基于认知弹性理论的数学结构不良问题教学策略研究

基于认知弹性理论的数学结构不良问题教学策略研究摘要：本研究旨在探究认知弹性理论在中学数学结构不良问题教学中的应用，以提高学生的学习效果和兴趣。首先，文章介绍了认知弹性理论的基本概念和相关理论。其次，针对数学结构不良问题的特点，提出了适合认知弹性理论的教学策略，包括激励、分组、反馈、重组等。最后，通过实验研究，验证了所提出的教学策略的有效性，并对未来教学实践进行了展望。研究结果表明，基于认知弹性理论的教学策略可以显著提高学生对数学结构不良问题的认知水平和学习兴趣，具有一定的推广价值。

关键词：认知弹性理论；数学结构不良问题；教学策略；学习效果；学习兴趣

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