Faculty of Education
The Chinese University of Hong Kong
Subject Curriculum and Teaching (Mathematics) 2000-2001
Instructors: / LEUNG Shuk Kwan, Susan梁淑坤(Room 309, Voice: 2609 6962) / EDD5108FSUEN Suk Nam 孫淑南(Voice: 2648 4411) / EDD5108G,
EDD5108S
TANG Mei Yue 鄧美愉(Voice: 9046 1776) / EDD5108R
WONG Ngai Ying 黃毅英(Room 421, Voice: 2609 6914)
e-mail:
web-site: / EDD5108A
Departmental Office (Department of Curriculum and Instruction):
Room 210, Voice: 2609 6905, Fax: 2603 6724
Course Outline
1. Introduction to mathematics education
1.1The changing goal of mathematics education
1.2 Mathematics for all
2. The mathematics curriculum
2.1 The evolution of the Hong Kong mathematics curriculum
2.2 Holistic review of the Hong Kong mathematics curriculum
2.3 The Hong Kong mathematics curriculum at different learning stages
2.4 Textbooks
3. Teaching/learning models
3.1 Psychological basis
3.2 Expository model
3.3 Advance organiser
3.4 Discovery learning
3.5 Individualised learning
3.6 Spiral teaching
3.7 Mastery learning
4. Preparing mathematics lessons
4.1 Lesson planning
4.2 Remedial teaching
4.3 Mixed-ability classes and curriculum tailoring
5. Classroom technique
5.1 Teaching skills and questioning techniques
5.2 Learning environment
5.3 Use of teaching aids and manipulatives
5.4 Information technology and mathematics teaching
5.5 Enhancement of problem solving abilities
6. Evaluation
6.1 Evaluation and test construction
6.2 Analysis of assessment results
6.3 Criterion-referenced tests and alternative assessment
7. Mathematics activities
7.1 Mathematics club and recreational mathematics
7.2 Enhancement of spatial abilities
7.3 Mathematics contests and statistical projects
7.4 Use of history of mathematics in mathematics education
7.6 Mathematical visual art
8. The professional growth of a mathematics teacher
8.1 Continuous education of the mathematics teacher
8.2 The role of professional organisations
Dates of Class Meeting (subject to further amendments)
Group A (HTB G5)Wed/Fri 2:00pm – 4:00pm / Group R (HTB G5)
Tue 6:00pm - 8:00pm
Group S (CCV 203)
Tue 5:30pm – 7:30pm / Group F (HTB G5)
Group G (CKB 108)
Sat 8:30am - 10:35 am
2000 Sep / 6, 8, 15, 20*, 22, 27, 29# / 5, 19, 26 / 9, 16, 23, 30*
Oct / 4, 11#, 13, 18#, 20, 25#, 27 / 3*, 10, 17, 24, 31# / 7, 14, 21, 28#
Nov / 29 / 7#, 14#, 21#, 28 / 4#, 11#, 18#, 25
Dec / 6, 13 / 5, 12 / 2, 9, 16
2001 Jan / 10, 17, 31§ / 9, 16, 30 / 13, 20
Feb / 6, 13, 20§ / 3, 10, 17§
* Group presentation on learning models
# Micro-teaching for full time and individual presentation on teaching capsules for part time.
§Handing in of teaching aid
Coursework Assignment
The main objective of the coursework assignment is to help teacher-students apply various concepts and ideas introduced in this course to their day-to-day teaching and share ideas and experiences of teaching with others. Each of the following assignments constitutes a coherent part of the whole coursework assignment. The way of handing in parts of the project several times during the semester is to enhance learning by ensuring better supervision and guidance throughout the project. Thus, you are required to submit ALL assignments on time. Failure in any one of these parts may result in an unsatisfactory grade.
(A) Group presentation of teaching/learning model
Form five groups of three or four members among yourselves. Choose one model for each group among the following: (a) expository, (b) advance organizer, (c) discovery, (d) individualized, and (e) spiral teaching/learning models. Based on the given reading material, present these models in the 4th class meeting.
(B) Developing a teaching capsule
Choose a topic in the Hong Kong Secondary Mathematics/Additional Mathematics Syllabus.
1. (a) For part-time students, make an investigation among your students to understand their difficulties in learning their topic. Append with their responses and workings if possible. Write a summary of these teaching/learning difficulties and design a lesson plan of a double period of the topic with the above difficulties addressed. Design also a worksheet of another double period.
(b) For full-time students, design a lesson plan of a double period and a worksheet of another double period with at least ideas from at least 1 overseas mathematics textbooks and 1 journal articles incorporated. Teaching aids should be used.
For both groups, hand in the summary, lesson plan and worksheet in the 8th class period. Present your overall instructional design in the 8th to 11th class period (those dates marked with a "#" listed above, precise presentation schedule to be fixed after the choice of topics).
2. Based on the above, make a summary of the different components in the chosen topic which students may encounter difficulties in learning. Design accordingly (a) a game, (b) a teaching aid (or computer assisted learning programmes other than mere Power Point presentations), (c) a worksheet and (d) a diagnostic test relevant to the topic of your choice to be used in the lessons. Hand in the teaching aid in the last class meeting and the other parts on or before 31st March, 2001.
References
Bell, F.H. (1978). Teaching and LearningMathematics. Wm. C. Brown Co. QA11.B43 (CC)
Bolts, B. (1982). Mathematical Activities. Cambridge: Cambridge University Press. QA16.B64 1982 (CC)中譯：林傑斌(1995)。《數學樂園─茅塞頓開》。台北：牛頓出版社QA16.B6412 1999 (CC)。簡體字版：浙江科技出版社，1998。
Bolts, B. (1985). More Mathematical Activities. Cambridge: Cambridge University Press. QA16.B644 1985 (CC) 中譯：黃啟明(1995)。《數學樂園─老謀深算》。台北：牛頓出版社QA95.B65412 1995 (UL)。簡體字版：浙江科技出版社，1998。
Bolts, B. (1987). Even More Mathematical Activities. Cambridge: Cambridge University Press. QA16.B63 (CC) 中譯：林傑斌(1996)。《數學樂園─趣味盎然》。台北：牛頓出版社。簡體字版：浙江科技出版社，1998。
Bolts, B. (1989). Mathematical Funfair. Cambridge: Cambridge University Press. QA95.B62 (CC) 中譯：王榮輝(1996)。《數學樂園─舉一反三》。台北：牛頓出版社。簡體字版：浙江科技出版社，1998。
Bolts, B. & Hobbs, D. (1989). 101 Mathematical Projects. Cambridge: Cambridge University Press. QA11.B64 (CC) 中譯：蔡信行(1996)。《數學樂園─觸類旁通》。台北：牛頓出版社。簡體字版：浙江科技出版社，1998。
Brown, G. (1975). Microteaching. Harper & Row Publishers. LB1731.B73 (CC)
Cundy, H. M., & Rollett, A. P. (1961). MathematicalModels. Oxford University Press. QA11.C8 1961 (UL)
Curriculum Development Council, Hong Kong (1999). Syllabuses for Secondary Schools: Mathematics (Secondary 1-5). Hong Kong: Education Department. QA14.H6 H66513 1999 (CC Gov Doc)
Eves, H. (1990). An Introduction to the History of Mathematics (6th edition). Fort Worth: Saunders College Publishing. QA21.E8 1990 (CC). 中譯：歐陽絳(1993)。《數學史概論》。台北：曉園出版社。QA11.P6175 1999 (CC)
Krulik, S., & Reys, R.E. (Eds.). (1980). ProblemSolvinginSchoolMathematics. National Council of Teachers of Mathematics. QA1.N3 1980 (CC)
Larson, L.C. (1983). Problem-SolvingThroughProblems. Springer-Verlag. QA43.L37 (UL) 中譯：陶懋頎、單墫、蘇淳、嚴鎮軍(1998)。《通過問題學解題》。台北：九章出版社(與Springer Verlag合作)。QA43.L3712 1998 (CC)
National Council of Teachers of Mathematics (1973). InstructionalAidsinMathematics (34th Yearbook). QA1.N3 34th (UL)
Orton, A. (1987). Learning Mathematics: Issues, Theory and Classroom Practice. London: Cassell Educational Limited. QA11.O77 (CC) [second edition: QA11.O77 1992 (CC)]
Orton, A., & Frobisher, L. (1996). Insights into Teaching Mathematics. London: Cassell. QA14.G7O77 1996 (CC)
Orton, A., & Wain, G. (Eds.). (1994). Issues in Teaching Mathematics. London: Cassell Educational Limited. QA14.G7I67 1994 (CC)
Pólya, G. (1945). HowtoSolveIt. Princeton University Press. QA11.P6 1957 (UL)
Pólya, G. (1954). Mathematics and Plausible Reasoning. Princeton: Princeton University Press. QA9.P57 v.1 & v.2 (UL)
Posamentier, A.S., & Stepelman, J. (1995). Teaching Secondary School Mathematics: Techniques and Enrichment Units (4th ed.). New Jersey: Prentice-Hall. QA21.E812 1993 (UL)
Resnick, L. B., & Ford, W. W. (1981). ThePsychologyofMathematics for Instruction. Lawrence Erlbaum Association, Inc. QA11.R47 (CC)
Skemp, R.R. (1987). The Psychology of Mathematics Learning. Hillsdale, N.J.: Lawrence Erlbaum Associates. 中譯：陳澤民(1995)。《數學學習心理學》。台北：九章出版社。QA11.S5712 1995 (CC)
Wilder, R. L. (1952). An Introduction to the Foundations of Mathematics. John Wiley & Sons. QA9.W58 (UL)
李學數(1978-99)。《數學和數學家的故事》(1-8)。香港：廣角鏡出版社。QA99.L48 1978 (UL)
李儼、杜石然(1976)。《中國古代數學簡史》。香港：商務印書館。QA27.C5L47 1976 (UL)
梁宗巨(1992)。《數學歷史典故》。沈陽：遼寧教育出版社。QA21.L5 1992 (UL/NA Gen Ed)
馮振業(編) (1997)。《香港數學課程改革之路》。香港：香港數學教育學會。QA14.H6 H76 1997 (CC)
黃毅英(1997)。《邁向大眾數學的數學教育》。台北：九章出版社。QA11.H8652 1997 (CC)
黃毅英(編) (1999)。《數學內外：數學教育文集》。香港：天地圖書。QA12.S58 1999 (CC)
鄭肇楨(1980)。《數學遊戲》。香港：商務印書館。QA95.C48 (UL)
蕭文強(1978)。《為甚麼要學習數學》。香港：學生時代出版社。第二版(1992) 香港新一代文化協會。增訂本(1995)，台灣：九章出版社。QA7H83 (UL)
蕭文強(1989)。《數學証明》。南京：江蘇教育出版社。
蕭文強(1990)。《1,2,3, ...以外》。廣東：廣東教育出版社。(1992) 香港：三聯書店。(1994) 台灣：書林出版有限公司。QA99.H75 1993 (CC)
蕭文強(編) (1995)。《香港數學教育的回顧與前瞻》。香港：香港大學出版社。QA14.H6 H75 1995 (UL/UCH)
劉應泉(編) (1996)。《數學家族》(1-4)。香港：香港教育圖書公司。QA95.S48 1995 (UL/CC)
錢寶琮(1964)。《中國數學史》。北京：科學出版社。(1992 重印) QA27.C5C48 1964 (UL)
羅浩源(1997)。《生活的數學》。香港：香港教育圖書公司。QA99.L7 1997 (UL)
College Mathematics Journalper QA11.A1T9 (CC)
Journal for Research in Mathematics Educationper QA11.A1J68 (CC)
The Mathematical Gazetteper QA1.M3 (UL)
Mathematics Magazineper QA1.N351 (UL)
Mathematics Teacherper QA1.N28 (CC)
Mathematics Teaching in the Middle Schoolper QA13.M37 (CC)
《數學教育》(EduMath)per QA14.H6 S47 (CC)
《數學教學》per QA11.S58 (CC)
《數學傳播》per QA1.S443 (UL)
Some Websites for Mathematics Teachers
Hong Kong Association for Mathematics Education (HKAME)
HKUST Education Development Program - Mathematics
Curriculum Development Institute (Mathematics Unit)
(Hyperlinks to many other websites in mathematics education are available at these sites.)
TENTATIVE PLAN (not to be released to students)
- INTRODUCTION TO MATHEMATICS EDUCATION
[NY will give a brief introduction at Susan’s class on 9th September]
※Introduction to the course
※The changing goal of mathematics education
2. PSYCHOLOGICAL BASIS
※Behaviouralism (Thorndike, Watson, Pavlov)
※Skinner and programmed learning (conditioning)
※Piaget and cognitive process (information processing)
※Gagne's learning hierarchy
3. CURRICULUM
※The Hong Kong mathematics curricula
※The 2001 curriculum and the holistic review
※The tailoring guide
4. MODELS OF TEACHING (STUDENT PRESENTATION)
※Discovery learning
※Ausubel and meaningful verbal instruction
※Advance organiser
※Individualized learning
5. PREPARING MATHEMATICS LESSONS
※Curriculum tailoring, worksheets
※Behavioural objectives and task analysis
※Lesson plan
※Comments on textbooks
6. CLASSROOM TECHNIQUE
※Teaching skills
※Teaching aids
※Classroom management
7. VIDEO VIEWING
8. WORKSHEET
9. QUESTIONING TECHNIQUE AND PROBLEM SOLVING
[Susan will talk on problem solving/posing in NY’s class on 6th December]
※Questioning technique
※Problem solving strategies
※Enhancement of problem solving abilities
※Affective factors and problem solving performance
※The teaching of logical reasoning/proofs
10. ASSESSMENT
※Evaluation
※Glaser and criterion referenced tests
※Alternative assessments
※Bloom and mastery learning
11. HISTORY OF MATHEMATICS AND MATHEMATICS EDUCATION
[NY will talk at Susan’s class on 3rd February]
※Historical topics in mathematics
※The development of Chinese mathematics
12. TEACHING OF SIXTH FORM CURRICULUM
※The teaching of advanced level pure mathematics
※Advanced-supplementary level mathematics
※The teaching of statistics
13. THE MATHEMATICS CLUB
※Mathematics competition
※Mathematics trial
※Statistical projects
[Workshop: Conic sections]
14. GAMES AND MATHEMATICS
※Dienes and the use of mathematics games
※The enhancement of spatial abilities
※PTU games
[Workshop: The Platonic solids]
[Video: geometry in our world]
15. THE IMPACT OF HI-TECH ON MATHEMATICS EDUCATION
※Micro-computer
※Computer assisted learning
※Graphic calculators
16. PROFESSIONAL GROWTH OF THE MATHEMATICS TEACHER
※Professional growth and professional bodies
※The nature of mathematics and conceptions of mathematics
[Workshop: Curve stitching and paper folding and visual art]
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