探討圖形與符號表徵形式對高中生比例心理運算的影響

Exploring th e Effect of High School Stud en ts’ Selection of Mental Operation on Proportional Problem Representation

本研究運用整體反應時間技術探討表徵形式對高二學生比例問題的心理運算的影響。研究對象為16位高中二年級學生；研究工具為比例運算測驗題本，分為數字的符號表徵及圖形表徵兩種，兩種表徵形式題目呈現方式都是由易到難，題目內容包含柳丁汁比例問題的八個層次和三個階段，每個層次的問題都有4題，共32題；此題本的各項問題依據Noelting研究中的柳丁汁與水之比例關係編製而成。本研究的研究方法是透過學生的答題反應時間與答對率進行資料的收集與分析。研究結果顯示：（1）高二學生的整體反應時間在IIA層次兩種表徵形式中是最快的，且認為最簡單；（2）表徵形式是使高二學生的比例具體操作階段成為比例心理運算的關鍵階段，而具體操作階段中的IIB層次是心理運算由直接提取轉換為基於運算規則的重要層次。

This study investigated the influences of students’ selection of mental operation on two forms of representations in proportional questions by using the total response time analysis technology. There were 16 high school students(11th graders’) participated in this study. A proportional test which consisted of two representational capacity tests was applied for data collection.The two tests involved graphical and number symbolic which cover eight levels from easy to difficult and three stages from easy todifficult(Noelting, 1980a, 1980b). There are four questions for each level. Cognitive science usually adopts total response time and accuracy rate to measure human’s mental. The total response time and the response scores were used to analyze students’ performance on answering the proportional questions. The results showed: (a) students revealed the fastest total response time and highest response rate at IIA level; (b) the forms of representations are one of the important factors which could help 11th students for translating the selection of proportions’mental operation from concrete stage to critical stage. Furthermore, the IIB level might be the important level which could demonstrate 11th students’ translation of theselection of proportions’ mental operation from direct retrieval to procedural strategies. To sum up, the forms of representations might be one of the important factors to indicate 11th graders’translations on selection of proportional mental operation.