A Comparison of the Intended Mathematics Curriculum in China, Hong Kong and England and the Implementation in Beijing, Hong Kong and London Frederick Koon Shing LEUNG a thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in The University of London Institute of Education 1992 IN. UNW Abstract This thesis compares the various components of the intended junior secondary mathematics curriculum in China, Hong Kong and England and the implementation in Beijing, Hong Kong and London, and suggests factors to account for the differences in curriculum found. The three places under study were found to differ tremendously in their culture, education system and history of development of the mathematics curriculum. For the intended curriculum, the three places did not differ much in the aims of mathematics education on the utility of the product of mathematics, but great differences were found in the intrinsic aims and aims on the utility of the process of mathematics. The curriculum in all three places intended the use of a variety of teaching methods, but great differences were found in the mathematics content intended to be learned by the students. Results of a questionnaire showed that teachers in the three places differed greatly in their attitudes towards mathematics and mathematics education. Moreover, a pattern of responses emerged, with the responses of the Hong Kong teachers lying between those of the Beijing and London teachers. Through classroom observations, it was found that teachers in the three places differed in their classroom teaching, and analysis of selected topics from textbooks revealed that students in the three places learned very different mathematics in the classroom. Despite these differences, mismatch between the intended and implemented curriculum was found in all three places, although the kind of mismatch differed from place to place. Lastly, a framework of factors at four levels was suggested to account for the differences in curriculum. It was argued that factors at the classroom, school and societal levels all contributed to the differences found, but factors at the cultural level had to be drawn upon for a satisfactory explanation of the findings in this study. 2 Acknowledgement I would like to offer my sincere thanks to Professor Harvey Goldstein and Ms Janet Maw, my supervisors, for their support and encouragement throughout the course of my research. This thesis is an improvement over earlier manuscripts because of their stimulating advice and enlightening guidance. I would also like to thank Professor Celia Hoyles, who gave me valuable suggestions and encouragement at the initial stage of writing this thesis. Thanks are due to all those people in London, Beijing and Hong Kong who helped in the data collection, those who granted the researcher interviews, and those who provided the researcher with information and materials concerning the mathematics curriculum. Special thanks should be extended to Professor Su Shi-dong, who helped liaise with the education authority and institutions in Beijing. I am also indebted to all the teachers who completed the questionnaire and who allowed the researcher to observe their teaching. I would also like to express my appreciation to my colleagues at the Faculty of Education, University of Hong Kong for their support while I was writing this thesis, especially those who advised and helped in the word-processing and art work. Finally, I thank my wife Shirley, for her understanding and encouragement. Without her unfailing support and companionship, I would never have been able to finish writing this thesis. This thesis is dedicated affectionately to her and our beloved son King Ho. Frederick K.S. Leung March 1992 3 To Shirley and King Ho Table of Contents page L,istof'I'ables andFigures .......................................8 ChapterlIntroduction .......................................10 t.e1iixiitations ....................................13 TheResearchProblem.............................17 Chapter2LiteratureReview ...................................20 curriciilurii.....................................21 PastStudies .....................................33 Chapter3Methodology ...................................... 54 DataCollection . ................................. 54 ThePreliminary Visits .............................60 Development of the Instruments for Data Collection ........ 65 TheIi1ot Study ..................................77 Il1e ,fain Study ..................................82 Chapter4 TheContextsoftheCurriculum ......................... 89 The Chinese Culture in Contrast with Western Cultures ......90 The Education System in China, England and Hong Kong .... 98 A Brief History of Development of the Mathematics Curriculum in China, England and Hong Kong ...........108 5 Chapter5 ThelntendedCurriculum . .. 128 Aims and Objectives of Mathematics Education for JuniorSecondarySchoolStudents ...................131 IntendedTeachingMet.hods ..........................138 ThelntendedMathematicsContent .....................143 Chapter 6 Teachers' Attitudes towards Mathematics and MathematicsTeachingandLearning .................... 150 Characteristics of the Teachers Who Responded to tIieQuestionnaire ............................... 150 Teachers' Views of Mathematics - the Mathematics asaPrc)cess Scale ..............................153 Teachers' Views on Mathematics Education .............. 158 SuT1rr2r)r ....................................... 175 Chapterl ThelmplementedCurriculum ..........................177 l''1ethcxI of Data A.nalysis ............................178 ResultsoftheDataAnalysis.........................184 suniniary ....................................... 215 Chapter 8 Content of the Implemented Curriculum: Analysis of Selected TopicsfromtheTextbooksintheThreePlaces .............217 Introduction.....................................217 NegativeNumbers ................................220 Quadratic Equations and Quadratic Functions .............231 IsoscelesTriangles................................238 Statistics.......................................247 Summary .......................................256 6 Chapter9 OverailDiscussion . 258 Consistency of the intended Curriculum and ImplementedCurriculuni..........................259 A Framework for Explaining Differences in Curriculum ......266 Explanations of Differences in the Mathematics Curriculum .... 269 Chapter10 Conclusion .......................................281 SummaryofMajorFindings .........................281 ImplicationsoftheFindings .........................288 I_,izri tat ons .....................................292 FurtherResearch .................................295 ConcludingRemarks ...............................297 BIBI..IO3R.A.P}{'Y..............................................298 APPENDICES AListofPeoplelnterviewed ...............................315 B QuestionnaireforthePilotStudy ..........................317 C QuestionnairefortheMainStudy ..........................322 I. Beijing .....................................323 II. HongKong ..................................325 III. London .....................................327 D Classroom Observation Schedule for the Pilot Study ............329 E Classroom Observation Schedule for the Main Study ............330 F InterviewSchedule(forTeachers) .........................331 0 Juxtaposition of the Content in the three Curricula ..............332 H Subtraction of Negative Numbers ..........................339 7 List of Tables and Figures Tables 3.1 Number of Lessons Observed and Copies of Questionnaire ReceivedinthePilotStudy .............................78 3.2 Distribution of Grades of Lessons Observed in the Main Study ....... 86 5.1 Aims on the Utility of the Product of Mathematics ...............134 5.2 Aims on the Utility of the Process of Mathematics ...............135 5.3 Intrinsic t..iins . ........................................135 5.4 IntendedTeachingMethods ...............................141 5.5 Percentage of Time Spent on Various Mathematics Topics ......... 144 5.6 ASimplifledChartShowingtheMathematicsContent .............145 6.1 Characteristics of Teachers Who Responded to the Questionnaire .....150 6.2 TheMathematicsasaProcessScale .........................155 6.3 Teachers' Views on the Most Important School Subjects ...........159 6.4 Teachers' Views on the Aims of Mathematics Education ...........160 6.5 Influences on Mathematics Content Taught in the Classroom ........164 6.6 Factors Affecting Students' Success or Failure ..................166 6.7 Amount of Homework Expected of Students .................... 168 6.8 Teachers' Attitudes Towards Gender Differences ................. 169 6.9 MeansTableforltemlofSectionC ......................... 170 6.10 Resultsforltern2ofSectionC ............................. 171 6.11 Resultsforltem3ofSectionC ............................. 172 6.12 Resultsforltem4ofSectionC .............................173 8 7.1 NumberofStudentsinaClass .177 7.2 Durations of Various Events in the Classroom .... 185 7.3 Occurrences of Events Related to Classroom Practice .............186 7.4 EventsRelatedtothelntendedCurriculuni .....................198 7.5 Events Related to Views of Mathematics ......................201 7.6 Events Related to Views of Mathematics Teaching and Learning .....211 Figures 2.1 Tyler'sModel .........................................22 2.2 ....................................... 23 2.3 Kerr's ?vlodel .........................................24