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The study analyzes children’s approaches to representing unknown quantities in written notation and using their symbols to infer unknown values. Results indicate strong success for equal additive operations on known quantities (Study 1) and notable hesitation when creating representations for unknown quantities (Study 2), linked to difficulty choosing symbols without making incorrect assumptions about possible 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logical principle does the study focus on?","Question",{"text":112,"@type":113},"The study focuses on the principle that performing equivalent operations on both the left and right terms of an equation yields a new equation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do children use this principle in problem solving?",{"text":117,"@type":113},"The paper examines how third-grade children recognize and apply equivalence to isolate a variable on one side and reason about unknown values on the other.",{"name":119,"@type":110,"acceptedAnswer":120},"Why do children hesitate when representing unknown quantities?",{"text":121,"@type":113},"Children show considerable hesitation in producing written representations for unknown quantities because it is challenging to choose a symbol that does not constrain or impose incorrect presumptions about what the unknown value could 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\nABSTRACT  \nDOCUMENT RESUME  \nSchliemann,Analucia D.;Carraher,David W.;Brizuela,Barbara M.;Jones,Wendy  \nSolving Algebra Problems before Algebra Instruction.National Science Foundation,Arlington,VA.  \n1998-00-00  \n29p.;Earlier version presented at the Annual Early AlgebraMeeting(2nd,Medford,MA,1998).  \n9722732  \nReports -Research(143)--Speeches/Meeting Papers(150)MF01/PC02 Plus Postage.  \n*Algebra;Elementary Secondary Education;*Equations(Mathematics);Mathematics Instruction;*Problem Solving  \nIf equivalent operations are performed on the left term andright term of an equation,a new equation results.This principle allows oneto produce equations with a variable isolated on one side and its value(s)onthe other.It also underlies problem-solving in situations where equationsare not explicitly used,but the problem calls for recognizing that twoquantities are equal in value and using that information to derive  \nconclusions about values of unknown quantities.The present paper focuses onhow third-grade children recognize and use this logical principle in solvingproblems.It also looks at issues children face as they try to representunknowns through written notation and use their written symbols to drawinferences about unknown values.The results showed that children comfortablyrecognized that equal additive operations upon equal quantities produce equalresults(Study 1).Further,they easily produced written representations ofknown(numerically quantified or measured)quantities.However,the childrenshowed considerable hesitation about producing written representations forunknown quantities(Study 2).Their hesitation seems to stem from the  \nchallenge of finding a symbol to represent a quantity without constraining ormaking incorrect presumptions about values it may stand for.(Author)  \n\n| Reproductions supplied by EDRS are the best that can be made  \u003Cbr>from the original document.   |\n| --- |\n\n拿  \n8J  \nERIC  \nU.S.DEPARTMENT OF EDUCATIONOmce of Educarional Rosearch and ImorovemenlEDUCATIONAL RESOURCES INFORMATION梁CENTER(ERIC)This document has been reproduced asV received from the person or organizationoriginating it.  \nPERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HASBEEN GRANTED BY  \nA.Schliemann  \n□ Minorchanges have been made toimprove reproduction quality.  \nTO THE EDUCATIONAL RESOURCESINFORMATION CENTER(ERIC)  \nPoints of view or opinions stated in thisdocument do not necessarily representofticial OERI position or policy.  \n# Solving Algebra Problems Before Algebra Instruction\n\nAnalúcia D.Schliemann,Tufts UniversityDavid W.Carraher,TERCBárbara M.Brizuela,Harvard UniversityWendy Jones,Tufts University  \nThis study was conducted as part of a National Science Foundation grant (\\#9722732)awarded to the first author.An earlier version of this paper was presented at theSecond Early Algebra Meeting,University of Massachusetts-Dartmouth&TuftsUniversity,Medford,MA,1998.  \nBESTCOPYAVAILABLE  \nAbstract  \nIf equivalent operations are performed on the left and right terms of an equation,a new equation results.This principle allows one to produce equations with a variableisolated on one side and its value(s)on the other.It also underlies problem-solving insituations where equations are not explicitly used,but the problem calls for recognizingthat two quantities are equal in value and for using that information to deriveconclusions about values of unknown quantities.  \nThe present paper focuses on how third-grade children recognize and use thislogical principle in solving problems.It also looks at issues children face as they try torepresent unknowns through written notation and use their written symbols to drawinferences about unknown values.The results showed that children comfortablyrecognized that equal additive operations upon equal quantities produce equal results(Study 1).Further,they easily produced written representations of know","cbCaiiU6I3GZ0FSl","https://ap.wps.com/l/cbCaiiU6I3GZ0FSl","pdf",386995,31,"English","# Abstract\n# Introduction","[{\"question\":\"What logical principle does the study focus on?\",\"answer\":\"The study focuses on the principle that performing equivalent operations on both the left and right terms of an equation yields a new equation.\"},{\"question\":\"How do children use this principle in problem solving?\",\"answer\":\"The paper examines how third-grade children recognize and apply equivalence to isolate a variable on one side and reason about unknown values on the other.\"},{\"question\":\"Why do children hesitate when representing unknown quantities?\",\"answer\":\"Children show considerable hesitation in producing written representations for unknown quantities because it is challenging to choose a symbol that does not constrain or impose incorrect presumptions about what the unknown value could be.\"}]","Solving Algebra Problems before Algebra Instruction | PDF",1792061769,78]