本研究先藉由文獻分析法瞭解擴散性思考、數學問題發現與數學學業成就三者的內涵，繼而依據它們的內涵並佐以學習、問題解決的角度，建立起三者間關係的假設，並透過實證調查研究法來驗證這些假設。本研究之研究對象為台北縣市五所國中的318位國三學生，研究工具為「新編創造思考測驗」、「數學問題發現測驗」、「第一次數學科基本學力測驗」，並以次數統計、集群分析、相關分析、變異數分析、逐步迴歸分析進行資料分析。本研究主要的研究結果如下： 一、學生能夠發現各種思考產物類型與數學類型的問題。其中，關係性問題與發現性問題最多人提出，而單位性、類別性與驗證性問題則較少人提出。 二、學生的數學問題發現型態有個別差異。 三、擴散性思考與數學問題發現間為顯著中低度相關。 四、擴散性思考與數學學業成就多為顯著中低度相關。 五、數學問題發現與數學學業成就間為顯著中低度相關。 六、能問大量且層次高數學問題的學生其數學學業成就比較不會問數學問題的學生為佳。 七、擴散性思考之流暢力、數學學業成就、擴散性思考之變通力可以有效預測數學問題發現之問題數。 八、擴散性思考之流暢力、數學學業成就、擴散性思考之變通力可以有效預測數學問題發現之問題獨特性。 九、數學學業成就與擴散性思考之流暢力可以有效預測數學問題發現之問題品質。 十、數學問題發現之問題品質、數學問題發現之問題數可以有效預測數學學業成就。 本研究最後針對數學教育以及未來研究提出若干具體建議。 / First, this study probed into the contents of divergent thinking, mathematical problem finding, and mathematical achievement by literature review. Then the researcher made hypotheses of the relationships between divergent thinking, mathematical problem finding, and mathematical achievement based on the contents of them and the views of learning and problem solving, and designed survey research to examine these hypotheses. The subjects were 318 9th grade students from five junior high schools in Taipei county and Taipei city. The data- collection instruments included：(a) New Creativity Test; (b) Mathematical Problem Finding Test; (c) Basic Educational Indicator Tests of Mathematics. After utilizing frequency, cluster analysis, correlation analysis, ANOVA, and stepwise regression, the main results of this investigation are：(a) Students can find problems of all kinds of intellectual products and mathematics. Among them, problems of relations and problems to find were found most and problems of units and classes and problems to prove were found least ; (b) There are individual differences between mathematical problem finding styles; (c) The correlations between divergent thinking and mathematical problem finding are significantly positive; (d) Most of the correlations between divergent thinking and mathematical achievement are significantly positive; (e) The correlations between mathematical problem finding and mathematical achievement are significantly positive; (f) Students who can finds many high-level problems have higher mathematical achievement than those who can not; (g) Fluency of divergent thinking, mathematical achievement, and flexibility of divergent thinking can be used to predict the number of problems of mathematical problem finding effectively; (h) Fluency of divergent thinking, mathematical achievement, and flexibility of divergent thinking can be used to predict the rarity of problems of mathematical problem finding effectively; (i) Mathematical achievement and fluency of divergent thinking can be used to predict the quality of problems of mathematical problem finding effectively; (j) The quality of problems and the number of problems can be used to predict mathematical achievement effectively. Finally, the researcher brings up some suggestions on mathematical education and the future research.

本研究主要目的是以文獻分析、問卷調查、潛在成長模式等方法探討數學焦慮、數學學習動機與數學學業成就等三個變項的縱貫模式及因果結構模式。根據五百二十九位國三學生所填的五波調查問卷資料，進行兩部分研究。 研究一乃在估算數學焦慮、數學學習動機、數學學業成就的潛在改變量模式及 數學焦慮、數學學習動機、數學學業成就兩兩之間的因果結構模式。結果發現1.數學焦慮縱貫模式上，符合「焦慮遞增理論」；2.數學學習動機縱貫模式上，符合「動機先升後降理論」；3.數學學業成就縱貫模式上，符合「成就先升後降理論」； 4.數學焦慮與數學學習動機因果結構模式上，符合「動機焦慮交互激發效果理論」；5.數學焦慮與數學學業成就因果結構模式上，符合「焦慮成就交互抑制效果理論」；6.數學學習動機與數學學業成就因果結構模式上，符合「動機成就交互激發效果理論」。 研究二則依據研究一二變項因果結構統計驗證成立的三套理論，建構出三變項因果結構六模式，並驗證有無中介效果。結果顯示，1.前焦慮、中動機、後學業成就因果模式上，符合「動機未完全中介前焦慮、後學業成就理論」；2. 前動機、中焦慮、後學業成就因果模式上，符合「焦慮未完全中介前動機、後學業成就理論」；3.前焦慮、中學業成就、後動機因果模式上，符合「學業成就未完全中介前焦慮、後動機理論」；4.前學業成就、中焦慮、後動機因果模式上，符合「焦慮未完全中介前學業成就、後動機理論」；5. 前動機、中學業成就、後焦慮因果模式上，符合「學業成就未完全中介前動機、後焦慮理論」；6.前學業成就、中動機、後焦慮因果模式上，符合「動機未完全中介前學業成就、後焦慮理論」。 除了上述結果外，研究也對數學焦慮、數學學習動機與數學學業成就縱貫模式的趨勢與時間效果量，國三學生轉折點界定，數學焦慮、數學學習動機與數學學業成就適當模式產出及個別中介角色剖析有深入探討。 / This study, using literature review, questionnaire survey, and latent growth model, investigated the longitudinal model and causal model among math anxiety, learning motivation, and academic achievement. After collecting 529 students with 5 waves, I conducted two studies. The purpose of study 1 was to estimate the latent change model and the causal model of math anxiety, learning motivation, and academic achievement. Results showed that 1. The anxiety increasing theory was supported by the math anxiety longitudinal model. 2. The first increasing then decreasing theory was supported by the math learning motivation longitudinal model. 3. The first increasing then decreasing theory was supported by the math academic achievement longitudinal model. 4. The reciprocal activated effect theory was supported by the math anxiety and learning motivation causal models. 5. The reciprocal inhibitive effect theory was supported by the math anxiety and academic achievement causal models. 6. The reciprocal activated effect theory was supported by the math learning motivation and academic achievement causal models. According to the final three theories stated above and proved by study 1, I constructed the six causal models in order to verify the mediated effects of math anxiety, math learning motivation, and math academic achievement. I found that 1. Math learning motivation did not mediate fully the effects on early math anxiety and late math academic achievement. 2. Math anxiety did not mediate fully the effects on early math learning motivation and late math academic achievement. 3. Math academic achievement did not mediate fully the effects on early math anxiety and late math learning motivation. 4. Math anxiety did not mediate fully the effects on early math academic achievement and late math learning motivation. 5. Math academic achievement did not mediate fully the effects on early math learning motivation math and late math anxiety. 6. Math learning motivation did not mediate fully the effects on early math academic achievement and late math anxiety. In addition, the research also explored the longitudinal model trend and effect, the key period for 3rd year junior high school students, the proper models, and the mediated roles among math anxiety, learning motivation, and academic achievement.