| 摘要: | 本研究之目的在探討數學知識信念量表的因素結構與心理計量品質，以及此因素結構是否具有多樣本的相等性，並探討數學知識信念是否具有領域特定性，以及高中職學生數學知識信念剖面的概況。其次，分析背景變項對數學知識信念的效果，以及探討數學知識信念與動機因素及數學表現的關係。本研究以台灣地區公私立高中職學生為母群，樣本包括960名學生。本研究以自編之「高中職學生數學科學習狀況調查表」為研究工具，所得資料以描述統計、變異數分析、驗證性因素分析（CFA）、潛在剖面分析（LPA）、階層迴歸（完全二因子交互作用交乘項模式）、卡方考驗等，進行統計分析。本研究之主要發現如下：本研究所建構的數學知識信念量表具有良好的信度與建構效度，數學知識信念具有稍弱的領域特定性，而多樣本的CFA也支持了本研究所發展的數學知識信念量表題項的適切性與其概念架構的普遍性。不同性別、科組別、社經地位的受試者在數學知識信念上有顯著的差異，不同年級者則無。數學知識信念各構面對數學自我效能、內在目標導向、興趣價值等具有條件效果與交互作用效果；而對數學控制信念、課業價值、學業延宕滿足、數學表現則僅有條件效果達到顯著。運用LPA發現數學知識信念的叢集解為模型E4，亦即四個叢集的觀察體在數學知識信念的指標變項上的變異、共變、平均皆有差異，複核效化的結果亦支持模型E4有適切的模型品質。不同性別、科組別、社經地位之高中職學生隸屬於數學知識信念叢集的情形有別，但不同年級者則無顯著差異。叢集身份的線性合併對數學自我效能、控制信念、內在目標導向、效用性價值、興趣價值有中等的預測效果，而對學業延宕滿足、數學表現有稍弱的預測效果。兩兩叢集在依變項的比較九成有區辨效果，隸屬不同叢集的觀察體在依變項上的平均也大多有顯著差異。研究者亦呈現四個叢集在動機因素及數學表現的整體剖面。最後，依據上述的結論提出建議，供教學與輔導實務及後續研究之參考。
The purposes of this study were firstly, to explore and conform the factor structure of the Math Epistemological Beliefs Inventory (MEBI) and its factor invariance across different groups, secondly, to analyze the relationship between math epistemological beliefs and background variables, and thirdly, to answer how math epistemological beliefs were related to motivations and in-class math performance. The target population was senior high and vocational high school students in Taiwan, and from which the sample of 960 subjects was randomly selected. The measure was the Math Learning Questionnaire developed by the researcher. Data were analyzed using descriptive statistics, analysis of variance, confirmatory factor analysis (CFA), latent profile analysis (LPA), hierarchical regression (full two-way interaction analysis), and chi-square test of homogeneity of proportions. The findings included: MEBI was with good reliability and construct validity, and some weak domain-specificity. A series of multi-group CFAs supported the MEBI was consistent across different groups. ANOVAs indicated that gender, sectors, and SES were related to math epistemological beliefs. The conditional and interaction effects of the math epistemological beliefs on the math self-efficacy, intrinsic goal orientation, and interest value were significant; however, for math control belief, utility value, delay of gratification, and math performance only conditional effects were significant. LPA indicated the final cluster solution is Model E4, i.e., four clusters with different variances, covariances, and means of math epistemological beliefs indicator variables, and the cross-validation also supported model E4 was with good model quality. Chi-square test indicated students with different gender, sectors, and SES belonged to cluster being different in proportion. The linear combination of cluster identity moderately and significantly predicted math self-efficacy, control belief, intrinsic goal orientation, utility value, interest value, and weakly significantly predicted delay of gratification and math performance. Paired clusters could 90 percents successfully discriminate dependent variables, and the differences of mean of dependent variables between clusters were largely significant. The whole profile of math epistemological beliefs, motivations, and math performance was depicted. Finally, the implication was discussed, and suggestions for teaching, guidance and research were provided. |
