Some Kinds of Learning Approach

1. Some Kinds of Learning Approach • Contextual Teaching and Learning (USA) • Open-Ended Approach (Japan) • Teaching in Context (Australia) • Concrete-Pictorial-Abstract (Singapore) • Realistic Mathematics Education, especially for Math (Holland) • Lesson Study Fajar Arwadi, Sriwijaya - Utrecht University

2. Fajar ArwadiSriwijaya - Utrecht University CONCRETE PICTORIAL ABSTRACT think globally act locally

3. Characteristics think globally act locally Fajar Arwadi, Sriwijaya - Utrecht University

4. CRITICAL ELEMENTS • Use appropriate concrete objects to teach particular math concept/skill • Use appropriate drawing techniques or appropriate picture representations of concrete objects • Use appropriate strategies for assisting students to move to the abstract level of understanding for a particular math concept/skill • When teaching at each level of understanding, use explicit teaching methods think globally act locally Fajar Arwadi, Sriwijaya - Utrecht University

5. How to implement • Describe & model math concept skillusing concrete objects (concrete level of understanding). • Provide students many practice opportunities using concrete objects. • Describe & model how to perform the skill by drawing or with pictures that represent concrete objects (representational level of understanding). • Provide many practice opportunities where students draw their solutions or use pictures to problem-solve. • Describe and model how to perform the skill using only numbers and math symbols (abstract level of understanding). • Provide many opportunities for students to practice performing the skill using only numbers and symbols. • Ensure students maintain their skill level by providing periodic practice opportunities for the math skills. think globally act locally Fajar Arwadi, Sriwijaya - Utrecht University

6. The advantages • Helps passive learner to make meaningful connections • Teaches conceptual understanding by connecting concrete understanding to abstract math process • Provides a graduated framework for students to make meaningful connections. • Blends conceptual and procedural understanding in structured way think globally act locally Fajar Arwadi, Sriwijaya - Utrecht University

7. Fraction Problem Fajar Arwadi, Sriwijaya - Utrecht University

8. Algebraic Problem • College students Bob and John both work part-time on weekends at the local restaurant, and are paid at the end of the day on Sunday. When they receive their pay Bob gets $10 more than John. Together they have $130. How much money does each person have? Fajar Arwadi, Sriwijaya - Utrecht University

9. Concrete: Count out $130 in play money. Give Student A (Bob) $10. Then divide the rest of the money ($120) between Student A (Bob) and Student B (John). Find out how much money each student has. Bob has $70 and John has $60. Fajar Arwadi, Sriwijaya - Utrecht University

10. Pictorial: Represent the $130 has $10 drawings on an overhead or on a board: $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 Identify the $10 for Bob (shown in bold italic): ($10) $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 Count how much money is left. ($120) Divide the remaining money equally between bob and John: Bob: ($10) + $10 $10 $10 $10 $10 $10 John: $10 $10 $10 $10 $10 $10 Count how much money Bob has: $70 Count how much money John has: $60 Fajar Arwadi, Sriwijaya - Utrecht University

11. Abstract The amount of money of Bob = x, John = (x - $10) • x + (x - $10) = $130 • 2 x - $10 = $130 • 2 x = $130 + $10 • 2 x = $140 • x = $70 (Bob) • x - 10 = $60 (John) Fajar Arwadi, Sriwijaya - Utrecht University

12. Review of Literature • David A. Sousa, BrainHow the Brain Learns Mathematics • Dr. SutartoHadi, M.Si., M.Sc. FKIP UniversitasLambungMangkurat, Banjarmasin Fajar Arwadi, Sriwijaya - Utrecht University

13. Thank You Very Much Fajar Arwadi, Sriwijaya - Utrecht University