The Analysis of Intended Mathematics Curriculum …3 1. The Concept of Curriculum According to Howson (1981), curriculum must bemore than syllabus-it must encompass aims, contents,

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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