The purpose of this rescarch is to investigate the correlation between deaf or hearing-difficulty students in metacognition and mathematical problem solving. Another goal is to acheive more in-depth understanding of how the students solve algebraic word problems. The first phase of the study is a survey, and the second phase is a case study--thinking aloud are adopted, and there are 10 secondary school students participated in this study There are seven students from Form 1 and three students from Form 2 in special education school in Macao. According to the information provided from the school, researcher located the degree of hard of hearing. Based on the language comprehension test, students can be classified into different language competence groups. A “metacognitive scale” is used as the research instruments to measure students’ metacognitive competence. “Non-routine mathematical problem test”and “Thinking aloud” are adopted to test the total time they used. Finally, based on the test results, subjects are ranked, and the correlation between metacognition and mathematical problem solving are generated. The results of the research as follows: 1. In the view of target-setting, self-control, self-evaluation, self-correction, hearing disable students in F2 have an obvious difference from students in F1 It reveals that students in different grades have a distinction in target-setting, self-control, self-evaluation, self-correction. 2. On the total time used in problem solving and the checking time in mathematical problem solving, hearing disable students in F2 have an obvious difference from students in F1. It indicates different grade of junior students have a big difference in mathematical problem solving. 3. For the hearing disable students, there is a positive correlation with metacognition and mathematical problem solving. Therein to, the highest correlation between metacognition and mathematical problem solving is the self-control, self-evaluation, and self-correction. 4.Different degree of hearing disability among students, there is no obvious difference in metacognition. 5. Expect the negative correlation between target-setting and language understanding others as self-control, self-evaluation and self-correction are in positive correlation. Therein to, self-control and self-correction have the most correlation in statistics. At last, researcher bring forward a serious advice to listening problem teaching and the future study by using the results of research and conclusion. Key words: Metacognition, Mathematical Problem Solving, Algebraic problem-solving , deaf or hearing-difficulty

本研究旨在研究澳門聽覺障礙學生，其後設認知與代數解題之相關情形，期望對聽覺障礙學生在代數解题方面取得更深入的瞭解。 本研究探用調査及放聲思考法，研究樣本爲澳門某特殊教育學校的中一及中二的聽覺障礙學生，共10人(中一學生7人；中二學生3人)。 在本研究中，研究者首先根據該學校提供的資料，找出這些研究對象的聽力損失程度，並根據語言治療師的測試，爲這些學生進行語言理解排名，然後利用研究工具『後設認知量表』了解研究對象在數學方面的後設認知的情形，並探用『非例行性數學題目』，利用放聲思考法，測試出每位學生在解題時所用的分析及驗證所用的時間總和是多少。最後，將上述測試所得的資料，用排名的方式，找出後設認知與代數解題之相關情形。 研究結果發現： 1. 初二聽覺障礙學生在目標設定、自我監控、自我評鑑、自我修正等後設認知方面與初一聽覺障礙學生存在顯著差異，這結果顯示了不同年級初中聽覺障礙學生其後設認知上的目標設定、自我監控、自我評鑑、自我修正確實存在顯著差異。 2. 就代數解題的分析時間與驗證時間的總和上，二年級聽障學生與一年級聽障學生存在顯著差異，這顯示出初中不同年級聽覺障礙學生其代數解題時間上存在顯著的差異。 3. 對於聽覺障礙學生來說，其後設認知與代數解題歷程有顯著的正相關。其中，尤以後設認知中的自我監控、自我評鑑、自我修正與代數解題歷程的相關性為較高。 4. 不同聽障程度的初中聽覺障礙學生，其後設認知並沒有顯著的差異。 5. 除了目標設定與語言理解程度不相關外，自我監控、自我評鑑、自我修正均與語言理解程度者都存在正相關，其中以自我監控及自我修正的相關性較高，在統計上達到顯著水準。 最後，研究者就本研究所得到的研究結果及結論對聽覺障礙的教學及未來的研究提出一系列建議。 關鍵詞：後設認知、數學解題、代數解題、聽覺障礙