高中数学课程描述(英文)

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MathematicsCourseDescription.

Mathematicscourseinmiddleschoolhastwoparts:compulsorycoursesandoptionalcourses.Compulsorycoursescontentlotsofmodernmathematicalknowledgeandconceptions,suchascalculus,statistics,analyticgeometry,algorithmandvector.Optionalcoursesarechosenbystudentswhichisaccordingtheirinterests..

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CompulsoryCourses:.

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SetTheory.

Coursecontent:.

Thiscourseintroducesanewvocabularyandsetofrulesthatisfoundationaltothemathematicaldiscussions.Learningthebasicsofthisall-importantbranchofmathematicssothatstudentsarepreparedtotackleandunderstandtheconceptofmathematicalfunctions.Studentslearnabouthowentitiesaregroupedintosetsandhowtoconductvariousoperationsofsetssuchasunionsandintersections(i.e.thealgebraofsets).Weconcludewithabriefintroductiontotherelationshipbetweenfunctionsandsetstosetthestageforthenextstep.

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KeyTopics:.

Thelanguageofsettheory.

Setmembership.

Subsets,supersets,andequality.

Settheoryandfunctions.

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Functions.

Coursecontent:.

Thislessonbeginswithtalkingabouttheroleoffunctionsandlookattheconceptofmappingvaluesbetweendomainandrange.Fromtherestudentspendagooddealoftimelookingathowtovisualizevariouskindsoffunctionsusinggraphs.Thiscoursewillbeginwiththeabsolutevaluefunctionandthenmoveontodiscussbothexponentialandlogarithmicfunctions.Studentsgetanopportunitytoseehowthesefunctionscanbeusedtomodelvariouskindsofphenomena..

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KeyTopics:.

Single-variablefunctions.

Two–variablefunctions.

Exponentialfunction.

Logarithmicfunction.

Power-function.

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Calculus.

Coursecontent:.

Inthefirststep,thecourseintroducestheconceptionoflimit,derivativeanddifferential.Thenstudentscanfullyunderstandwhatislimitofnumbersequenceandwhatislimitoffunctionthroughsomespecificpractices.Moreover,themethodtocalculatederivativeisalsointroducedtostudents..

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KeyTopics:.

Limittheory.

Derivative.

Differential.

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Algorithm.

Coursecontent:.

Introducetheconceptionofalgorithmandthemethodtodesignalgorithm.Thenthefiguresofflowchartsandtheconceptionoflogicalstructure,likesequentialstructure,contractureofconditionandcyclestructureareintroducedtostudents.Nextstepstudentscanusetheknowledgeofalgorithmtomakesimpleprogramminglanguage,duringthisprocedure,studentalsoapproachtogrammaticalrulesandstatementswhichisassimilarasBASIClanguage..

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KeyTopics:.

Algorithm.

Logicalstructureofflowchartandalgorithm.

Outputstatement.

Inputstatement.

Assignmentstatement.

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Statistics.

Coursecontent:.

Thecoursestartswithbasicknowledgeofstatistics,suchassystematicsamplingandgroupsampling.Duringthelessonstudentsacquiretheknowledgelikehowtoestimatecollectivitydistributionaccordingfrequencydistributionofsamples,andhowtocomputenumericalcharacteristicsofcollectivitybylookingatnumericalcharacteristicsofsamples.Finally,therelationshipandtheinterdependencyoftwovariablesisintroducedtomakesurethatstudentsmasteredinhowtomakescatterplot,howtocalculateregressionline,andwhatisMethodofSquare..

KeyTopics:.

Systematicsampling.

Groupsampling.

Relationshipbetweentwovariables.

Interdependencyoftwovariables.

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BasicTrigonometryI.

Coursecontent:.

Thiscoursetalksaboutthepropertiesoftrianglesandlooksattherelationshipthatexistsbetweentheirinternalanglesandlengthsoftheirsides.Thisleadstodiscussionofthemostcommonlyusedtrigonometricfunctionsthatrelatetrianglepropertiestounitcircles.Thisincludesthesine,cosineandtangentfunctions.Studentscanusethesepropertiesandfunctionstosolveanumberofissues..

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KeyTopics:.

CommonAngles.

Thepolarcoordinatesystem.

Trianglesproperties.

Righttriangles.

Thetrigonometricfunctions.

Applicationsofbasictrigonometry.

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BasicTrigonometryII.

Coursecontent:.

Thiscoursewilllookattheveryimportantinversetrigfunctionssuchasarcsin,arcos,andarctan,andseehowtheycanbeusedtodetermineanglevalues.Studentsalsolearncoretrigidentitiessuchasthereductionanddoubleangleidentitiesandusethemasameansforderivingproofs..

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KeyTopics:.

Derivativetrigonometricfunctions.

Inversetrigfunctions.

Identities.

Pythagoreanidentities.

Reductionidentities.

Anglesum/Differenceidentities.

Double-angleidentities.

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AnalyticGeometryI.

Coursecontent:.

Thiscourseintroducesanalyticgeometryasthemeansforusingfunctionsandpolynomialstomathematicallyrepresentpoints,lines,planesandellipses.Alloftheseconceptsarevitalinstudent’smathematicaldevelopmentsincetheyareusedinrenderingandoptimization,collisiondetection,responseandothercriticalareas.Studentslookatintersectionformulasanddistanceformulaswithrespecttolines,points,planesandalsobrieflytalkaboutellipsoidalintersections..

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KeyTopics:.

Parametricrepresentation.

Parallelandperpendicularlines.

Intersectionoftwolines.

Distancefromapointtoaline.

Anglesbetweenlines.

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AnalyticGeometryII.

Coursecontent:.

Studentslookathowanalyticgeometryplaysanimportantroleinanumberofdifferentareasofclassdesign.Studentscontinueintersectiondiscussionbylookingatawaytodetectcollisionbetweentwoconvexpolygons.ThenstudentscanwrapthingsupwithalookattheLambertianDiffuseLightingmodeltoseehowvectordotproductscanbeusedtodeterminethelightingandshadingofpointsacrossasurface..

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KeyTopics:.

Reflections.

Polygon/polygonintersection.

Lighting.

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SequenceofNumber.

Coursecontent:.

Thiscoursebeginwithintroducingseveralconceptionsofsequenceofnumber,suchas,term,finitesequenceofnumber,infinitesequenceofnumber,formulaofgeneraltermandrecurrenceformula.Then,theconceptionofgeometricsequenceandarithmeticsequenceisintroducedtostudents.Throughpracticesandmathematicalgames,studentsgraduallyunderstandandutilizetheknowledgeofsequenceofnumber,eventuallystudentsareabletosolvemathematicalquestions..

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KeyTopics:.

Sequenceofnumber.

Geometricsequence.

Arithmeticsequence.

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Inequality.

Thiscourseintroducesconceptionofinequalityaswellasitsproperties.Inthefollowinglessonsstudentslearnthesolutionsandarithmeticofone-variablequadraticinequality,twovariablesinequality,fundamentalinequalityaswellhowtosolvesimplelinearprogrammingproblems..

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KeyTopics:.

UnequalrelationshipandInequality.

One-variablequadraticinequalityanditssolution.

Two-variableinequalityandlinearprogramming.

Fundamentalinequality.

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VectorMathematics.

Coursecontent:.

Afteranintroductiontotheconceptofvectors,studentslookathowtoperformvariousimportantmathematicaloperationsonthem.Thisincludesadditionandsubtraction,scalarmultiplication,andtheall-importantdotandcrossproducts.Afterlayingthiscomputationalfoundation,studentsengageingamesandtalkabouttheirrelationshipwithplanesandtheplanerepresentation,revisitdistancecalculationsusingvectorsandseehowtorotateandscalegeometryusingvectorrepresentationsofmeshvertices..

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KeyTopics:.

Linearcombinations.

Vectorrepresentations.

Addition/subtraction.

Scalarmultiplication/division.

Thedotproduct.

Vectorprojection.

Thecrossproduct.

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OptionalCourses.

MatrixI.

Coursecontent:.

Inthiscourse,studentsareintroducedtotheconceptofamatrixlikevectors,matricesandsoon.Inthefirsttwolessons,studentlookatmatricesfromapurelymathematicalperspective.Thecoursetalksaboutwhatmatricesareandwhatproblemstheyareintendedtosolveandthenlooksatvariousoperationsthatcanbeperformedusingthem.Thisincludestopicslikematrixadditionandsubtractionandmultiplicationbyscalarsorbyothermatrices.Attheend,studentscanconcludethiscoursewithanoverviewoftheconceptofusingmatricestosolvesystemoflinearequations..

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KeyTopics:.

Matrixrelations.

Matrixoperations.

Addition/subtraction.

Scalarmultiplication.

MatrixMultiplication.

Transpose.

Determinant.

Inverse.

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Polynomials.

Coursecontent:.

Thiscoursebeginswithanexaminationofthealgebraofpolynomialsandthenmoveontolookatthegraphsforvariouskindsofpolynomialfunctions.Thecoursestartswithlinearinterpolationusingpolynomialsthatiscommonlyusedtodrawpolygonsondisplay.Fromtherestudentsareaskedtolookathowtotakecomplexfunctionsthatwouldbetoocostlytocomputeinarelativelyrelaxedstudyingenvironmentandusepolynomialstoapproximatethebehaviorofthefunctiontoproducesimilarresults.Studentscanwrapthingsupbylookingathowpolynomialscanbeusedasmeansforpredictingthefuturevaluesofvariables..

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KeyTopics:.

Polynomialalgebra(singlevariable).

addition/subtraction.

multiplication/division.

Quadraticequations.

Graphingpolynomials.

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LogicalTermsinMathematics.

Coursecontent:.

Thiscourseintroducestherelationshipsoffourkindsofstatements,necessaryandsufficientconditions,basiclogicalconjunctions,existingquantifieranduniversalquantifier.Bylearningmathematicallogicterms,studentscan