本研究主要目的為瞭解台灣國中生數學學習概念在數學學習中之重要性。共422位學生(212位男生，210位女生)參與研究調查，以量化研究方式分別調查學生的「數學學習概念」、「數學學習堅毅性」以及他們的「數學學習成效」，並以質性訪談問題與調查25位學生(12位男生，13位女生)，以深入瞭解學生學習數學時的看法。研究主要包含三項目標，將學生數學學習概念分類為低中高階數學學習概念，並以結構方程式模型分析學生之數學學習概念、數學學習堅毅性以及數學學習成效之關聯性，最後欲了解不同性別學生之數學學習模型有何關聯與差異性。
經由二階驗證性因素分析競爭模式比較，研究結果選用最佳配適度，將國中學生之數學學習概念分為低階、中階與高階學習概念，其中低階數學學習概念有「記憶」、「測驗」，中階數學學習概念有「計算與練習」、「增進知識」以及「理解」，高階數學學習概念則有「應用」、「思考方式」以及「看見新觀點」。
經結構方程式模型分析結果可知，傾向使用「低階數學學習概念」的學生，在數學學習的堅毅程度上是不佳的，面對數學課業上的困難較容易放棄且無法繼續努力，數學的學習成效也會更不佳。若是傾向使用「中階數學學習概念」的學生，在數學學習的堅毅表現是較努力且不易放棄的，他們課業上遇到難題時，會透過不斷的嘗試練習，努力去理解問題真正的含意，進而解決難題，這樣的情況也會讓之後遭遇更高難度的題目時，不易放棄或是否定自我能力。但這類型的學生面對壓力時容易釋懷會感到無所謂，可能也因此沒有壓力，而數學科上的表現不積極，可能導致成績不佳。若是使用「高階數學學習概念」的學生，他們在學習時，喜歡使用聯結舊有知識、舉一反三的方式來學習，並且喜歡獲得不同的觀點來看待事物，自然願意挑戰更難的問題，因為他們較能掌握數學最基本的原理以應用到不同情境的數學問題，因此更能掌握常變化的數學問題，數學學習通常也會表現不錯。
而台灣不同性別國中生之數學學習模型，男學生與女學生在數學學習模型上有一些相異的特徵，其中女學生只要傾向使用低階數學學習概念，數學學習成效不佳是可以預見的。另外男生學習數學越傾向高階數學學習概念時，當他數學成績表現不如預期或是學習上遇到困境，會越願意主動尋求他人協助，以協助解決課業上的疑惑，進而能提升數學學科的表現；但具有同樣高階數學學習概念的女生，他們的數學學習成效則是不佳的，具有高階數學學習概念女學生認為，學數學與生活不太相關。
本研究結果也可回饋在國中教學現場中，教師們應該教導學生使用中高階數學學習概念學習數學，以及適時的了解學生問題所在，給予適當的鷹架，並且正視國中階段數學學科與生活脫節的情況，以幫助學生們的數學學習。

This study highlights the importance of Taiwanese junior high school students’ conceptions of learning Mathematics. Two questionnaires, “Conceptions of Learning Mathematics” (COLM) , “Hardiness of Learning Mathematics” (HOLM), and students' Achievement of Learning Mathematics (AOLM) were used in this study. The participants in this study included 422 junior high students (212 males and 210 females). The students’ views on learning Mathematics were investigated in depth by interviewing 25 students (12 males and 13 females). Three goals were included in this study. Firstly, students’ conceptions of learning Mathematics were divided into lower, middle and high levels. Secondly, the relationships between COLM, HOLM, and AOLM were explored using structural equation modeling (SEM). Finally, the gender differences in the Learning Mathematics Model were examined.
After comparing the competing second-order Confirmatory Factor Analysis models, goodness-of-fit indices were used to divide the students’ conceptions of learning Mathematics into lower, middle and higher levels. The results showed that the lower-level conceptions included “Memorizing” and “Testing” . The middle-level conceptions included “Calculating and Practicing” , “Increasing of Knowledge” and “Understanding” , while the higher-level conceptions included “Applying” , “Ways of Thinking” and “Seeing in a New Way.”
As a result, in general, the SEM analysis showed that students who tended to use lower-level conceptions had lower scores in HOLM than others did. The students with lower scores in HOLM usually quit and stop learning more easily when they face the difficulties of learning Mathematics, and then their AOLM become worse. Moreover, it was found that the students who tended to use middle-level conceptions worked hard on learning Mathematics. They seemed to keep working hard, and tried to practice more and understand the meaning of Mathematics problems, even though they faced more difficult Mathematics problems. In addition, the results showed that these students may feel less learning pressure and then show less learning ambition, so they get lower grades in Mathematics. The students who tended to use higher-level conceptions seemed to like to learn by relating their prior knowledge and seeing things from different perspectives. They also showed a willingness to accept challenges of difficult math problems. They seemed to be able to control the fundamental principles of Math which can be applied to different Mathematics problems. As a result, they can get high grades in Mathematics.
Through the Learning Mathematics Model of Taiwanese junior high school students, some gender differences were found. It was found that female students got lower grades when they tended to use lower-level conceptions. Male students who tended to use higher-level conceptions were more willing to ask others for help to solve learning problems, and then had better performance in Mathematics. Differing from previous studies, this study found that female students who tended to use higher-level conceptions had lower achievement in Mathematics. They thought there were not many correlations between learning Mathematics and their life.
This study provides some views and opinions on junior high students’ learning of Math. The results could be useful for helping know more about learning Mathematics. Teachers may teach students how to use both middle- and higher-level conceptions to learn Mathematics. They may also try to realize the real problems of students’ learning Mathematics, and then provide proper scaffolding for students. Teachers should seriously face the problems of the low correlations between learning Mathematics and life.

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