i
摘要
從事數學教學歷程，需尋找各教學單元中每一概念內容項目間的關聯性，其 中以施行測驗為方法來尋找最為便捷。本研究主要目的在建立一套小數轉換為分 數概念試題，並藉由試題關聯結構分析法對施測結果加以進行分析形成結構圖， 進而探究國小四年級學童在小數轉換為分數概念的知識結構，盼能從中獲得國小 四年級學童在小數轉換為分數概念之試題關聯結構圖中所呈現的訊息，再根據研 究結果與建議，作為未來教學及課程設計與研究之參考。 由試題關聯結構圖中所呈現的訊息，得到以下的結論： （1）「國小四年級學童小數轉換及分數結構概念測驗試卷」具有良好的信、效 度，難易適中且鑑別度高，是一份優良的測驗工具，具使用價值。 （2）試題性質相同、內容相似的試題，在專家的知識結構裡，試題之間理應在 試題關聯結構圖上具等價關係，但在學童的施測結果卻出現一些比較不同 的知識結構。 （3）受試學童的概念發展是由「純小數轉換為真分數」到「帶小數轉換為帶分 數」，最後再到「帶小數轉換為假分數」。 （4）學童在小數轉換為分數的答題表現上，小數點後數值的大小會影響學童的 知識結構。 （5）一位小數或二位小數轉換為分數之不同概念，並不是真正影響受試學童知 識結構關係的原因。 （6）在二位小數轉換為分數概念中，只要二位小數（百分位為0）轉換為分數之 概念，不管分數約不約分，對受試學童而言都是屬於較高層次的上位概念， 學童對此概念之基礎不甚穩固。 關鍵詞：小數轉換為分數概念 國小四年級學童 試題關聯結構分析法iii
The IRS Analysis of Decimal to Fraction Conversion Concepts
for the 4th grade students of elementary school
Abstract
During math teaching process, it must research the relation between each concept of unit. The most convenient is taking test.The purpose of this research is making a set of topics of decimal to fraction conversion with reliability and validity, analyze the
results of the test, and form the structural picture through IRS and then explore the 4th
grade students of elementary school cognitive structure in decimal to fraction conversion concepts. I hope to gain the message from the item relative structural
picture of the 4th grade students of elementary school in decimal to fraction conversion
concepts. Then according to the results and suggestions, it could be the references of teaching and curriculum designing in the future.
According to the information from IRS, it shows:
(1) “The test of decimal to fraction conversion for the 4th grade students of elementary
school” is not only a test with reliability and validity, but also a practical test.
(2) For the professional point of view, it should be equal between the testand IRS by giving the same structure test questions; however, the result from students’ evaluation shows the different cognition.
(3) The concept develop sequence of students start from “ decimal fraction to mixed fraction” to “mixed decimal to mixed fraction” , and finally develop to “mixed decimal to improper fraction.”
(4) The number of fractional part effect students’ cognition when students answer the questions.
(5) The concept of tenths decimal or hundredths decimal to fraction conversion is not the real reason to students’ cognition to resolve questions.
(6) Students who are given test not familiar with some concepts of hundredths decimal to fraction conversion, such as “when hundreds decimal place is zero, it will not effect a result no matter the fraction will be reduced or not”. Those concepts need
iv
the upper level cognitive development for students.
Keywords: concepts of decimal to fraction conversion, the 4th grade students of
