Research process, Changes and Implementation of
Mathematics Curriculum Standard of China

Capital Normal University, Beijing, P.R.China
Shangzhi Wang（2007.12.06）
Abstract
This paper introduces briefly the research process, changes and implementation of mathematics
curriculum standard of China. The paper consists of four parts. The first part outlines the research
process and mechanism of curriculum standard of both compulsory education and senior highschool education in the hope of shedding some light on mathematics education in China. The
second part is focused on the major changes in Chinese mathematics curriculum standard such as
curriculum sense、objectives、contents and teaching methods, etc. In the third part the author gives
a detailed account of some implementation work including social dissemination, textbook editing,teacher training, and experience sharing, etc. The curriculum reform is an government action
carried out from top to bottom, while curriculum implementation should be carried out in bothways, i.e. from top to bottom and from bottom to top. Here two projects are described. They are
the project of teaching research mechanism on school base and the project of long-distancetraining on the Internet. In the last part some problems are discussed.

Kay wards: mathematics curriculum standard, change, implementation

1、Research process and mechanism of mathematics curriculum standard of
China
1.1、Background of reform
To draw up the mathematics curriculum standard, we should first take into account thescientific, economical and social changes of our age. Since the 1950’s science and technology
have been developing at an increasingly fast speed, which turns many of our dreams into reality, toname a few, man’s setting foot on the moon and the rapid development in information technology.
Along with the development in science and technology, social economy has also achieved
enormous progress. Such changes in both technology and economy result in great social changes.
“ People-orient” has become the fundamental principle in dealing with all kinds of social
problems.
Knowing the development of mathematics is of essential importance for us. In the 20th
century, mathematics has achieved unprecedented progress. Many famous “open problems” arehave been solved, such as Fermat’ great problem. Mathematics is beginning to play an important- Shangzhi Wang 1 -role in more and more fields. Moreover, the role of mathematics is no longer restricted to scienceand technology. “High-tech is inherently the technology of mathematics.” It is widely accepted. In
many aspects, “ mathematics is directly producing social assets.”
We should also be aware of the changes in China. In the last thirty years, China has shifted fromplanning economy to market economy. Besides, China has achieved dramatic progress in science,technology, economy, as well as education. The ratio of university recruitment has reached 20%,
ten times more than that of the 1960’s. The development of the country require the cultivation ofcreative talents.
These changes make us reflect on our education in general and the education ofmathematics in particular.

1.2 Research process and mechanism
Towards the end of the twentieth century the Education Ministry put forward literacy
education for all-around development specially in elementary education and established a series ofpolicies which was put into effect to promote the education for all-around development. One ofthe documents is “The Elementary Education Curriculum Reform Program”. The program raised
an important task to draw up curriculum standard of all subjects in the elementary education andestablishes the objectives of curriculum standard, as well as work mechanism.

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Objective of establishing curriculum standard

To establish a new curriculum which can meet the requirement of the 21st century and whichreflects the nature of elementary education and the spirit of quality education in an attempt topromote the all-round development of every student and to enable them to become the master of
their own learning.

z

Setting up the research group

In March of 1999 the national research group of mathematics curriculum standard came into
existence. The research group consists of 15 core members in which the proportion of members
between university and elementary, middle school is about seven to three. The research group also
invited some other researchers like classic researchers to take part in the research work, whichbrought about some good research results.
In January of 2000, the Ministry of education started to set up the research group of all thesubjects in senior high school. Through bidding and evaluation, the research group was finallyestablished in April of 2000. The 19 core members of the research group, coming from normal
universities, middle schools, publishing houses, examination centers, are mathematicians,
researchers in mathematics education, teachers, teacher trainers, researchers in testing, etc.
Including the peripheral personnel, more than a thousand people got involve in the drawing up of
the curriculum standard.

z

The research group develops some fundamental study and some special
study. The study topics are as follows.
List of fundamental study topics:
1、New development of international mathematics curriculum reform- Shangzhi Wang 2 -2、Evaluation of Implementation Status quo of Chinese Mathematics Curriculum
3、Relation Research between Mathematics curriculum and psychology development rule ofstudent of elementary、middle school.
4、21st Century Social Development and Forecast Analysis of Requiring Mathematics
5 、 Modern Society, Economics, Science, Technology, Mathematics Development andMathematics Curriculum of Elementary and Middle School
6、International Comparison Research of Mathematics Curriculum
List of some special study topics:
7、Mathematics Curriculum Harmony Research of Compulsory education Stage and SeniorHigh school Stage
8、Mathematics Curriculum Content Research Of Compulsory education Stage and Senior Highschool Stage
9、Mathematics Curriculum Evaluation Research
10、Experiment Research Of New Content ( for example: Algorithm, some content of statistics
and probability, some content of calculus, some topics taking as an elective course, etc.)z

Teaching Experiment

We carried out experimental teaching of new contents ( for example, Algorithm, some contentsof statistics and probability, some contents of calculus, some topics taking as an elective course,etc.) in more than 40 schools from three provinces（Beijing、Guangdong、Xinjiang province）
and invite some teachers to teach these new contents.

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Draft and version of mathematics curriculum standard

We have undergone more than ten times of modification to get mathematics curriculum
standard (experiment version) done. In this process we arrange a series of symposiums to hear theopinion from teachers、educators、mathematicians、scientists、engineers、enterprisers, etc. We also
discuss with foreign experts who come from countries like France, Germany, Japan, Korea,
Netherland, Russia, Singapore, United States of America, etc , and some regions, for instance,
Hongkong, Macao and Taiwan. The Educational Ministry of China organizes the highest level ofexperts and official to examine and checkup formally the mathematics curriculum standard of
China.

2、Major changes of the mathematics curriculum standard
2.1 Major changes of mathematics curriculum rationale and objectives
While designing the mathematics curriculum, we mainly followed the following rationale:
1. Advocate the active role of the students and the leading role of the teacher. Emphasize theknowledge and skills, as well as the process of learning in which the students practise the ability tosolve mathematical problems and accumulate the experience of mathematical activities.
Meanwhile pay attention to the changes in students’ values, affect and attitudes The realization of
the three-dimension objectives will, in turn, enhance the all-round development of the students.
2. Focus on both the process of teaching and the process of learning, with more attention paid tothe learning process in order to promote the students’ learning ability. Advocate such learning- Shangzhi Wang 3 -methods as active participation, inquiry, and cooperation. Emphasize the role of the integration of
information technology and mathematics curriculum in enhancing both teaching and learning.
3. Stress the importance of fundamental knowledge, basic skills, living experience, andmathematical thinking. It is essential to develop students’ application awareness and ability. The
cultivation of students’ creativity should be started from children. Emphasize students’ ability toanalyze and solve problems, but also their ability to discover and raise questions. Both the ability
to deduce and ability to induce should be fostered in the students.
4. Provide a variety of coursed so as to cater for different personalities, interests and needs ofindividual student. In senior high school, an even larger range of choices should be provided.
5. Give prominence to the basic structure and the nature of mathematics while choosing thecontents.
6. Establish a proper and scientific evaluation system which emphasizes both students’
academic achievement but also their learning process.
In the following, we are going to introduce the rationale and objectives of mathematics
curriculum standard (MCS) for compulsory education and senior high school education.
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Basic Rationale of compulsory education MCS(1) The mathematics curriculum for the stage of obligatory education should exhibit
fundamental, universal and developmental characters. It seeks to realize:☺
Everybody learns valuable mathematics;☺
Everybody can acquire mathematics essential to him or her;☺
Different person can have different types and levels of development in mathematics.
(2) We cannot do without mathematics in our daily living, work and study. Mathematics
helps us process data, engage in computation, draw inferences and prove hypotheses.
Mathematical models can describe natural and social phenomena effectively. Mathematics casts
the foundation upon which all major technological advances are anchored, and it furnishes
languages, ideas and methods for the other sciences. Mathematics has special contribution inraising our inferential and abstraction capacities, imagination and creativity, etc. Mathematics is
one of the human cultures, and its contents, thinking, methods and languages are important
constituents of modern civilization.
(3) Contents of mathematics learning for school children ought to be realistic, meaningful
and challenging. These contents should facilitate school children to engage actively inmathematical activities, such as observation, experimentation, guessing, hypothesis testing,inference making, and communication. Contents should be presented in different ways so as tosatisfy the diverse learning needs of the students. Effective mathematics learning activities cannot
simply rely on imitation and memorization. Instead, hands-on practical work, autonomous
investigation and cooperative exchanges are important modes of mathematics learning. Because of
the differences in cultural environment, family background, and ways of thinking, our children’smathematics learning activities should be animating, lively, active, self-initiative and filled withindividual characters.

- Shangzhi Wang 4 -(4) Mathematical instructional activities should be based on children’s cognitive
developmental levels and built upon the knowledge foundation of their past experiences. Teachers
should stimulate children’s initiatives in learning, provide ample opportunities for children toparticipate and acquire widespread experiences in mathematical activities, help children genuinely
understand basic concepts, mathematical thinking and methods, as well as master basic knowledge
and skills in their autonomous explorations and cooperative exchanges. The children themselves
are masters of their own mathematics learning, whereas teachers are organizers, facilitators andcollaborators of mathematics learning.
(5) The primary aim of evaluation is to understand fully school children’s processes ofmathematics learning, stimulate children’s learning and improve teacher’s instruction. There is aneed to establish an assessment system with multiple ways and objectives of evaluation. Not only
learning outcomes, but also processes are emphasized in the evaluation of mathematics learning.
Teachers should pay attention to both levels of children’s mathematics learning and the emotions
and attitudes exhibited during mathematical activities. Teachers need to help children understandtheir self-concepts and build up their confidence.
(6) Development of modern information technology has great impact on the values, objectives,contents and pedagogy of mathematics education. Design and implementation of mathematics
curriculum should pay attention to the use of modern information technology. In particular, theeffects of calculators and computers on contents and methods of mathematics learning should be
sufficiently considered. There is a need to exploit and provide richer learning resources to thechildren, and to use modern information technology as a powerful tool for mathematics learningand problem solving. Teachers should endeavor to change school children’s learning styles so thatthey are willing to invest more energy in realistic, investigative mathematical activities.

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Basic Rationale of senior high school MCS

1. Construct a common foundation, provide a platform for development.
Senior secondary education belongs to basic education. Senior secondary mathematics
curriculum should exhibit fundamental characteristics, comprising two aspects of meanings: First,
after the stage of obligatory education, there is a need to provide students a higher level ofmathematical foundation to adapt to modern everyday living and future development, so as toallow them to acquire higher levels of mathematical literacy. Second, there is a need to prepare
students to further their studies in mathematics. The senior mathematics curriculum consists of thecompulsory series and the optional series. Compulsory series are meant to satisfy the common
mathematical needs of all students, whereas the optional series are for the individual needs. It isnoteworthy that the optional series are still fundamental to the needs of students’ development.
2. Provide multifarious curricula, and adapt choices to the needs of individuals.
Senior mathematics curriculum should demonstrate multifarious and selective characteristics
so that different students can have different developments in mathematics.
Senior mathematics curriculum should provide students room for selection and development.
There should be a number of levels and type of choices so as to foster students’ individual
development and thinking pertaining to their future career planning. Under the guidance of- Shangzhi Wang 5 -teachers, students can engage in autonomous selection of courses, and if necessary can undertake
appropriate conversion and modification. At the same time, senior mathematics curriculum shouldreserve some room for the teachers and schools to devise curriculum development plans to enrichand perfect continuously the options provided to the students in accordance with the basic needs
and individual conditions of the students.
3. Propose learning formats that are constructive, autonomous, and eager to explore.
Students’ mathematical learning activities should not be constrained to reception,
memorization, imitation and exercise. Instead, senior mathematics curriculum should promote
ways of mathematics learning such as autonomous exploration, hands-on practical, cooperative
exchange, reading and self-learning. These modes of learning can promote students’ initiatives inlearning so that under the guidance of the teachers the learning processes become one that are“re-create” in nature. At the same time, senior mathematics curriculum should set up learning
activities involving mathematical explorations and mathematical modeling. This would not only
create facilitative conditions for students to engage in constructive, self-initiated, and multifarious
modes of learning, but also stimulate students’ interests in mathematics learning, and encourage
students during the learning processes to develop habits of independent thinking and constructive
explorations. Through multiple formats of autonomous learning and exploratory activities, seniormathematics curriculum should strive to enable students to experience the processes ofmathematical discoveries and creation, and to develop their innovation consciousness.
4. Pay attention to elevate students’ abilities in mathematical thinking.
Senior mathematics curriculum should pay attention to elevate students’ mathematicalcognitive abilities, and this is a basic objective of mathematics learning. When we learn
mathematics and use mathematics to solve problems, we are continuously involving in intuitionand perception, observation and discovery, induction and analogy, spatial imagination, abstraction
and generalization, symbol representation, computation and evaluation, data processing, deductive
reasoning and proving, reflection and processes involving cognitive constructions. These
processes are concrete demonstrations of one’s mathematical cognitive abilities, and are
instrumental to help students engage in thinking and making judgment ofmathematical
patterns implicit in objective objects and events. Mathematical cognitive abilities demonstrateunique functions in the formation of objective reasoning.
5. Develop students’ mathematical application awareness.
Since the commencement of the second half of the 20th century, immense development inmathematical applications is one prominent characteristic of development in mathematics. During
the knowledge society era, mathematics moves from the backstage to the forefront. Integration ofmathematics and information technology enables mathematics generating worth for the society inmany aspects. At the same time, the prospect of mathematical development is widely extended.
For a long period of time mathematics education in China has not been sufficiently emphasized,
particularly in relating mathematics with practical reality and in connecting mathematics withother subject areas. Therefore, there is a need to enhance greatly mathematical applications andrelate mathematics to reality in senior mathematics. Recently, practices of mathematical modelingat the secondary and university levels in China reveal that promotion of instructional activities of- Shangzhi Wang 6 -mathematical applications fulfils the needs of the society, facilitates stimulation of learninginterests in mathematics, enhances students’ application awareness, and extends perspectives ofthe students.
Senior mathematics curriculum should provide practical backgrounds of basic contents toreflect the worth of mathematical applications, conduct learning activities of mathematicalmodeling, and set up some courses of special topics that exhibit some important mathematicalapplications. Senior mathematics curriculum should strive to enable students to experience thefunctions of mathematics in solving practical problems, and the connections of mathematics witheveryday living and other subject areas, as well as to enhance students to form and develop
application awareness progressively in mathematics, and practical abilities as well.
6. Keep in pace with society’s progress to know the “Double Basics”.
In China, there is a tradition of mathematics education paying particular attention to theteaching of fundamental knowledge, training of basic skills, and development of abilities. Seniormathematics curriculum in the new century should propagate this tradition. At the same time, due
to advances of the era, in particular due to the widespread applications of mathematics anddevelopment of computer technology and modern information technology, there is a need to form
new “Double Basics” that fulfils the needs of the era. For example, due to the needs to adapt to thedevelopment of the information era, senior mathematics curriculum should add contents ofalgorithms, so that the most basic information processing and statistical knowledge can be treatedas new fundamental knowledge and basic skills in mathematics. At the same time, there is a needto cut and diminish complicated computations, artificial tactics-oriented difficult problems, andcontents excessively emphasizing intricate details so as to conquer tendencies of phenomenon of“disorganization and disorientation of the double basics”.
7. Emphasize nature of mathematics and pay appropriate attention to formalization.
Formalization is a basic characteristic of mathematics. During teaching of mathematics,
learning how to express formalization is a basic requirement. However, expression offormalization should not be solely emphasized, and there is a need to pay attention to the nature ofmathematics as well. Otherwise, animating and lively mathematical cognitive activities would bedrowned in the sea of formalization. Modern development in mathematics makes clear that entire
formalization is impossible. Therefore, senior mathematics curriculum should revert back tosimplicity and truth, striving hard to reveal developmental processes and nature of concepts, rules,
and conclusions in mathematics. Mathematics curriculum should include logical deduction, andemphasize reasoning as well. Through analyses of typical examples and students’ autonomous
exploratory activities, students are enabled to comprehend mathematical concepts and processes
so that conclusions are drawn progressively, to realize the methods of thinking implicit in theseconcepts and processes, to quest for developmental trajectory of history of mathematics, as well as
to transform mathematics from the academic to the more acceptable educational form.
8. Exhibit the cultural values of mathematics.
Mathematics is an important constituent of human culture. Mathematics curriculum shouldreflect appropriately the history, application and developmental tendency of mathematics. In- Shangzhi Wang 7 -addition, it should reflect the function of mathematics in propelling social development and thesocial needs of mathematics. Apart from these, propelling function of social developments onmathematics developments, thinking system of the social sciences, the aesthetic value ofmathematics, and the innovation spirits of the mathematicians are included as well. Mathematics
curriculum should help students familiarize with the function of mathematics in the developmentof human civilization and the progressive formation of correct mathematical perspective. Becauseof these, senior mathematics curriculum should promote exhibition of cultural values ofmathematics, propose appropriate contents like “mathematical culture” as learning requirements.
There are needs to set up courses such as “selected topics in the history of mathematics”.
9. Pay attention to the integration of information technology and mathematics
curriculum.
Widespread applications of modern information technology are now exerting deep influenceson contents of the mathematics curriculum, mathematics teaching, and mathematics learning.
Senior mathematics curriculum should promote realization of organization of information
technology and curriculum contents (e.g. algorithms are integrated with related parts in themathematics curriculum). The basic rule of integration is to facilitate students to know the natureof mathematics. Senior mathematics curriculum should promote the use of information technology
to display those contents that in the past may not be presented easily. After guaranteeing theprerequisite of training of hand calculations, students should strive to use scientific calculators, allsorts of mathematics education educational platforms, so as to enhance integration of mathematics
teaching and information technology, encourage students to deploy computers and calculators tocarry out explorations and discoveries.
10. Establish reasonable, scientific evaluation system.
Demand of human developments by the modern society has caused deep changes to theevaluation system. Senior mathematics curriculum should establish an appropriate and scientificevaluation system, including aspects such as concepts, contents, formats and systems of evaluation.
Evaluation should not only pay attention to students’ mathematics learning outcomes, but also tomathematics learning processes; not only pay attention to the levels of mathematics learning of thestudents, but also to the changes of affection and attitudes exhibited in mathematical activities. In
mathematics education, evaluation should establish a variety of objectives, and pay attention to thedevelopment of students’ personality and potentials. For example, process evaluation should pay
attention to the evaluation of students’ understanding of mathematics concepts and mathematics
thinking processes. Teachers should pay attention to the evaluation of processes involving how
students pose, analyze and solve problems mathematically, as well as to the processes exhibiting
attitudes of cooperation with others, consciousness of expression and exchanges, and spirits of
exploration. Regarding learning activities such as mathematical exploration and mathematicalmodeling, teachers should develop corresponding contents and methods of evaluation.

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Overall Objectives of compulsory education MCS
Through mathematics learning at the obligatory stage of schooling, students are able to:☺ Acquire important mathematical knowledge (including mathematical facts,- Shangzhi Wang 8 -mathematical activity experiences), basic mathematical thinking methods, and necessary
application skills that are essential for adapting to future social life and further development;☺ Begin to know how to deploy various ways of mathematical thinking to observe,
analyze realistic world, solve problems encountered in daily living and studies in otherdisciplinary areas;☺ Realize the intimate relationships between mathematics and nature, as well as between
mathematics and human society, know the worth of mathematics, increase understanding ofmathematics, and gain confidence in learning mathematics with good results;☺ Possess some degree of creative spirits and practical abilities, and develop sufficiently inareas of general abilities, affection and attitudes.
The overall objectives are concisely stated below:

Knowledge and Skills---

Involve in processes of how authentic problem situations are abstracted as number
and algebra problems; master fundamental knowledge and basic skills pertaining
to numbers and algebra; able to solve simple problems.
Involve in and explore the processes of how shapes, sizes and positions of objects
and figures are related and transformed; master fundamental knowledge and basic
skills pertaining to space and figures; able to solve simple problems.
Involve in the processes of problem posing, data collection and processing,decision making and prediction; master fundamental knowledge and basic skills
pertaining to statistics and probability; able to solve simple problems.

Mathematical Thinking--

Involve in the processes of applying mathematical symbols and figures to describe
the phenomenal world; establish initial number sense and symbol sense; develop
abstract mathematical thinking.
Enrich knowledge of space and objects in the phenomenal world, establish initialspace concepts; develop iconic mathematical thinking.
Involve in how information is described by data processing and organization, as
well as how inferences are made; develop statistical thinking.
Involve in how observation, experimentation, guessing, and proving are done inmathematical activities; develop reasonable analogical and induction abilities andinitial mathematical deduction ability; able to present one’s ideas systematicallyand clearly.

Problem Solving--

Begin to learn how problems can be posed and comprehended from themathematical perspectives; able to apply knowledge and skills acquired forproblem solving in an integrated manner; develop application awareness.
Formulate some strategies for problem solving; experience that problems can besolved in a variety of ways; develop practical abilities and creative spirits.
- Shangzhi Wang 9 --Learn how to cooperate with others; able to communicate with others about one’s
processes and products of thinking.
Begin to form an awareness of evaluation and reflection.

Affection and Attitudes--

Able to participate positively in mathematical learning activities; demonstratecuriosity and eagerness in mathematics learning.
Experience success in mathematical activities; develop strong will in overcoming
difficulties; develop confidence in mathematics learning.
Begin to know the intimate relationships between mathematics and human lives,
as well as the values and influences of mathematics on human civilization;
experience that mathematical activities are full of explorations and creative
productions; sense the rigor of mathematical knowledge and appreciate thecertainty of mathematics conclusions.
Form an attitude that is pragmatic and realistic; develop habit of doubts andengage independent thinking.

The above-mentioned four objective areas should be regarded as an intimatelyinterrelated organic whole. They are very important for human development, andshould be realized in rich and wonderful mathematical activities. In particular,
development of mathematical thinking, problem solving, affection and attitudes
cannot be separated from knowledge and skills acquisition. Likewise, knowledge andskills acquisition needs to satisfy one prerequisite, i.e. to facilitate the realization of
the other three objective areas.
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Curriculum Objectives of senior high school MCS

Overall objectives of senior mathematics curriculum are: Based on the foundation of thenine-year obligatory education mathematics curriculum, students move a step further to elevatetheir mathematics literacy necessary for future citizenship, so as to satisfy individual development
and societal progress. Concrete objectives are listed as follow:
1.
Acquire necessary fundamental knowledge and basic skills in mathematics; understand basic
mathematical concepts and nature of mathematical conclusions; familiarize with thebackground of genesis and application of concepts and conclusions; realize mathematicalthinking and methods inherent in mathematics, and the function they play in the ensuingstudies. Through different forms of autonomous learning, exploratory activities, experience
the processes of mathematical discoveries and creation.
2.
Elevate abilities of spatial imagination; abstract generalization, deductive reasoning,
computation and evaluation, and data processing.
3.
Elevate abilities in posing, analyzing and solving problems (including simple and practicalproblems), abilities in mathematical expression and exchanges, as well as abilities inacquiring mathematical knowledge independently.
4.
Develop mathematics application and innovation awareness; strive to engage in thinking andmaking judgments for some mathematical models implicit in the realistic world.
5.
Elevate interests in mathematics learning; establish confidence in learning mathematics well;- Shangzhi Wang 10 -

form spirits of perseverance and dedication, as well as scientific attitudes.
Possess a certain degree of mathematical perspective; progressively recognize the scientificvalue, application value and cultural values of mathematics; form habits of critical thinking;pay high regard to the rational spirits of mathematics; realize the aesthetic meaning ofmathematics, so as to move a step further to establish dialectical and historical world view ofobjectivism.

6.

2.2 Major changes of mathematics curriculum contents
What we teach is more important than how to teach, so we spend a lot of time and energy tothink what knowledge and skill should be in curriculum.

1) The changes of curriculum structure and selectivity
z The change of curriculum structure of compulsory education
The curriculum content in compulsory education consists of four parts: number and operation;
graph and geometry; statistics and probability; integration and practice. The integration andpractice become important content in mathematics curriculum and have concrete and special
requirements in different learning stage. These are more different from before.

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The change of curriculum structure of senior high school

The curriculum content in senior high school consists of obligatory curriculum and elective
curriculum. The obligatory curriculum contains five modules and the elective curriculum includes
elective curriculum 1、2、3、4.
The compulsory curriculum comprises of 5 modules:
Mathematics 1: Set, concept of function, and basic elementary function I (exponentialfunction, logarithmic function, power function).
Mathematics 2: Preliminary solid geometry, preliminary plane analytic geometry.
Mathematics 3: Preliminary algorithms, statistics, probability.
Mathematics 4: Basic elementary function II (trigonometric function), vectors on a plane,
trigonometric identity transformation.
Mathematics 5: Solution of a triangle, sequence, inequality.
The elective curriculum 1 is for student of liking humanities and social studies and contains
two modules. The elective curriculum 2 is for student of liking science and technology andcontains three modules.
The elective curriculum 1 Consists of 2 modules.
Optional Study 1-1: Common logic terminology, conic section and equation, derivative andits application.
Optional module 1-2: Case studies of statistics, inference and proof, extension of number
system and introduction of complex number, block diagram.
The elective curriculum 2 Consists of 3 modules.
Optional module 2-1: Common logic terminology, conic section and equation, vectors inspace and solid geometry.
Optional module 2-2: Derivative and its application, inference and proof, extension of
number system and introduction of complex number.

- Shangzhi Wang 11 -

Optional module 2-3: Principle of enumeration, case studies of statistics, probability.
The elective curriculum 3 includes 6 topics:
3-1: Selected topics of history of mathematics
3-2: Information security and cryptogram
3-3: The geometry of the sphere3-4: Symmetry and group
3-5: Euler’s formula and classification of closed surfaces
3-6: Trisection of an angle and extension of a number field.
Student can select any topic in the elective curriculum 3 to study.
The elective curriculum 3 includes 10 topics:
4-1: Selected topics of geometrical proofs.
4-2: Matrix and transformation.
4-3: Sequence and difference.
4-4: Coordinates system and parametric equations.
4-5: Selected topics of inequalities.
4-6: Elementary number theory.
4-7: Optimum seeking method and preliminary experimental design.
4-8: Overall planning (critical path method) and preliminary graph theory.
4-9: Risk and decision making.
4-10: Switching circuits and Boolean algebra.
Student can select any topic in the elective curriculum 4 to study and these contents in theelective curriculum 4 can become a part content of promotion examination which student could
selects.

2) To intensify mathematics major venation
We intensify mathematics major venations in mathematics curriculum, such as:
Operation----operation of numbers, operation of polynomials, operation ofvectors, etc----application of operation—discussing equation、inequality、function.
Quantity、 Function(variety) 、Model----measure of quantity, conversion ofdifference measures of quantity--equality relationship of quantity(equation),inequality relationship of quantity(inequality), equality relationship of variety
quantity(function)—model of distance、velocity and time, model of gross、price andquantity, a series of functions, etc.
Graph（geometry）----basic graphes and their basic properties and some angle ofview to cognize and know properties of graph(transformation geometry、analytic
geometry and vector geometry, etc)
Etc.
We arrange mathematics contents around these major venations.
3) To reduce some content in traditional mathematics curriculum and to add
some content
For example, we reduce some contents of Euclidean geometry and add some contents ofgeometry transformation (reflection、translation and revolution) and vector geometry in different- Shangzhi Wang 12 -

stage.
We add some contents of algorithm and put idea of algorithm program to cognize process ofproblem solving.
Etc.
If someone will know the contents of Chinese mathematics curriculum standard in detail,please read English version of them.

2.3 Changes of teaching rationale
In curriculum standard we emphasize diversification teaching mode and manner. For instance,teaching with enlightening and illumining; teaching with collaborating and work together;teaching with exploring and probing into something; teaching with using a question for discussion
and using a task to work together; etc. We can use different mode and manner to teach different
content and we alternate using different mode and manner to teach in a class. We advocate
grasping the all and the one of curriculum and learning cell (chapter) design to increase teachingefficiency. Etc .

2.4 Reform of assessment
Reform of assessment and evaluation is very hard and difficult work but we do not shy away
and blench. We do our best to find a good way to assessment integration literacy and we also
explore assessment of school work of student and explore assessment of school development. We
will use other paper to introduce these.

3、Implementation of Mathematics curriculum standard
Up to now all student has already entered into implementation of compulsory education
mathematics new curriculum and the student of senior high school in 15 provinces has alreadyentered into implementation of senior school mathematics new curriculum. It is very importantand difficult how to implement new curriculum when the curriculum standard has designed. As weknow, the curriculum reform is the government action carried out from top to bottom. But
curriculum implementation should be carried out in both ways, i.e. from top to bottom and frombottom to top. We like to introduce a detailed account of some implementation work including
social dissemination, textbook editing, teacher training, and experience sharing, etc. Particularly
we present tow projects, teaching research mechanism on school base and the project oflong-distance training on the Internet, which are to be put forward according to Chinese
practicality.

3.1 Social Dissemination
Curriculum reform is not only educational problem, but is also social problem. We need society
understanding include、teachers、parents of student、educationist、mathematicians，etc. The
Educational Ministry establishes a project of social dissemination and requires local government
to emphasize social dissemination. This work exerts very important function in implementation of
curriculum reform.

- Shangzhi Wang 13 -

3.2Textbook Editing
In this curriculum reform The Educational Ministry establishes policy of diversification of
textbook editing. This is big change. There have been 8 system of textbook in elementary school、
6 system of textbook in junior middle school and 6 system of textbook in senior middle school.
These textbooks have different characteristics and student of different place can select different
textbooks.

3.3Manager and Teacher training of school in diversification mode and manner
As we know China is large country and there are more than twenty million managers andteachers of school. The problem of managers and teachers training is most important when the
curriculum standard has designed. The training work is huge and includes a lot of problems whichcontain experts team, expenses, time, etc.
We must mobilize all levels of government and social potence including publishing company
and specialty academy, etc.
The Educational Ministry establishes policy in three levels training, national level、provincelevel and district level including many county. The Educational Ministry organizes core teachers
training in national level and local government organizes other level training. Every teacher can
get one time training at least.

3.4Professional direct and Experiment communication
The Educational Ministry organizes many different symposiums and proseminars to direct
work of experiment districts and communicate some good teaching experience. The Educational
Ministry ask local government to do same jobs. The most of members of research group of
curriculum standard are major strength of specialty to support implementation of curriculum
reform.

3.5“Grass Root Project”
The curriculum implementation should be carried out in both ways, i.e. from top to bottom
and from bottom to top. “Grass Root Project” is work from bottom to up. There are two projects,
the project of teaching research mechanism on school base and the project of long-distancetraining on the Internet, which are very important and powerful to put forward curriculum reform.

4、Problems and Reflecting
We are very honour to take part the work of research and implementation of mathematics
curriculum standard. Through almost eight years work, we like to give some suggestions to leaderof Education.
z To establish long cooperation and communication mechanism of mathematics and scienceeducationz To establish an internet flat roof of resource sharing of mathematics and science educationz To establish the mechanism of cycle improving on curriculum standard of mathematics
and science- Shangzhi Wang 14 -z

To develop foundational research of mathematics and science education including
curriculum content(for example geometry, etc), teaching, evaluation, etc

Reference
1. Mathematics Curriculum Standards (Experimental Version) of Full-time Obligatory Educationof China (2001)
2. Unscramble of Mathematics Curriculum Standards (Experimental Version) of Full-time
Obligatory Education of China (2001)
3. Mathematics Curriculum Standards (Experimental Version) of Ordinary Senior Secondary of
China (2003)
4. Unscramble of Mathematics Curriculum Standards (Experimental Version) of Ordinary Senior
Secondary of China (2003)- Shangzhi Wang 15 -