本研究旨在探討影響國中學生數學希望感之因素，試圖找出不同數學成就目標類型在追求數學希望感之模式與途徑上有何差異，其途徑分別以數學學業表現及數學課堂投入為中介變項，另亦探討師生互動關係之「接近性」及「影響性」對不同目標類型學生在數學希望感模式上之預測力。本研究以就讀 104 學年度第一學期新竹市公立國民中學三年級學生為主要對象，蒐集共 599 份有效問卷。施測所得資料主要運用結構方程模型來考驗各項假設，並以AMOS Bayesian搭配VB程式設計法檢驗本研究提出之雙中介模型及中介調節效果。
本研究的發現如下:
ㄧ、在趨向精熟目標之希望感模式中，數學課投入在趨向精熟目標與數學希望感間具有部分中介效果。
二、在逃避精熟目標之希望感模式中，數學學業表現及數學課投入在逃避精熟目標與數學希望感間無中介效果。
三、在趨向表現之希望感模式中，數學課投入以及數學學業表現同時在趨向表現目標與數學希望感間具有部分中介效果。
四、在逃避表現之希望感模式中，逃避表現目標對於數學希望感無預測力。
五、師生關係之接近性，在趨向精熟對數學希望感之直接效果以及趨向表現對數學希望感之間接效果，具有顯著調節作用。

The purpose of the study was twofold: one was to discuss the relationships among achievement goal orientations, academic achievement, math engagement and math hope, and the other was to examine the dual mediating effects of academic achievement and math class engagement. Moreover, the moderating effects of influence and proximity of teacher- student relationship in the abovementioned mediation model were examined. Quantitative research design, questionnaire survey, and structural equation model (SEM) were employed in this study. Survey responses from 599 9th graders of six junior high schools in Hsinchu City were used to verify the math hope model. Bayesian collocating with VB programming methods was used to examine the dual mediated effect and also the moderated mediation effect. Meanwhile, the results of the research were summarized as follows:
(1) In mastery- approach goal model, math class engagement had a partial mediating
effect on math hope.
(2) In mastery-avoidance goal model, both academic achievement and math class
engagement had no mediating effect.
(3) In performance-appraoch- goal model, academic achievement and math class
engagement had partial mediating effects at the same time.
(4) In performance-avoidance goal model, avoidance-performance goal cannot predict
the math hope. Therefore, there's no further analysis of mediating effects.
(5) Proximity of teacher- student relationship had moderating effect in the direct effect of mediation model of mastery-approach goal and indirect effect of mediation model of performance-appraoch goal.

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