五至七年級電腦化比例推理能力評量的發展與應用   全文下載

The Development of a Computerized Assessment on Proportional Reasoning Ability for 5th to 7th Graders

本研究參酌美國比例推理發展軌跡的理念，研發電腦化比例推理能力評量。評量設計依年級分為三式，五至七年級學生樣本共715人。五年級式別平均答對率為0.49，內部一致性為 .77。六年級式別平均答對率為0.55，內部一致性為 .82；七年級式別平均答對率0.66，內部一致性為 .84。學生比例推理能力與在校成績相關組型，各年級學生比例推理能力皆與在校數學相關為最高，與在校國語相關最低。試題的實徵難度與評量設計所依據的發展階段尚屬一致，惟少數試題中額外的關鍵成分明顯影響難度變異，如變量間呈現等差關係、或題目中含分半與單位分數。換言之，實徵難度可豐富發展理論不同階段中相關認知成分交互運作的脈絡。研究中以實徵難度值-1與0為切點，將試題分為三個層次。24題中，基礎層次有9題，主要為只改變芒果或冰塊的甜度比較題。其次，9題為精熟層次，內容為芒果份數改變各種倍數的缺失值問題。最後，進階層次6題，主要為依數字計算容易程度，活用含整數倍數的策略選擇題。年級與性別二因子變異數分析發現交互作用未達顯著，僅年級因子達顯著，η²為 .08。性別因子未達顯著，與臺灣國中、小學生數學成就無性別差異的結果大致相符。

The hypothesized learning progression or learning trajectory in proportional reasoning were adopted to develop a computerized assessment on proportional reasoning ability in this study. According to student’s learning experiences, three different forms were assembled for the 5th, 6th and 7th graders with common items. Totally, there were 715 students included in the study as sample. For the form of 5th grade, the average proportion-correct is 0.49 and the alpha is .77. For the form of 6th grade, the proportion-correct is 0.55 and the alpha is .82. For the form of 7th grade, the proportion-correct is 0.66 and the alpha is .84. The correlation coefficient between students’ proportional reasoning ability and school achievement is highest in mathematics, and is lowest in language. Most of the item difficulties were concordance with the developmental stages. Some crucial elements such as constant additive differences distracters, halving and unit fractions affect item difficulties substantially. The grade and gender two-way ANOVA revealed that the interaction was not significant. Only the grade factor was significant, and η² was .08. The gender factor was not significant. This result was consistent with the gender similarities hypothesis in mathematics achievement for Taiwan elementary and middle school students.