本研究以學生在學校的感受 (學習投入、學習倦怠)與生活中的身心狀況 (憂鬱程度、生活滿意度)，歸類出中學生的數種類型，並進一步比較各類型學生的數學成就與數學的學習情緒（享受、驕傲、憤怒、羞愧、無聊）之間的關係。本研究以問卷方式調查了新北市七所中學裡共696位12-14歲的青少年在學校的感受、生活中的身心狀況以及在學習數學時的情緒，發現過半數的學生對於學校的學習是投入的，但有將近三分之二的學生對於學習感到倦怠。以身心狀況看來，大多數的學生對整體的生活是滿意的。對於數學的學習而言，多數的學生在學習數學時能感覺到享受或驕傲，但過半數的學生對於負向的憤怒、羞愧以及無聊情緒的感受度也不小。
以Latent Class Analysis分析後發現有四個類型的學生，分別是參與型、價值認同型、倦怠型和憂鬱型。這四類型的學校學習投入、生活滿意度逐漸下降，而倦怠和憂鬱情況則是有上升的情形。在積極參與的這組表現中，數學成就與學習情緒方面有顯著差異，包含對學習數學的享受中表現高於其他三組，其他三組則是沒有顯著差異。驕傲的情緒中這一組也高於其他三組，但中間兩組沒有顯著差異。憤怒的情緒四組有逐漸上升，而羞愧、無聊等方面，積極參與的學生表現都低於其他三組，中間兩組則無顯著差異。
對於四組之路徑分析結果顯示，對於多數的(77%)的學生而言，整體學習的投入與倦怠對於學習數學時所產生的情緒有重要的預測能力，而數學學習情緒當中的正負情緒則是對於數學成就有預測之能力。從四種類型的學生也可以看出學生在投入程度以及倦怠程度對於學習情緒的影響最為重要，教師在教學時應注意在認知和情意上以適當的教學方式來激勵學生學習的參與度，並藉由降低學習倦怠來促進正向情緒及抑制負向情緒，藉此提升學生的學習成效。

The present study explored the patterns of middle students’ school well-being (school engagement and school burnout) and overall well-being (depression and life satisfaction). The questionnaires were conducted to survey the school engagement, burnout, well-being, mathematics achievement emotions, and mathematics achievement of 696 secondary school students ranging from 12 to 14 years old. This study found that half of the students were involved in school learning, but nearly two-thirds of the students experienced learning burnout. However, in terms of physical and mental situation, most students were satisfied with their overall lives. Moreover, with respect to studying mathematics, most of the students expressed a certain degree of enjoyment or pride of learning. Nevertheless, more than half of the students felt anger, shame, and boredom.
Based on the Latent Class Analysis, the participants in the study were divided into four types; that is, the Engaged, the Stressed, the Burnout, and the Depressed. Their school engagement and life satisfaction were gradually decreasing in all of these four types while their school burnout and depression were on the rise. The Engaged had significantly higher achievement and positive learning emotions than the other three groups. The Burnout and the Stressed felt similarly in pride, same, and boredom.
The results showed that for most students their school engagement and burnout could significantly predict their mathematics learning emotions. Some of the positive and negative emotions in mathematics learning could predict the achievements of mathematics learning. From this study, the students with high degree of investment and low burnout had a great impact on their learning mood. Therefore, teachers are supposed to apply appropriate teaching methods to enhance students’ engagement. In addition, teachers may improve students’ achievement by reducing learning burnout to promote positive learning emotions and eliminating negative emotions to enhance students’ learning efficiency.

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