The present study seeks to: (1) explore the problem-solving performance of Macao 15-year-old students in the Programme for International Student Assessment (PISA) 2003 Study; (2) explore the learning and item characteristics influencing problem-solving performance of Macao 15-year-old students; (3) provide recommendations to stakeholders (e.g. Government, principals and teachers) in accordance with the study results. Through analyzing PISA2003 mathematical literacy study data, this study analyses the problem-solving performance of 1250 15-year-old students in Macao. Mathematics learning characteristics statistically significantly related to problem-solving proficiency level are explored, and cognitive components affecting item difficulty of the released items are analyzed. There are three findings. First, the problem-solving ability performance of Macao’s 15-year-old students is very favorable. Higher grade level of the student is associated with higher problem-solving performance. About 42% of the sampled students are good at reasoning, and they are good decision-making problem solvers. Second, to analyse the mathematics learning characteristics of students in relation to the levels of problem-solving proficiency, the results are as follows: (1) the higher the problem solving proficiency level of the student the higher their confidence in solving problems; (2) Students at the highest problem solving proficiency level are able to handle a variety of problems which are not limited to routine problems; (3) The majority of Macao students are able to think about some new methods when solving mathematics problems, and they are good at using control strategies in their 6 mathematics learning, as well as prefer cooperative learning environments. Students locating at different problem-solving proficiency levels use control strategies differently and there are different degree of preference levels for cooperative learning environments. Third, problem-solving, symbols and formalism, as well as reasoning and argument, are three cognitive components which can explain about 72% of the variance of the difficulty of released PISA2003 items. The more the number of the cognitive components and the higher the level of the cognitive components of the released items, the more difficult the items become. Higher problem-solving ability is needed to answer the more difficult items. According to the above findings, this study proposes recommendations for the Government, principals and teachers for informed policy making

本研究主要目的是：(1) 探討澳門15歲中學生在PISA2003的問題解決表現； (2) 探討影響澳門 15 歲中學生問題解決表現的學習及試題特徵；(3) 根據研究結 果為教育持分者 (例如：教育當局、校長和教師等) 提供建議。本研究引用 PISA2003 數學素養調查數據，對澳門 1250 名 15 歲中學生的問題解決表現進行 統計分析，探討與問題解決表現精練水平有顯著關聯的數學學習特徵，以及引用 PISA 公開題目進行影響題目難度的認知成份分析。研究發現有三。第一，澳門 15 歲中學生的問題解決能力表現理想，學生就讀年級越高，問題解決能力越強； 當中約 42%的學生精於推理，是善於判決的問題解決者。第二，分析不同精練水 平問題解決能力學生的學業特徵，得知：(1) 問題解決精練水平越高，解題自信 心越強；(2) 最高問題解決精練水平學生能處理多元化問題，也不限於常規性的 問題；(3) 澳門大部分學生解答數學問題時都會想些新方法，都善於運用數學控 制策略學習數學，都較喜歡合作學習環境，不同問題解決能力水平的學生所運用 的控制策略和對合作學習環境的喜歡程度略有不同。第三，解難、符號和形式， 以及推理和論證這三種認知成份能夠解釋澳門學生回答 PISA2003 公佈題目 72% 的難度變異。題目所涉及的認知成份數目越多，且認知成份層次總和越大，題目 難度也越深，答對題目是需要較高的問題解決能力。根據上述的研究結果，本研 究對教育當局和教師提出建議，以供參考之用