shanghai math - worcester polytechnic institute · shanghai math curriculum textbook exercise book...
TRANSCRIPT
![Page 2: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/2.jpg)
OUTLINE
• Education policy
• Math curriculum
• Math teacher
• Math teaching
![Page 3: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/3.jpg)
Education Policy: from Student to Teacher
College Entrance Examination
Normal University:
Undergraduate Programme
Comprehensive University:
Undergraduate Programme
Teacher Certification
Recruitment Examination
Professional Training
Education Master’s Programme
Postgraduate Programme
![Page 4: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/4.jpg)
Shanghai Teacher Recruitment Standards
Established by Shanghai Education Commission:
• Kindergarten: Diploma or higher• Primary school: Undergraduate/Bachelor or higher• Junior/Senior/Vocational secondary school:
Undergraduate/Bachelor or higher
Recruit round 5,000 teachers each year
• 857 secondary education schools (general 768, and vocational 89)• 757 primary schools• 29 special education schools• 1, 462 kindergartens• 36 international schools
![Page 5: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/5.jpg)
Shanghai Math Curriculum
The city has its own curriculum and textbooks
![Page 6: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/6.jpg)
Philosophy of Shanghai’s Math Curriculum (From Shanghai School Math Curriculum Standards, 2004)
• Develop students’ mathematical literacy
• Focus on fundamental aim: Mathematics for all
• Diversify curriculum for different learning needs
• Integrate technology into the math curriculum
• Pay attention to learning process
• Guide students to explore
• Strengthen educational function of evaluation
• Encourage individualized development of students
![Page 7: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/7.jpg)
Math Textbooks
• Almost all Shanghai schools use the same math textbooks.
• Textbook writers work in committees of experts:
– Organized by Normal university
– Use feedback systematically gathered from math teachers
– Drafts inspected and approved by Shanghai Education Commission
for publication.
• Textbook writers also prepare supplementary materials:
– Teacher guides and reference materials for teaching.
– Exercise books for students to practice math after school
![Page 8: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/8.jpg)
Shanghai Math Curriculum
Textbook Exercise book Teacher guide
![Page 9: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/9.jpg)
Textbook Exercise book Teacher guide
![Page 10: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/10.jpg)
Emphasis on math from context
Sample: Positive number and negative number copied from Grade 5 textbook
![Page 11: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/11.jpg)
九章算术
数书九章
Math in Real Life
“Nine Chapters on Mathematical Art”• Used for 2,000 years, till about 1600• Covered practical topics, e.g.,
• Chapter 1: Fields• Chapter 2: Millet and Rice
“Mathematical Treatise on Nine Topics”• Compiled in 13th century• 18 volumes, also on practical topics, e.g.,
• Topic 1: Estimation• Topic 2: Seasons and Weather
![Page 12: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/12.jpg)
Emphasis on mathematical reasoning
Sample: Isosceles triangle copied from Grade 7 textbook
![Page 13: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/13.jpg)
Euclid’s Elements
徐光启XU, guangqi(1562-1633)
Euclid(BC330-BC275)
![Page 14: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/14.jpg)
Math Teacher
![Page 15: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/15.jpg)
Teacher Profile
• Strong grasp of mathematics
• Professional skills to teach mathematics in school:
– Plan lessons
– Conduct lesson in class
– Mark homework
– Mentor students
– Evaluate students’ progress in learning
![Page 16: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/16.jpg)
Teacher Development
• Stronger system for professional development
– Organized structures for discussion and sharing of experiences:
• Math teaching research group
• Lesson planning group
– Systematic mentoring of new or junior teachers
– On- and off-campus teaching and research activities:
• Lesson observation
• Lesson explanation
• Lesson evaluation
![Page 17: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/17.jpg)
Math Teaching
![Page 18: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/18.jpg)
Instructional Model: Demonstration
(N.A.Kaiipob,1893-1978)
• Russian-inspired
• Main instructional model till the 1980s
• Model’s 5 typical parts:– Introduction or Review
– Teaching of new topic
– Practice to consolidate knowledge
– Summary of lesson
– Homework assignment
![Page 19: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/19.jpg)
Instructional Model: From One to Many
![Page 20: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/20.jpg)
Math Lesson
• Structured
• Orderly
• Coherent
• Complete
![Page 21: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/21.jpg)
Teaching: Look for Balance
• Aligns with China’s traditional philosophy
Lao Tzu(About 570 BC)
Confucius
(551~479 BC )
![Page 22: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/22.jpg)
Memorization & Understanding
• Memorization is the foundation for understanding
• Leading understanding from memorization
• Understanding promotes memorization
Prof. ZHANG, Dianzhou
![Page 23: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/23.jpg)
Multiplication
1 2
x 23
-------
36
24
---
276
1. Why move “24” forward? 2. No idea. But I did it right!
……3. Finally I realized one day.
12x23=12x(3+20)=12x3+12x20=36+240=276
![Page 24: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/24.jpg)
Concrete & Abstract
• Concrete and abstract are two aspects of mathematics
– Concrete is easy to understand, but
– Abstract is the only way to generalize ideas
![Page 25: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/25.jpg)
From Manipulation to Algorithm(From Mrs. Wu)
42÷2=
40÷2=20
2÷2=1
20+1=21
21 42÷3= 30÷3=10
12÷3=4
10+3=14
14
34 4 21
……3
34
…
…
3 0 1 3
……3
Row calculation Columnar calculation
10+4=14
![Page 26: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/26.jpg)
Diversifying Teaching Strategy
• Conceptual variation:– Change non-essential properties of a concept, thus
highlighting its immutable property.
• Procedural variation:
– Start from simple questions, resolve similar and
related problems by changing conditions.
• Multiple solutions to an exercise
• Multiple questions to an exercise
• Multiple variation to an exercise
Prof. GU, Lingyuan
![Page 27: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/27.jpg)
A Case of Parallelogram Area
(A lesson designed by Mrs. Gan)
![Page 28: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/28.jpg)
Figure changes, area same
Position changes, figure same
![Page 29: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/29.jpg)
Method changes, conclusion same
Situation changes, formula same
Do you know another method?
![Page 30: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/30.jpg)
Classroom Interactions• Most effective: Teacher Demonstrating & Student Exploring
Teac
he
rs Not advisable:• If only teacher talks
or does not talk at all
Good practice:• Ask questions, elicit
and listen to answers
• Use heuristic strategy
• Provide interpretation, feedback
Stu
de
nts Not advisable:
• If left to explore entirely on their own
• If they don’t participate at all
Good practice:• Answer questions in
class, explore, communicate, demonstrate, discuss
• Think deeply, reflect
![Page 31: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/31.jpg)
Main Classroom Activities in Shanghai Math Lessons:Prominence of Interaction Time
20.8228.73
18.81
38.53
18.1924.75
45.81
17.82
45.4
69.1345.99
59.09
52.48
62.12
62.26
52.06
59.44
49.76
10.05
0
7.02
5.018.01
2.13
17.26
4.830
25.2815.08
3.978.73 4.98
05.48
0
10.95
0
10
20
30
40
50
60
70
80
90
100
A B C D E F G H I
Lecture demonstration Interaction Exercise Discussion
Source: data from my PhD thesis, ECNU, 2008)
![Page 32: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/32.jpg)
Mastery: Going Forward Step by Step
![Page 33: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/33.jpg)
Concluding Remarks
• Shanghai mathematics education is not perfect
• The way forward involves:
– Seeking a balance between tradition and
transformation
– Continuous reform to address deficiencies
![Page 34: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/34.jpg)
34
How Chinese Learn Mathematics: Perspectives from Insiders
![Page 35: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/35.jpg)
How Chinese Teach Mathematics: Perspectives from Insiders
35
![Page 36: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/36.jpg)
Thank you so much
![Page 37: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/37.jpg)
![Page 38: Shanghai Math - Worcester Polytechnic Institute · Shanghai Math Curriculum Textbook Exercise book Teacher guide. ... How Chinese Learn Mathematics: Perspectives from Insiders. How](https://reader031.vdocuments.us/reader031/viewer/2022021801/5b387d927f8b9a1a678b6dee/html5/thumbnails/38.jpg)