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There are three aspects of mathematical thinking were described, one of them is VISUALIZATION (the others are patterning and number sense)

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- 1. Empower YourTeachers to Deliver aWorld-Class Programme on Teacher Leadership and Teacher Development by: Poppy Ardhyani Grade 5 Teacher Sekolah Bogor Raya November 2009
- 2. World-Class Programme (Singapore Curriculum)• Engaging 1. Learning by doing (especially for young children) 2. Learning by inquiry (a strategy to have students to investigate a problem instead of giving them the formula to solve it) 3. Learning by interacting 4. Learning by reflecting, e.g. maths journal at the end of the class (what can I do to solve the problem, what can I do to help my friend) Relevant Whom you teach will contribute to what your country needs in economical development Effective Schools that can bring the average students to perform above average
- 3. Sharing Effective Teaching Strategies on How to Teach Measurement for Upper Primary Measurement is one of the four broad areas of mathematical knowledge (algebra, geometry, algorithm, and trigonometry) There are three aspects of mathematical thinking were described, one of them is VISUALIZATION (the others are patterning and number sense)
- 4. What is Visualization Skill?The ability of the mind to work with abstract ideas – to analyze and synthesize ideas.Aim: to let students construct a formula of what they see (Constructivism - Piageat).
- 5. Examples1. Draw kinds of polygon of area 5 squared!
- 6. 2. Can you draw a square of area 5 squared? This square consists of: 1 small square = 1 squared 4 triangles (composition of 2 triangles equals to 2 squared) = 4 squared Area = 5 squared Visualization will help students form “conceptual knowledge” (informal knowledge) first knowledge in maths
- 7. Finding a Formula• Find the area of the shaded area! ( is indifferenced)! This figure shows a square of side 14 cm, 1 circle of diameter 14 cm, and 2 quadrants. 1. Area of that square is 196 cm2. 2. Area of the circle is approximately d2 y196 cm2. 3. Area of 1 quadrant is ¼ x 196 y 49 cm2.
- 8. This figure shows a triangle (yellow shaded) of base ½ of diameter = ½ x 14 = 7 cm. 4. Area of that triangle is ½ x 7 x 7 = 24.5 cm2. 5. Area of 1 shaded area y Area of the quadrant – area of the triangle y 49 cm2 - 24.5 cm2 = 24.5 cm2 . 6. Therefore the area of 2 shaded area is approximately: 2 x 24.5 cm2 y 49 cm2.Conceptual knowledge will helpstudents develop “the proceduralknowledge” (formal knowledge) the2nd knowledge in maths
- 9. Problem Solving Tips 4 Steps of Problem Solving Tips for Solving A Problem (Practically)1. Understanding the problem 1. Finding the fact2. Devising a plan 2. Starting counting whenever you are ready3. Carrying out the plan 3. Doing the easiest problem first then spending the rest of the time for solving the higher order problem4. Looking back 4. Looking back Public acknowledge the concept and procedure which is called “conventional knowledge” the 3rd knowledge in maths
- 10. Do’s & Don’t’s in teaching measurement for the elementary level 1. Word “capacity” to explain empty container. 2. Word “volume” to explain the volume of liquid and solid. 3. Use “side” instead of “width or length” to explain square 4. Teacher’s should not use too many symbols in maths. 5. Keep students learning in informal way (let them build their conceptual knowledge by visualization skill)
- 11. What counts as maths proficient? 1. Procedural fluency 2.Conceptual reasoning/ meaning 3.Strategic competency 4.Reasoning (adaptive reasoning)THINGS 5.Productive disposition
- 12. Thank you foryour attention….. Prepared by: Poppy Inspired by: Dr. Yeap Ban Har

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