A Study on the Anxiety Cased by the Learning
Mathematical Symbols —
A perspective from metacognition with the case on G-7
Ui-Li Chiang
Abstract
This study is to explore the factors of anxiety that students would have when they face mathematical symbol, we also study students’ difficulties in understanding and using symbols from metacognition point of view. We adopt both qualitative and quantitative methods to collect and analyze the data. We develop a mathematical symbolic anxiety scale to analyzing the distribution of students’ mathematical symbolic anxiety. In qualitative analysis, we increase the validity of the questionnaire through local concept map, validating data by triangulation to promote the reliability and validity. The researcher designs some questionnaire of mathematical symbolic anxiety interviewing by referring to the dimension of mathematical symbolic anxiety scale, according to the four-type mistakes words-symbol proposed by Mr. Gho; design questionnaire of meta-cognition according to the theory of metacognition (Flavell), and coding by the information of the interviews and tests to analyze and compare with.
In quantitative analysis, the finding indicates that the difference of the distribution in class inconsistency in mathematics is as follows. Students with high performance on mathematical study tend to have low anxiety. On the contrary, low performance students tend to have high anxiety. But students with average performance are with a uniform distribution in their anxiety scale. Also there are significant differences between feminine and masculine students. Especially, feminine students have higher anxiety scales than masculine students on the acceptance of symbol, persistence, the judgment of mathematical ability, problem solving and the total anxiety scales. For students with distinct performance on mathematical study, persistence is the only significant factor. By post-test, students with low performance reach much higher anxiety scale than others.
There are many factors results in students’ anxiety to mathematical symbols. First, they are not familiar with the mathematical concept of the symbol; second, they are confused with distinct meanings of a symbol; third, they pay too much attention on problem solving solve problems; forth, they don’t have right attitude to study mathematics. Therefore, they are anxious about mathematics and they fear the symbols. From metacognition point of view, we discuss students’ abilities to understand and properly use mathematical symbols. For the metacognitive knowledge, we find that students’ difficulties include: unfamiliar with the definition of the symbols, insufficient strategic knowledge on symbols, the lack of retrospective abilities on symbols, not clear on the timing of using symbols; For the metacognitive experience, students’ difficulties are anxiety on mathematics, attitude on learning new symbols, the tendency on reaction when facing difficulties, unpleasant experiences, such as low performance on mathematic, low mathematical attitude.
目錄
第一章 緒論 1
第一節 研究背景與研究動機 1
第二節 研究目的與待答問題 3
第三節 名詞解釋 4
第二章 文獻探討 5
第一節 符號與數學符號 5
第二節 數學焦慮 10
第三節 後設認知 18
第三章 研究方法 28
第一節 研究流程 28
第二節 研究工具的發展 29
第三節 研究樣本與過程 36
第四節 資料收集與分析 41
第四章 研究結果及發現 46
第一節 統計資料的分析與討論 46
第二節 探討學生學習數學時，因符號所產生焦慮之成因 53
第三節 以後設認知觀點探討理解、處理數學符號時，遭 72
遇困難之相關因素
第五章 結論與建議 95
第一節 結論 95
第二節 研究限制 100
第三節 建議 100
參考文獻
一. 中文部分 105
二. 英文部分 107
附錄 112
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