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

Fajar Arwadi Sriwijaya - Utrecht University CONCRETE PICTORIAL ABSTRACT Fajar Arwadi Sriwijaya - Utrecht University think globally act locally

Characteristics think globally act locally Concrete Pictorial Abstract think globally act locally Fajar Arwadi, Sriwijaya - Utrecht University

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

How to implement Describe & model math concept skill using 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

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

Fajar Arwadi, Sriwijaya - Utrecht University Fraction Problem Fajar Arwadi, Sriwijaya - Utrecht University

Fajar Arwadi, Sriwijaya - Utrecht University 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

Fajar Arwadi, Sriwijaya - Utrecht University 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

Fajar Arwadi, Sriwijaya - Utrecht University 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

Fajar Arwadi, Sriwijaya - Utrecht University 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

Fajar Arwadi, Sriwijaya - Utrecht University Review of Literature David A. Sousa, Brain How the Brain Learns Mathematics Dr. Sutarto Hadi, M.Si., M.Sc. FKIP Universitas Lambung Mangkurat, Banjarmasin   Fajar Arwadi, Sriwijaya - Utrecht University

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