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Concrete-Representational-Abstract Instruction

Concrete-Representational-Abstract Instruction. Objectives. At the end of this training you will be able to describe the components of concrete-representational-abstract (CRA) instruction create a lesson supported by the CRA sequence relate the benefits of CRA.

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Concrete-Representational-Abstract Instruction

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  1. Concrete-Representational-AbstractInstruction 2010 Region 3 Education Service Center / Texas A&M University

  2. Objectives At the end of this training you will be able to • describe the components of concrete-representational-abstract (CRA) instruction • create a lesson supported by the CRA sequence • relate the benefits of CRA 2010 Region 3 Education Service Center / Texas A&M University

  3. Components of Effective Math Instruction Explicit strategy instruction using a step-by-step approach Mastery at each step Effective teaching components (teacher modeling, guided practice, independent practice, immediate corrective positive feedback) A wide range of examples and nonexamples Clear, concise instruction with definitions of potentially confusing terms and skills Cumulative review 2010 Region 3 Education Service Center / Texas A&M University

  4. CRA Instructional Sequence CRA is a three-part instructional strategy Each subsequent part builds on previous instruction The sequence promotes student learning and retention 2010 Region 3 Education Service Center / Texas A&M University

  5. Research Evidence • Teaching equivalent fraction concepts and procedures (Butler et al., 2003) • Fraction circles and beans • Coloring portion of items to make fraction • Abstract symbols and algorithm • Teaching multiplication facts and related word problems (Morin and Miller, 1998) • Paper plates and wooden blocks • Pictures of containers and items • Numbers 2010 Region 3 Education Service Center / Texas A&M University

  6. CRA Sequence 2010 Region 3 Education Service Center / Texas A&M University

  7. CRA Principles The CRA sequence should be very explicit and systematic, with multiple opportunities for both guided practice and independent practice. 2010 Region 3 Education Service Center / Texas A&M University

  8. Definition of Concrete The use of manipulatives or models that represent the concept being studied is critical. It is the “doing” step of instruction. Students must be fluent in manipulation of the concrete materials and must be able to explain the connection to the skill. Howell and Barnhart (1992) identified six steps in teaching from concrete to representational levels. 2010 Region 3 Education Service Center / Texas A&M University

  9. Stage I: Concrete Step 1: Free exploration Step 2: Purposeful exploration Step 3: Number cards Step 4: Number sentence Step 5: Mathematical word problems Step 6: Verbal explanation (Howell and Barnhart, 1992) 2010 Region 3 Education Service Center / Texas A&M University

  10. Step 2: Purposeful Exploration 2010 Region 3 Education Service Center / Texas A&M University

  11. Step 3: Number Cards 6 + 3 = 9 2010 Region 3 Education Service Center / Texas A&M University

  12. Step 4: Number Sentence 3 stars + 4 stars = 7 stars 2010 Region 3 Education Service Center / Texas A&M University

  13. Step 5: Mathematical Word Problems There are three green buttons in a box. There are also two yellow buttons in the box. How many buttons are in the box altogether? 3 2 + = 5 2010 Region 3 Education Service Center / Texas A&M University

  14. Step 6: Verbal Explanation Students should verbalize what they did to solve the problem and why. Students should be taught to mastery level for each step before moving to the next step. 2010 Region 3 Education Service Center / Texas A&M University

  15. Activity Activity #1 • Working with a partner, teach students to solve a subtraction problem by using manipulatives. • Keep the steps in mind: Step 1: Free exploration Step 2: Purposeful exploration Step 3: Number cards Step 4: Number sentence Step 5: Mathematical word problems Step 6: Verbal explanation 2010 Region 3 Education Service Center / Texas A&M University

  16. Guidelines for Using Manipulatives Handout #1 • Select manipulatives that clearly illustrate the concept. • Use a variety of manipulatives that illustrate the concept. • Provides verbal explanations while incorporating the manipulatives. • Provide multiple opportunities for guided practice. • Encourage the use of manipulatives and strategies across settings. • Plan a graduated instructional sequence that will allow transition from concrete to symbolic representation.(Maccini and Gagnon, 2000) 2010 Region 3 Education Service Center / Texas A&M University

  17. Definition of Representational Replacing concrete manipulative objects with pictures or drawings The “seeing” step of instruction Division into a semiconcrete level and a semiabstract level Six steps in the representational stage (Howell and Barnhart, 1992) 2010 Region 3 Education Service Center / Texas A&M University

  18. Stages and Levels Abstract stage Semiconcrete level Semiabstract level Representational stage Concrete stage (Howell and Barnhart, 1992) 2010 Region 3 Education Service Center / Texas A&M University

  19. Stage 2: Representational (Howell and Barnhart, 1992) Step 1: Picture representation cards Step 2: Number sentences (semiconcrete) Step 3: Mathematical word problems Step 4: Graphic representation Step 5: Number sentences (semiabstract) Step 6: Mathematical word problems 2010 Region 3 Education Service Center / Texas A&M University

  20. Step 1: Picture Representation Cards 2010 Region 3 Education Service Center / Texas A&M University

  21. Activity for Step 1 Activity #2 2010 Region 3 Education Service Center / Texas A&M University

  22. Step 2: Number Sentences (Semiconcrete) Activity #3 2010 Region 3 Education Service Center / Texas A&M University

  23. Step 3: Mathematical Word Problems Activity #4 Number sentence: 3 + 6 = 9 2010 Region 3 Education Service Center / Texas A&M University

  24. Step 4: Graphic Representation Activity #5 2010 Region 3 Education Service Center / Texas A&M University

  25. Step 5: Number Sentences (Semiabstract) 3 + 4 = 7 2010 Region 3 Education Service Center / Texas A&M University

  26. Step 6: Mathematical Word Problems 4 + 12 = 16 Jackie has $4 allowance left. Her mom gives her $12 more today. How much allowance does she have altogether? 2010 Region 3 Education Service Center / Texas A&M University

  27. Definition of Abstract The “symbolic” step of instruction Written mathematical numbers are used to represent concepts or skills Thinking strategy to solve word problems, with five questions to ask (Howell and Barnhart, 1992) 2010 Region 3 Education Service Center / Texas A&M University

  28. Stage 3: Abstract (Howell and Barnhart, 1992) Five questions used as procedural prompts that help students become independent problem solvers: 1. What is the question? 2. What are the numbers in the problem? 3. What do I need to do with the numbers? 4. What is the answer? 5. How can I check the answer? 2010 Region 3 Education Service Center / Texas A&M University

  29. Hint Words Handout #2 • Preteach vocabulary • Addition—add, in all, sum, together, total • Subtraction—subtract, more, less, difference • Multiplication—multiply, time, by, each, of • Division—divide, group, how many times • Tips • Follow CRA sequence, and teach to mastery for each stage before moving to the next • Use explicit and systematic instruction • Provide many opportunities to respond • Use real-life contexts 2010 Region 3 Education Service Center / Texas A&M University

  30. Step 1: What Is the Question? How many more? Adam has 12 marbles, and Jack has 6 marbles. How many more marbles does Adam have? 2010 Region 3 Education Service Center / Texas A&M University

  31. Step 2: What Are the Numbers? How many more? Adam 12 Jack 6 Adam has 12 marbles, Jack has 6 marbles. How many more marbles does Adam have? 2010 Region 3 Education Service Center / Texas A&M University

  32. Step 3: What Do I Need to Do with the Numbers? How many more? Adam 12 12 Jack 6 – 6 2010 Region 3 Education Service Center / Texas A&M University Adam has 12 marbles, Jack has 6 marbles. How many more marbles does Adam have?

  33. Step 4: What Is the Answer? How many more? Adam 12 12 Jack 6 – 6 6 Adam has 12 marbles, and Jack has 6 marbles. How many more marbles does Adam have? 2010 Region 3 Education Service Center / Texas A&M University

  34. Step 5: How Can I Check the Answer? How many more? Adam 12 //// / ////// 12 Jack 6 //// / – 6 ////// 6 2010 Region 3 Education Service Center / Texas A&M University Adam has 12 marbles, and Jack has 6 marbles. How many more marbles does Adam have?

  35. Activity Activity #7 Work with a partner. Plan to teach students to multiple four by six with the CRA sequence. • Identify what manipulatives to use • Make up a word problem • Identify what activities to use for each step in each stage • Discuss what other strategies you will use to teach the skill 2010 Region 3 Education Service Center / Texas A&M University

  36. Closure Take out your Change of Practice Plan. Think about what you learned in this module, and relate it to your classroom. Write down some ideas of what you want to start using in your classroom. 2010 Region 3 Education Service Center / Texas A&M University

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