基于認(rèn)知彈性理論的數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題教學(xué)策略研究

基于認(rèn)知彈性理論的數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題教學(xué)策略研究摘要：本研究旨在探究認(rèn)知彈性理論在中學(xué)數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題教學(xué)中的應(yīng)用，以提高學(xué)生的學(xué)習(xí)效果和興趣。首先，文章介紹了認(rèn)知彈性理論的基本概念和相關(guān)理論。其次，針對(duì)數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題的特點(diǎn)，提出了適合認(rèn)知彈性理論的教學(xué)策略，包括激勵(lì)、分組、反饋、重組等。最后，通過(guò)實(shí)驗(yàn)研究，驗(yàn)證了所提出的教學(xué)策略的有效性，并對(duì)未來(lái)教學(xué)實(shí)踐進(jìn)行了展望。研究結(jié)果表明，基于認(rèn)知彈性理論的教學(xué)策略可以顯著提高學(xué)生對(duì)數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題的認(rèn)知水平和學(xué)習(xí)興趣，具有一定的推廣價(jià)值。

關(guān)鍵詞：認(rèn)知彈性理論；數(shù)學(xué)結(jié)構(gòu)不良問(wèn)題；教學(xué)策略；學(xué)習(xí)效果；學(xué)習(xí)興趣

Abstract:Theaimofthisstudyistoexploretheapplicationofcognitiveelasticitytheoryinteachingmathstructureproblemstoimprovestudents'learningeffectivenessandinterest.Firstly,thearticleintroducesthebasicconceptsandrelatedtheoriesofcognitiveelasticitytheory.Secondly,basedonthecharacteristicsofmathstructureproblems,weproposeteachingstrategiessuitableforcognitiveelasticitytheory,includingmotivation,grouping,feedback,restructuring,etc.Finally,throughexperimentalresearch,theeffectivenessoftheproposedteachingstrategiesisverified,andthefutureteachingpracticeislookedforwardto.Theresultsshowthatteachingstrategiesbasedoncognitiveelasticitytheorycansignificantlyimprovestudents'cognitivelevelandlearninginterestinmathstructureproblems,andhavecertainpromotionalvalue.

Keywords:cognitiveelasticitytheory;mathstructureproblems;teachingstrategies;learningeffectiveness;learninginteresInrecentyears,mathstructureproblemshavebecomeanimportantpartofmathematicaleducation.However,studentsoftenencounterdifficultiesinsolvingthesetypesofproblems,whichmayleadtoadecreaseintheirlearninginterestandcognitivelevel.Therefore,itisnecessarytoexploreeffectiveteachingstrategiestoimprovestudents'learningeffectivenessandinterestinmathstructureproblems.

Cognitiveelasticitytheoryproposesthatcognitiveabilityisnotfixed,butcanbedevelopedthroughappropriatetrainingandlearning.Basedonthistheory,teachingstrategiescanbedesignedtoimprovestudents'cognitiveflexibility,creativity,andadaptability.Inthecontextofmathstructureproblems,effectiveteachingstrategiesincludeprovidingmultipleproblem-solvingmethodsandencouragingstudentstoexploredifferentapproaches,promotingcriticalthinkingandlogicreasoningskillsthroughdiscussionandanalysisofexamples,andusingreal-lifesituationstoenhancetherelevanceandsignificanceofmathstructureproblems.

Toverifytheeffectivenessoftheseteachingstrategies,experimentalresearchwasconductedonagroupofmiddleschoolstudents.Theresultsshowedthatstudentswhoreceivedthecognitiveelasticity-basedteachingshowedsignificantimprovementintheiroverallcognitivelevelandtheirinterestinsolvingmathstructureproblems.Moreover,theywereabletoapplyvariousproblem-solvingstrategiesautonomouslyanddemonstratemorecomprehensiveanddeepunderstandingofthemathematicalconceptsunderlyingthestructureproblems.

Inconclusion,teachingstrategiesbasedoncognitiveelasticitytheoryhaveconsiderablepotentialforpromotingstudents'learningeffectivenessandinterestinmathstructureproblems.FutureteachingpracticeshouldcontinuetoexploreandoptimizethesestrategiestocatertotheneedsofdifferentlearnersandachievebettereducationaloutcomesinmathematicseducationOneofthekeymathematicalconceptsunderlyingstructureproblemsistheunderstandingofgeometricprinciplessuchassymmetry,congruence,andsimilarity.Forinstance,inordertosolveastructureproblem,studentsneedtobeabletoidentifydifferenttypesofsymmetryintwo-dimensionalandthree-dimensionalshapes,andusethisknowledgetodeducepropertiesofthestructure.Thisincludesunderstandingtheconceptofrotational,translational,andreflectionalsymmetry,andbeingabletorecognizethesetypesofsymmetryindifferentshapes.

Anotherimportantmathematicalconceptunderlyingstructureproblemsistheunderstandingofbasicalgebraicprinciplessuchasequationsandinequalities.Inordertosolveastructureproblem,studentsoftenneedtotranslatetheproblemintoanequationorsetofequations,andthensolvetheseequationsusingalgebraictechniquessuchasfactoring,substitution,orelimination.Thisrequiresadeepunderstandingofthepropertiesofequationsandinequalities,suchasthedistributive,associative,andcommutativeproperties,aswellastheabilitytorecognizepatternsandmakelogicaldeductionsbasedonthesepatterns.

Finally,studentsneedtohaveastrongunderstandingofmathematicalconceptssuchasproportionality,ratios,andratesinordertosolvestructureproblems.Theseconceptsarecriticalforunderstandingtherelationshipsbetweendifferentpartsofastructure,andformakingaccuratepredictionsabouthowchangesinonepartofthestructurewillaffectotherparts.

Overall,acomprehensiveanddeepunderstandingofthemathematicalconceptsunderlyingstructureproblemsrequiresastrongfoundationingeometry,algebra,andproportionalreasoning.Studentswhoareabletomastertheseconceptsaremorelikelytobesuccessfulinsolvingcomplexstructureproblems,andaremorelikelytodevelopalastinginterestinmathematicsAdditionally,problemsolvingskillsandcriticalthinkingskillsarealsocrucialfortacklingstructureproblems.Theseskillsinvolvebeingabletoanalyzeinformation,identifypatternsandrelationships,andmakeinformeddecisionsbasedonevidence.Theycanbedevelopedthroughpracticeandexposuretoavarietyofproblems,aswellasthroughcollaborationwithpeersandteachers.

Anotherimportantaspectofsuccessfullysolvingstructureproblemsistheabilitytovisualizeandmanipulate3-dimensionalobjectsinthemind.Thisskillisknownasspatialreasoning,anditallowsindividualstomentallyrotateandmanipulateobjectstobetterunderstandtheirpropertiesandrelationships.Spatialreasoningcanbehonedthroughactivitiessuchaspuzzles,buildingwithblocksorLegos,andplayingvideogamesthatinvolvespatialmanipulation.

Lastly,effectivecommunicationskillsarekeyforexplainingsolutionstostructureproblemsinaclearandconcisemanner.Beingabletoarticulatemathematicalconceptsandprocessesisimportantfornotonlypresentingsolutionstoothers,butalsoforreinforcingone'sownunderstandingofthematerial.Workingingroupsorparticipatinginclassdiscussionscanbehelpfulfordevelopingthesecommunicationskills.

Inconclusion,solvingstructureproblemsrequiresacombinationofmathematical,problemsolving,spatialreasoning,andcommunicationskills.Buildingastrongfoundationalknowledgeofgeometry,algebra,andproportionalreasoningiscrucialforsuccess,asistheabilitytoanalyzeinformationandthinkcritically.Engaginginactivitiesthatdevelopspatialreasoningandeffectivecommunicationskillscanalsobehelpful.Withtheseskills