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The Analysis of IntendedThe Analysis of IntendedMathematics Curriculum ofMathematics Curriculum ofPrimary Schools in MongoliaPrimary Schools in Mongolia
Presented at Conference of Japan Academic Society ofPresented at Conference of Japan Academic Society ofMathematics EducationMathematics Education
Education Faculty, Hiroshima University, JapanEducation Faculty, Hiroshima University, Japan24 June 200724 June 2007
PurevdorjPurevdorj OyunaaOyunaaDepartment of Education, IDECDepartment of Education, IDEC
Hiroshima UniversityHiroshima University
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Structure of the PaperStructure of the Paper
The Concept of CurriculumThe Concept of Curriculum
Historical Review of the CurriculumHistorical Review of the Curriculum
The Structure of MathematicsThe Structure of MathematicsStandards of Primary SchoolsStandards of Primary Schools
Characteristics of MathematicsCharacteristics of MathematicsStandards of Primary SchoolsStandards of Primary Schools
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1. The Concept of Curriculum1. The Concept of Curriculum
According to According to HowsonHowson (1981), (1981), curriculum must becurriculum must bemore than syllabus-it must encompass aims,more than syllabus-it must encompass aims,contents, methods, and assessment processescontents, methods, and assessment processes..
There are different levels of curriculum, which areThere are different levels of curriculum, which arelabeled as (a) labeled as (a) intendedintended, (b) , (b) implementedimplemented, and (c), and (c)attained curriculumattained curriculum ( (RobitailleRobitaille et al. 1993). et al. 1993).
44(Robitaille et al. 1993, p. 26)
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2. Historical Review of the Curriculum2. Historical Review of the Curriculum
Before 1990, in socialist era, the representative forBefore 1990, in socialist era, the representative forthe intended mathematics curriculum was thethe intended mathematics curriculum was theProgram of the Mathematics Subject.Program of the Mathematics Subject.
According to According to BegzBegz (2001): (2001):
1. Period, between 1900 and 19401. Period, between 1900 and 1940The curriculum tried to include some indigenousThe curriculum tried to include some indigenous
subjects, which related to Mongoliansubjects, which related to Mongoliantraditional lifestyletraditional lifestyle..
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2. 2. Period, between 1941 and 1980Period, between 1941 and 1980Modern European education was introduced inModern European education was introduced in
Mongolia, while it departed from the subjectsMongolia, while it departed from the subjectsthat related to local and indigenousthat related to local and indigenouscircumstancescircumstances
Translation of textbooksTranslation of textbooks 100 Russian teachers100 Russian teachers
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3. 3. Period, between 1980 and 1998Period, between 1980 and 1998
From teacher-centered learning to student-From teacher-centered learning to student-centered learning,centered learning,
Ecosystem of learning was not limited by wallsEcosystem of learning was not limited by wallsof classroom,of classroom,
Bloom Taxonomy was emphasized in students`Bloom Taxonomy was emphasized in students`evaluationevaluation
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3. The Structure of the Mathematics3. The Structure of the MathematicsStandards of Primary SchoolsStandards of Primary Schools
The representatives for the intended mathematicsThe representatives for the intended mathematicscurriculum in Mongolia are the officialcurriculum in Mongolia are the officialdocuments: the documents: the mathematics standards andmathematics standards andthe content framework of primary schoolsthe content framework of primary schools..
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The mathematics standards are organized intoThe mathematics standards are organized intofour parts:four parts:
3.1 The concepts of mathematics education3.1 The concepts of mathematics education
3.2 The Content standard3.2 The Content standard
3.3 The Evaluation standard3.3 The Evaluation standard
3.4 The Foundations of methodology 3.4 The Foundations of methodology developmentdevelopment
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3.1 The concepts of mathematics education3.1 The concepts of mathematics education
need of mathematics educationneed of mathematics educationneed of individualneed of individualneed of societyneed of society the goal of the mathematics education inthe goal of the mathematics education in
Mongolian societyMongolian society..
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3.2 The Content standard3.2 The Content standard
Number and CalculationNumber and Calculation AlgebraAlgebra GeometryGeometry Probability and StatisticsProbability and Statistics
ObjectivesObjectives KnowledgeKnowledge SkillsSkills Fundamental process of learningFundamental process of learning Continuity codeContinuity code
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3.3 The Assessment standard3.3 The Assessment standard
Categorized criteria for assessment of students`Categorized criteria for assessment of students`mathematics learning based on four domains andmathematics learning based on four domains andstudents` cognitive stagesstudents` cognitive stages
3.4 The Foundations of methodology 3.4 The Foundations of methodology developmentdevelopment
The principles describe particular features of high-The principles describe particular features of high-quality mathematics educationquality mathematics education
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4. Characteristics of Mathematics4. Characteristics of MathematicsStandards of Primary SchoolsStandards of Primary Schools
Principles in Foundation of MethodologyPrinciples in Foundation of MethodologyDevelopmentDevelopment
Four Comprehensive Potentials inFour Comprehensive Potentials inMathematics StandardsMathematics Standards
Students` Real Life Problem SolvingStudents` Real Life Problem Solving
The The ConcenterConcenter Model of Mathematics Model of MathematicsContentsContents
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4.1 4.1 Principles in Foundation of MethodologyPrinciples in Foundation of MethodologyDevelopmentDevelopment
Equity principleEquity principle Selecting principle of learning contentSelecting principle of learning content Teaching principleTeaching principle Learning principleLearning principle Technology principleTechnology principle Assessment principleAssessment principle
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Principles of Mongolian standardsPrinciples of Mongolian standardsTeaching PrincipleTeaching Principle: : The teaching should to be based onThe teaching should to be based on
theory of educational philosophy and psychology, knowledgetheory of educational philosophy and psychology, knowledgeand managementand management
Learning PrincipleLearning Principle: : The learning should to be based on theThe learning should to be based on theprinciple which students create knowledge by doingprinciple which students create knowledge by doing
Principles of the NCTMPrinciples of the NCTMTeaching PrincipleTeaching Principle: : Effective mathematics teaching requiresEffective mathematics teaching requires
understanding what students know and need to learn and thenunderstanding what students know and need to learn and thenchallenging and supporting them to learn it wellchallenging and supporting them to learn it well
Learning PrincipleLearning Principle: : Students must learn mathematics withStudents must learn mathematics withunderstanding, actively building new knowledge fromunderstanding, actively building new knowledge fromexperience and prior knowledgeexperience and prior knowledge
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4.2 Four Comprehensive Potentials in4.2 Four Comprehensive Potentials inMathematics StandardsMathematics Standards
Communicate Mongolian and mathematicalCommunicate Mongolian and mathematicallanguagelanguage
Express own thinking, logicallyExpress own thinking, logically Recognize by modeling the mutual relation of realRecognize by modeling the mutual relation of real
life problemslife problems Solve the faced problems by modeling and Solve the faced problems by modeling and
calculatingcalculating
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Communicate Mongolian and mathematical Communicate Mongolian and mathematical languagelanguage
Please write the following sentences by numbersPlease write the following sentences by numbersand read, loudlyand read, loudly
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Express own thinking, logicallyExpress own thinking, logically
Please explain how we can represent size of thePlease explain how we can represent size of theproper fractions by real things.1proper fractions by real things.1
Recognize by modeling the mutual relation of realRecognize by modeling the mutual relation of reallife problemslife problems
Please find out the price of products in Please find out the price of products in ““ELBAELBA””shop by using next table and discuss the price.shop by using next table and discuss the price.
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4.3 Students` Real Life Problem Solving4.3 Students` Real Life Problem Solving
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4.4 The 4.4 The ConcenterConcenter Model of Mathematics Model of MathematicsContentsContents
One and twoOne and twodigit numbersdigit numbers
Three digitThree digitnumbersnumbers
Six digitSix digit
numbers
numbers
multi digitmulti digitnumbersnumbers
fractionfraction
Geom
etry
Geom
etry
AlgebraAlgebra
Prob
abili
tPr
obab
ilit
y an
dy
and
stat
istic
sst
atis
tics
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Video ViewingVideo Viewing
Grade 4 of the Primary school in Grade 4 of the Primary school in aimagaimag. The. Theclass was organized by 5 groups. In theclass was organized by 5 groups. In thebeginning of the class, a teacher tells the rulebeginning of the class, a teacher tells the ruleof the group work.of the group work.
-- All students of each group need to All students of each group need to participate, activelyparticipate, actively
-- All students of each group will solve All students of each group will solve problems one by oneproblems one by one
-- Groups will be assessed end of the lessonGroups will be assessed end of the lesson
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Topic: Addition and Subtraction of NaturalTopic: Addition and Subtraction of Naturalnumbersnumbers
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Thank you very muchThank you very much
ありがとうございましたありがとうございました