國民中小學學生社會心理環境變因與其數學信念及數學焦慮關係之研究

A Study of the Relationship between the Socio-Psychological Factors of Primary and Junior High School Students and Their Belief and Anxiety in Math

本研究從學生社會化觀點，探討國民中小學生社會心理環境與其數學信念及數學焦慮的關係。本研究先採用分層隨機取樣法；次則採用叢集抽樣法。發出問卷1600份，回收問卷1402份，有效問卷1364份。研究工具包括「數學信念量表」、「數學焦慮量表」、「父母影響歷程量表」、「教師行為量表」及「人際關係量表」等五種；統計方法採用皮爾森積差相關、單因子多變項變異數分析、、雙因子變異數分析、單因子單變項變異數分析、區別分析、逐步多元迴歸及典型相關等方法。研究結果綜合歸納為下列十一點：一、國民中小學生性別、年級對其數學信念、數學焦慮無顯著交互作用。二、女學生、國小六年級、低數學成就學生其數學焦慮較高。三、國小學生、單親家庭及低數學成就學生有較負向的數學信念。四、教師對學生行為表現愈積極、正向者，學生的數學信念較正向、數學焦慮較低。五、父母影響歷程行為對學生數學信念、數學焦慮有顯著影響作用。六、同儕人際關係對學生數學信念、數學焦慮高低有顯著影響作用。七、數學信念較正向學生，其數學焦慮較低。八、父母心理支持、學生數學成就為有效預測數學信念之指標；而數學成就更為預測數學焦慮最主要變項。九、個人變項、家庭變項及學校變項等十個控制變項可透過三個「典型因素」有效解釋整體數學信念總變異量的30.0％。而此三個典型因素又可以直接解釋數學信念總變量的31.5％。十、個人變項、家庭變項及學校變項等十個控制變項可透過四個「典型因素」有效解釋學生整體數學焦慮總變異量的26.8％。而此四個典型因素又可以直接解釋數學焦慮總變量的53.7％。十一、父母影響歷程、教師行為及人際關係等社會心理變因可以有效區別高低數學信念(或高低數學焦慮)之國中小學生。

This study is to investigate the relationship between the socio-psycho environments of primary and junior high school students and their belief and anxiety in Math through the viewpoint of the socialization of students. this study adopt the method of stratified random sampling as well as cluster sampling. We issued 1600 questionnaires. among the returned ones， 1364 are valid. “Questionnire of Student’s living experiment” was administered. Basic statistics， t-test， two-way ANOVA， Pearson’s product-moment correlation， MANOVA， stepwise multiple regression， canonical analysis and discriminant analysis were employed to analyse the data collected. Major findings and conclusion were described as follows: 1.Sex and grade differences appear no significant interaction in the belief and anxiety in Math. 2.Female students， six grades in primary schools and studens having low achievement in Math have higher anxiety in Math. 3.Elementary students， students from single-parent family and low achievers in Math have negative Math belief. 4.The more positive tend to be the teacher’s behaviors towards the students’ performance， the more positive the students’ belief and the less the students’ anxiety of Math will be. 5.Behavioral influences from parents are significant on students’ belief and anxiety of Math.