[ 摘要 ]

本研究主要目的在探討國小學童小數加減之表現。研究對象為屏東地區國小五年級學童，透過分層隨機抽樣方式，選出253名有效樣本進行施測。測驗工具為自編之筆試試題，以概念理解、程序應用與問題解決作為評量學童小數加減表現的三個不同面向。另外透過運算類型（加減關係；異同位數）和學童背景（男、女性別；漢民族、原住民和新移民族群）探討不同變項對學童小數加減表現的影響。

本研究應用S-P表理論區分出學童學習及答題表現類型，並依據學童學習的類型，再結合次序理論對學童小數加減能力結構進行次序性和階層性的探討。主要統計方法包括單因子變異數分析、二因子變異數分析、S-P表分析和次序理論。

本研究主要結果整理如下：

一、國小學童小數加減表現，在「程序應用」面向顯著優於小數加減「概念理解」面向和「問題解決」面向。

二、國小學童在小數加減不同面向表現，其細項能力具有明顯的不同。在概念理解的表現，會受到圖形表徵的影響，以離散量（內多）表徵方式表現最不好；在程序應用的表現，會受到小數位數關係影響；在問題解決的表現，會受到解題知識的影響，以「語意瞭解」與「問題表徵」表現優於「解題策略」。

三、對於小數加減運算類型，國小學童在加法和減法的表現沒有顯著差異；在「同位小數」的表現顯著優於「異位小數」。

四、性別對國小學童的小數加減表現沒有顯著的影響。

五、族群對學童的小數加減表現有顯著的影響，尤以原住民學童的表現值得關切。

六、應用S-P表理論的學生注意係數和試題注意係數，可診斷學童的學習成效，針對學童的學習表現類型予以分類，並從中獲得有關改進小數加減教學及學習輔導的訊息。

七、應用次序理論分析學習成就不同的學童和學習成就相同答題表現不同的學童，其小數加減能力結構的次序性和階層性不同，細項能力之間的關連各具有特色和意義。

最後，依據研究結果，進一步對於國小數學教學、課程編排，以及未來研究者提出具體之建議，以供參考。

[ 英文摘要 ]

This research is to explore the performance of elementary school students’ ability on decimal addition/subtraction. The questionnaire investigation method, stratified sampling, was adopted and took 253 fifth grade students as the valid samples in Pingtung county. The measurement tool is “ decimal addition/subtraction ability diagnosis test. ”There are three main dimensions to test above statement: conceptual understanding, procedural knowledge, and problem solving. The students learning ability can be more understandable after finishing this research, according to the analysis of different types of operations, sex, populations with above performance. With utilizing S-P theory, this research distinguished the solving problems types and testify the degree of students’ learning effectiveness. Following this, it analyzed further on students’ ability on sequence of stratum of decimal addition/ subtraction via ordering theory.



The main statistical approaches are ANOVA analysis, S-P theory analysis, ordering theory analysis.



The followings are the findings.



1. Performance in procedural knowledge is significant better than conceptual understanding and problem solving.

2. There is significant difference in detailed operation. The performance in conceptual understanding is affected by the rectangular grids; the content of discrete as the multiple objects is the worst of all. The performance of procedural knowledge is affected by the numbers of decimals. The performance of problem solving shows that the ability of “meaning understanding” and “problem features” are better than “solving problem strategy.”

3. On the types of operations, there is no difference between addition and subtraction. Performance on equal-digit decimals is better than different-digit decimals。

4. There is no significant difference on the variable of sex.

5. There is no significant difference on the variable of population, but aboriginal students are needed to pay more attention.

6. Students’ learning effectiveness can be tested if using student caution index and item caution index from S-P theory. Then the learning performance can be classified and get the related information to improve teaching.

7. Those who have the different and the same learning achievement, show distinguished abilities of stratified structural sequence. Each connection within detailed ability has its own meaning.



There are more suggestions based on above findings shown in the text.