本研究旨在探討國小低年級學童對等號意義的認知情形,及其在等式判讀、等式解題的表現,以及教師對其等號概念發展情形之了解。本研究採問卷調查法,研究工具為自編的「國小低年級學童等號概念探討問卷」、「國小低年級教師對學童等號概念了解情形之問卷」,研究樣本為桃園縣99學年度國小低年級學童共783名及國小低年級教師共174名。問卷所得資料利用SPSS進行分析,研究結果如下: 一、國小低年級學童對於等號概念的認知,屬於運算定義者較多(佔總人數的的56.6%),而屬於關係定義者較少(佔總人數的43.4%);且學童對等號概念的認知在母親國籍別上達顯著性差異,在年級、性別上則未達顯著性差異。 二、國小低年級學童的等式判讀表現在年級、母親國籍別、等號概念上達顯著性差異,在性別上則未達顯著性差異。其中,二年級的表現優於一年級、母親為本國籍之子女的表現優於非大陸籍之新住民子女,具備等號關係性概念之學童表現優於僅具備運算性等號概念之學童。 三、國小低年級學童的等式解題表現在年級、母親國籍別、等號概念上達顯著性差異,在性別上則未達顯著性差異。其中,二年級的表現優於一年級、母親為本國籍之子女的表現優於非大陸籍之新住民子女,具備等號關係性概念之學童表現優於僅具備運算性等號概念之學童。 四、國小低年級教師對於學童等號概念的學習情形不了解,大多是高估了國小低年級學童在等號概念試題的答題表現;且教師對於學童等號概念學習情形的了解在個人背景變項之教學年資、教育程度上達顯著性差異,在教育背景上則未達顯著性差異。其中,於低年級教學年資為「6-11年」之教師較「0-5年」、「11年以上」之教師了解學童在等號概念的學習情形。 本研究根據研究結果,進一步針對課程教學、未來研究提出具體建議。
Abstract This study investigated first and second-grade students’ understanding of the equal sign, identification of the equal sign in number sentences, and performance in solving number sentences as well as their teachers’ understanding of the equal sign concept development in students. The research tools were two self-developed questionnaires, including “Questionnaire on the Equal Sign Concept among First and Second-grade Students” and “Questionnaire on First and Second-grade Teachers’ Understanding of the Equal Sign Concept Development in Students”. The questionnaire survey was administered to 783 first and second-grade students and 174 first and second-grade teachers in Taoyuan County during the academic year of 2010. Their responses were analyzed using SPSS to derive the following conclusions: 1. Among the participating first and second-grade students, 56.6% identified the equal sign as an operational symbol while 43.4% identified it as a relational symbol. Besides, their understanding of the equal sign varied significantly by their mother’s nationality but not by grade or gender. 2. In terms of first and second-grade students’ performance in identification of the equal sign in number sentences, students’ performance varied significantly by their mother’s nationality, personal conception of the equal sign but not by gender. Among them, second-grade students outperformed first-grade ones, students whose mothers were Taiwanese outperformed students whose mothers were immigrants from nations excluding China, and students having the relational concept of the equal sign also outperformed those having only the operational concept of the equal sign. 3. In terms of first and second-grade students’ performance in solving number sentences, students’ performance varied significantly by their mother’s nationality, personal conception of the equal sign but not by gender. Among them, second-grade students outperformed first-grade ones, students whose mothers were Taiwanese outperformed students whose mothers were immigrants from nations excluding China, and students having the relational concept of the equal sign also outperformed those having only the operational concept of the equal sign. 4. First and second-grade teachers’ insufficient understanding of students’ learning of the equal sign concept was mainly attributed to their overestimation of students’ performance in solving number sentences. Their understanding of students’ learning of the equal sign concept varied significantly by service duration, highest education level, but not by education background. Teachers who had “6~11” year experience of teaching first and second-grade students knew better about students’ learning of the equal sign concept than those who had “0~5” or “more than 11” year experience. Based on research results, this study also proposed specific suggestions on teaching of the equal sign concept and future research.
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