Transcript LiJun - Center for the Study of Mathematics Curriculum

Curriculum Development
in China
Perspectives from
curriculum design and implementation
Li Jun
East China Normal University
A very brief history review
Ancient
Rites, Music, Archery, Chariot-Riding, Calligraphy, and Arithmetic
Apply the calculating techniques in solving the real world problem
Nine chapters on the mathematical art
After 1840
Western mathematics and modern school systems were introduced
Ancient China mathematics was replaced by western mathematics
gradually in the modern system
Chinese translation of European, Japanese and American textbooks
A very brief history review
1949-1958
The Soviet Model was imported
Textbooks were adapted based on those of the Soviet Union
National unified textbook policy (PEP, an affiliated Press of the MOE)
After 1958
Curriculum was designed based on practical conditions of China
Attempts at a balance between Confucian and Western-style
education. The characters of former Soviet Union textbooks in
1950s sediment in China.
Some of the central control made less rigid.
Characteristics of the Chinese
Mathematics Textbooks (before 2001)
Coherent, systematic
Few topics, more
teaching times
Topics relate to
each other
Theorem-based
curriculum
Accumulation of
difficulty
More topics in
each item
Multi-steps and
theorem-based
reasoning
Bao, (2004)
High composite
difficulty
Emphasized the rules and regulations of basic knowledge, and the rigor of proof,
including the basic training of logic reasoning.
How many different mathematics textbook
series are developed and approved for ……
Primary: 7
Junior secondary: 11
Senior secondary: 7
Textbook is a mediator between general
intentions and classroom instructions
INTENDED
Intentions,
Aims & Goals
POTENTIALLY
IMPLEMENTED
Textbooks and Other Organized
Resource Materials
(Valverde et al., 2002)
In China, “less and less” is not true
“more and more”
IMPLEMENTED
Strategies, Practice
& Activities
ATTAINED
Knowledge, Ideas,
Constructs, Schemas
Birth of textbook
Appears on the MOE web site for textbook selection, with price
Check and Approved by the NTMAC
Modify Textbook
Textbook Review by National Teaching Material Authorization Committee
Experiment Report
(Not necessary now)
Textbook Writing
Approved by MOE
A Proposal & Sample Chapters
Textbook selection
• Usually, all schools within a city select the
same textbook series in the same year
educational bureau directors
teaching supervisors
headmasters
classroom teachers
parents
Textbook selection Committee
2 days reading,
decision making
discussion & vote
textbook evaluation report
is provided by Province
Textbook competition becomes strong now.
Low price, High quality, Good service
Students buy textbooks, exercise books & calculators
Textbook Authors
Famous Mathematician
General Editor
Subeditor
Writer
Subeditor
University Faculty
Writer Writer Writer Writer Writer Writer
University Faculty Teaching Researchers
Schoolteachers
editors
In addition to author textbooks for publisher, they have to
finish their regular jobs. They are rewarded by the publisher.
But before 2000, the PEP textbooks were mainly designed and wrote by inhouse editors. The authors were also required to collect data at schools and
prepare for the experiment reports.
Curriculum Materials
Textbooks
Teacher’s manuals
Student exercise books
Prepared by the same
textbook writing team
Other Supplemented Materials:
Hypertexts in electronic devices, such as CD ROMs,
web-based educational products, etc.
Teacher Journals, problem booklets, workbooks,
other teachers’ teaching plans, etc.
Various Intensions of the Textbooks
• Mathematical:
– modernization, big ideas The curriculum
• Pedagogical:
– meaningful learning
• Sociological Contexts:
– technology, application
• Cultural Traditions:
– history, value
development after
2000 in China was
mainly driven by
international
comparative studies
and guided by
university faculty.
Teaching time for different topics
Grades 7- 9
6% 1%
6%
introduction
38%
17%
algebra
geometry
statistics
project learning
stage review
32%
Statistics and probability: 69 teaching hours
Total: 410 teaching hours
Research Influence
SOLO Level
P
Data-based
Reasoning
Blank, fully irrelevant, illogical, egotistic answers or inability to become
engaged in item answers.
Summary Description
U
Explains that probability just means may or may not happen and believes chance cannot be measured
mathematically so chance comparison is impossible.
Considers an incomplete set of outcomes in solving problem.
M
qualifying uncertainty or estimating subjective chance value. For example, assigns an equal chance to
each possible outcome for fairness.
Interprets most likely to happen as meaning it should happen or interprets chance by frequency but
without fully understanding the role of repetition.
Uses rudimentary non-proportional reasoning in chance comparison.
R
Groups all possible outcomes in favor of a target event together and uses ratio as a measure of
probability.
Uses proportional reasoning in chance comparison.
Knows that a larger number of repetitions is a more reliable predictor and expresses the idea of making
a few repetitions automatically.
E
Assigns a calculated probability value in complicated situations, for example, involving two bags, two
spinners and bases chance comparison on the values.
Uses a generative strategy to construct sample space in a two- or three-stage experiment to work out
probability.
Suggests collecting data from a series of experiments and finding trends across sampling.
Experience to
Uncertainty
May consider all possible outcomes for a one-stage and sometimes
for a two-stage experiment in
Estimate Chance by
Relative Frequency
Predict Probability by
Formula
Examine Probability by
Different Approaches
Make Learning be Attractive
• Connection
– Students’ mathematical reality (cognitive
structure)
– Students’ living reality
• Context
– Game “Run to 30”
fairness of games
• Concrete
– Standard deviation formula
• Challenge
“make up”
reasonable
not all mathematics could be or should be
challenge the limits of oneself or exceed others
– Spinner size
misconception
Voices of mathematicians, standards
writing group, and schoolteachers
• The principles
should be
reconsidered；
• The framework
should be
reconsidered；
• Geometry teaching
should be
reconsidered；
• Curriculum
development should
not be in haste
Stick to the principles；
Encourage practical research；
Enhance communications with other
interested parties
Basically agree with the principles;
Suggest to revise both standards
and textbooks immediately;
Need practical supports rather than
high expectations;
Worry about students’ achievements
in assessments and their future
studies in senior high schools
(Bao,2004)
Old: PEP, 2001
New: ECNU, 2001
Grade 8 textbooks
Comparison on composite difficulty
between new and old textbooks (Bao, 2004)
Investigate into Textbooks Use (Grades 7~9)
• Zhu & Song, (2004): Investigation and research of
adaptability to new mathematics curriculum standardsbased textbooks in the south-west area
– More than 1000 schoolteachers took the questionnaire
– More than 50 schoolteachers and students were interviewed
– Four series of new standards-based textbooks at junior high
school level were investigated
• Yang, (2005): An investigation of new standards-based
mathematics textbooks use in junior high schools
– 76 schoolteachers and 862 students from 16 junior high schools
in the region of Hefei took the questionnaires
– Two series of new standards-based textbooks were investigated
How Well Textbooks Satisfy Schoolteachers?
• Textbooks published before 2000
– Before 2000, the PEP series dominated the
textbook market, constituting more than 70%
or more of the market’s supply. The PEP series
modified time after time in the past 50 years
and satisfied schoolteachers well at that time.
• New standards-based textbooks
– The new standards and the first volume
textbook was published at the same year. So
each series of new standards-based textbooks
have to be modified year by year but major
changes on the curriculum arrangements are
happening after 4 years experiments.
Southwest Schoolteachers’ Evaluations of the
Standards-based Textbooks Zhu & Song, (2004)
Curriculum
Arrangements
City teachers
Average
scores
3.88
Countryside
teachers
3.94
B
Contents
Difficulty
City teachers
3.01
B
Countryside
teachers
2.90
C
Practical
Operability
City teachers
3.18
B
Countryside
teachers
3.18
B
Connections to
other school
subjects
City teachers
2.63
C
Countryside
teachers
2.75
C
A: 4.00~5.00; B: 3.00~3.99;C: 2.00~2.99;
D: 1.00~1.99; E: 0.00~0.99
Grades
B
To what extent do you feel satisfied with the
new standards-based textbooks? Yang, (2005)
• The majority of teachers and students felt satisfied with
the new editions mathematics textbooks, but the quality of
the textbooks should be improved. Especially, “Examples”
and “Exercise Problems” need to be redesigned very
carefully. The spiral curriculum model should be applied
appropriately.
Very Much
Not at all
0
1
2
3
4
5
5.3%
32.9%
46.0%
14.5%
0%
2.2%
9.5%
31.2%
37.8%
17.5%
Teachers
1.3%
Students
1.7%
The role of textbooks in teachers’ teaching
• The majority of the teachers depended highly on the textbooks,
and they depended on textbooks in deciding what to teach
more than in deciding how to teach. Teachers usually did not
depend on textbooks in “review lessons”.
• Over 90% of the teachers admitted that they did add some
contents not required by the new curriculum but appeared in
the old textbooks, such as some important theorems, formulae
and examples.
• Teachers used almost all the textbook examples in their
classroom teaching. However, they also selected examples from
other teaching materials and exercise books or they simply
designed or modified examples by themselves.
The use of columns in textbooks
• All columns, except “project learning”, were
emphasized by the teachers. But the
students seem enjoy “project learning”
• The two columns that students like most are
“explore” and “reading material”
• The three kinds of teaching methods that
students like most in order
– whole class discussion leading by teacher
– Manipulation
– questioning and answering between teachers and
students
the burden of junior high
school students
• About 75% of the students answered
that the time they spent doing
exercises outside textbooks is as long
as or longer than the time they spend
on doing exercises in textbooks.
Textbook Reading
• over 60% of the teachers said they
usually or often requested their
students to read textbook before (or
after) lessons and to be active in
classroom, while the students read less
than they were expected.
Overview
• A very brief history review and the
forming of the characteristics of our
textbooks
• The number of series, the birth of, the
selection of, the authors of, the
intensions of our textbooks
• The investigations into textbooks use