the "greatest common factor (GCF)" and "least common multiple (LCM)". 3.A lot of teachers, but only a few students, think that one is NOT a "prime number". Some of the students can not identify the odd numbers and prime numbers. |
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