The Comparison Between The Analytical Skills Of Mathematics Open-ended Problems Of Senior High Graduates In Shanghai And Macao

The open-ended question has long been a wide concern in mathematics educational circles. Compared to traditional problems, which are with one standard answer or even one correct solution, the former type has obvious advantage over the nurture of students’creativity. Learning the way to solve open-ended problems can help call into play students’learning motivation, and stimulate their interest in learning, widen their thoughts. The above is beneficial to the nurture of students’ ability to express and to evaluate, and is also beneficial to students’ application in mathematics.Being a capitalist society, Macao SAR differs greatly from the socialistic mainland China in both their political and their economic system. The proposed study concerning quality education between Shanghai and Macao, especially about the current state and situation of their students’ analytical skills of mathematics open-ended problems, through experiments and observations which combine both theories and applications, sums up the two places’ experience gained through the development of education by means of mathematics open-ended problems, explore the regular pattern of such education, provides valuable lessons to scholars of the two places; thus it has essential practical value.There are eight chapters in this thesis.Chapter1provides a brief introduction to the research background, research objectives, significance, research problems, methodology as well as procedure.Chapter2deals with a clear explanation of the mathematics open-ended problems, expounding how mathematics open-ended problems were created and some current situations of related research overseas and in the nation.Chapter3gives details to analytical skills of mathematics open-ended problems, defining analytical skills, the concepts of mathematics open-ended problems, and the explanation of the analytical skills.Chapter4initially confirms the research subjects and research methods (including testing, oral interviews, referring to PISA tools, comparing research testing tools). A pre-test and an attributive analysis were conducted to find out the analytical skills of mathematics open-ended problems of Shanghai and Macao students. Investigation and research-related activities underwent afterwards.Chapter5introduces the situation of the schools involved in the research, explaining the overall situation of the research experiments and questionnaires.Chapter6shows the comparison and analysis of the analytical skills of mathematics open-ended problems of senior high graduates from Shanghai and Macao. It entails the analysis of questionnaire survey.Chapter7entails the analysis of the classroom teaching, the interviews of the teachers and the students, as well as the evaluation of the classroom teaching.Chapter8reflects on the results found from the comparison and the analysis, contributing to an important experiential lesson, which forms valuable data and suggestions to the making and revolution of new teaching references. They have become important reference to help improve the teaching, the curriculum and the teaching tools of the mathematics open-ended problems of the two places.The results of the study state that Macao students perform not as well as Shanghai students in their analytical skills of the relatively more abstract Algebra problems. Macao students, nevertheless, perform a bit better than students in Shanghai as for their analytical skills of Geometry. As a whole, Shanghai students are more advantaged than the Macao counterparts in their overall ability in learning. As for recommendations, students from the two places require a stronger guidance from their teachers. When dealing with Mathematical problems, how to draw the solution in a purposeful, conscious and clearly aimed way from the teacher-student and student-student perspective is crucial. It involves means like multiple solutions for a problem and a unified solution for different problems.