本研究主要目的在探討基隆地區九年級學生背景變項因素與數學焦慮、數學學習成就的關係。本論文採用的研究方法包含問卷調查法、結構式訪談法，研究對象以基隆市十六所公立國民中學（包含三所綜合高中附屬國中部）九年級學生共4,513人，研究樣本是選取8所國中，抽樣16個班級，回收480份問卷，有效問卷425份，可用率達88.7%。使用的工具為「基隆地區國中九年級學生數學焦慮問卷」，內容包括學生基本資料、數學學習成就量尺分數及數學焦慮量表。以SPSS12.0進行描述性統計分析、t檢定、單因子變異數分析、皮爾遜積差相關、多元迴歸分析。
本研究由資料分析獲致以下結果：
一、 基隆地區國中九年級學生數學焦慮狀況，整體分布在中度焦慮程度；數學學習成就，整體分布在中成就。
二、 部分背景變項對基隆地區九年級學生數學焦慮（擔憂、厭惡、測試焦慮、壓力知覺四構面）有顯著差異。
三、 部分背景變項對基隆地區九年級學生數學成就有顯著差異。
四、 基隆地區九年級學生之數學焦慮與數學學習成就呈現中度負相關。高度數學焦慮的學生數學成就低於中度數學焦慮學生的數學學習成就，而中度數學焦慮的學生數學成就低於低度數學焦慮學生的數學學習成就。高數學成就的學生數學焦慮程度低於中數學成就學生的數學焦慮程度，而中數學成就的學生數學焦慮程度低於低數學成就學生的數學焦慮程度。
五、 數學焦慮四構面對於數學學習成就的預測力：數學焦慮四構面對基隆地區國中九年級學生之數學學習成就可解釋之總變易量為33%，其中又以「厭惡」構面最能預測學生的數學學習成就，「擔憂」構面次之。
最後根據本研究的結論，研究者分別就數學教師教學與輔導的經營面、學校行政管理面以及未來研究提出一些建議。
The main purpose of this study was to investigate the relationship among demographic variables, mathematics anxiety and mathematical achievement of 9th-grade students in Keelung area. Methodologies used through out this study include questionnaires and structured interviews. Subjects were 4,513 students came from 16 class of 8 randomly selected public junior high schools. A total of 480 questionnaires, 425 questionnaires were valid, availability was 88.7%. Coverage of this questionnaire included individuals information, mathematics anxiety scale table and mathematical achievement scoring. We used SPSS12.0 for descriptive statistical analysis, t examination, single-factor variable analysis, Pearson correlation and multiple regression analysis.
From the data analysis, the results of this study were the following
1. The general distribution of 9th grade students was of moderate anxiety and mathematical achievement.
2. Some demographic variables （fear, disgust, test anxiety and perceived stress） had significant association with mathematics anxiety.
3. Some demographic variables had significant association with mathematical achievement.
4. Mathematics anxiety and mathematical achievement had moderate negative correlation. The higher the mathematics anxiety, the lower the mathematical achievement was, and vice verse.
5. The variance of using the four anxiety factors to predict mathematical achievement was 33%. "Disgust" is the mandatory factor and "Fear" was the second one.
Based on the result, several suggestions were proposed for math teaching, school administration and further research.
