EXT 3-6 Sampler

8 RTI Explicit InstructionUsingC–R–A DevelopingConceptualUnderstanding Extensions enables all students tobe successful, regardlessof their academicbackground, English languageproficiency, or special learningneeds. Using truemanipulativeswithin theC–R–Aprocess is the most important strategy for improving success and closing the achievement gap. The Concrete–Representational–Abstract (C–R–A) developmental approach isbased on stagesof learningasdescribedby cognitivepsychologist JeanPiaget and learning theorist JeromeBruner. TheC–R–Apedagogy isused in every lesson todevelop conceptual understandingandprovideaccess for all students. Instructionmoves students through the three stages: Stagesof Learning “Touch it. See it. Say it.” • Conceptual learningbegins at the concrete levelwith realworldexperiences and truemanipulativeactivities. Students look, touch, feel, andexploreobjects tohelpdiscover thebig ideawithin themathematical concept, e.g., 10ones is the sameas 1 ten. • Representational stage involves communicationas studentsdrawpictures and work in small groups towriteand talkaboutmath. The student page shows a pictorial representationofmanipulatives linking thehands-onexperience to theabstract stage. • The abstract numerals and symbols areusedas studentsbeginapplyingand practicing their new learning. As studentsmove through these stagesof learning, theyalsoexperience the three learning styles: kinesthetic , visual , and auditory . LearningStyles “We remember 10%ofwhat wehear, 30%ofwhat we see, and 90%ofwhat wedo.” —JeanPiaget “Evidence indicated that manipulatives provide valuable support for studentswhen teachers interact over timewith students tohelp thembuild links between the object, the symbol, and the mathematical ideaboth represent.” —Adding ItUp, NationalResearch Council, 2001 Kinesthetic Visual Auditory Tier 3 Tier 2 Tier 1 3 Concrete, Manipulative Representational, Visual Abstract, WrittenSymbols