探討國小六年級學生數學解題策略與偏好之研究

本研究旨在探討國小六年級學生對視覺化與非視覺化的數學解題策略之偏好。研究中以新竹縣某國小六年級三個班級共80位學生為樣本，以測驗問卷方式進行施測。問卷共有十題數學試題，內容分為兩個部分作答：第一部分請學生依題意自由的進行解題，策略不限；第二部分請學生從視覺化與非視覺化解題策略的選項中去選擇偏好的解題策略，並簡述其選擇的原因，並挑選出較具代表性的9位學生進行半結構式的訪談。最後，由學生在兩部分的答題情形分析其解題策略的使用與偏好間的關係及其選擇原因之探討。本研究主要結果如下：一、大部分的學生在進行數學解題時，無論是否成功解題，都偏好以非視覺化解題策略之數學符號進行解題。少部分的學生會使用視覺化解題策略，但也有使用了圖示輔助，卻仍無法成功解題的學生。而非視覺化解題策略之文字表徵則是沒有任何人使用此方式進行解題。二、當自行作答與偏好選擇相符時，大部分學生認為與其想法相同也比較快又容易理解。而影響學生選擇視覺化解題策略的原因主要有二：一，經常使用圖解，是在解題時就習慣畫圖的學生，在偏好上就會選擇視覺化解題策略；第二，當題目比較難或是複雜時，會使用或選擇圖示以幫助自己理解，但學生自行作答所畫的圖示不一定為線段圖，可能是示意圖或腳本圖示。三、當自行作答與偏好選擇不相符時，關鍵在於解題步驟的細膩程度與題目的難易度。大部分學生使用非視覺化解題策略之數學符號解題，但在選擇偏好時，如果有詳細過程步驟的策略，才會是學生偏好選擇的方法；當學生發現自行解題錯誤或題目較難時，會改變自己使用或偏好的解題策略，讓自己更容易理解題目。四、當面對熟悉或新習得的題型，「教師的教學與教科書的呈現」會影響其偏好選擇。

關鍵字

非視覺化；表徵；視覺化；解題策略

並列摘要

The purpose of this study is to investigate the preference of sixth-grade students in elementary school for mathematical problem solving via visualization or non-visualization strategies. In this study, there were 80 sixth graders in total enrolled from 3 different classes in an elementary school at Hsinchu County. The enrolled students received a questionnaire with 10 mathematical problems. The answers to the questionnaire are divided into two parts. In the first part, students were allowed to solve these problems as their free will without limitations. In the second part, students were asked to choose from the visualization or non-visualization strategies to solve these problems, and then to briefly describe the reason for their choice. There were 9 representative students further selected for a semi-structured interview. Based on the two parts of the answers from the questionnaire, we tried to analyze students' preferred strategies for mathematical problem solving and clarify the underlying reasons. The main results of this study are as follows. 1.Most of the students preferred the non-visualization strategy to solve mathematical problems, no matter if the answer was correct or incorrect. A small number of the students would use visualization strategy, but there were still some students who failed to solve the problem despite using diagram assistance. Of note, no students choose to use text representation of the non-visualization strategy in this study. 2.Most of the students considered the preferred strategy was easier and faster to understand when the strategy was consistent with their free will. There are two factors influencing students to choose the visualization strategy. First, students who preferred visualization strategy are usually using a diagram to solve problems at their baseline. Second, when the problem is more difficult or complicated, students tend to use a diagram to facilitate problem understanding and reasoning. The diagram might not always be a line-diagram, but also a schematic diagram or script diagram. 3.When the preferred strategy is different from students' free will, the key points are the meticulousness during problem-solving, and the degree of difficulty among those problems. Most of the students used mathematical symbols representation of the non-visualization strategy to solve problems. Nevertheless, students also preferred to choose those strategies with detailed steps for problem-solving. When students found they solved the problem incorrectly, or when the problem was more difficult, they would change their preferred strategy in order to get a better understanding of the problems. 4.When facing new question types, "teacher's lecture and the content on the textbook" would influence a student's preferred strategy.