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The ABCDs of Singapore Math,[object Object],Lower School Professional Development,[object Object],St Edward’s School,[object Object],Vero Beach FL,[object Object],www.banhar.blogspot.com,[object Object],Yeap Ban-Har, Ph.D.,[object Object],Singapore,[object Object],banhar.yeap@pathlight.org.sg,[object Object],DaQiao Primary School,[object Object]
Catholic High School (Primary),[object Object]
introduction,[object Object],Wellington Primary School,[object Object]
Classroom Task,[object Object],Lesson Study Problem ,[object Object],Wellington Primary School,[object Object],Move 3 sticks to make 3 squares.,[object Object]
Move 3 sticks to make 3 squares.,[object Object]
Move 3 sticks to make 3 squares.,[object Object]
Move 3 sticks to make 2 squares.,[object Object]
Move 3 sticks to make 2 squares.,[object Object]
Move 3 sticks to make 2 squares.,[object Object]
88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. ,[object Object],	How many girls wore swimming goggles on that day?,[object Object],Teacher-Constructed Test Item,[object Object],Fairfield Methodist Primary School,[object Object]
[object Object],	How many girls wore swimming goggles on that day?,[object Object]
88,[object Object],34,[object Object],54,[object Object],[object Object],How many girls wore swimming goggles on that day?,[object Object]
34 – 20 = 14,[object Object],54 – 34 = 20,[object Object],34,[object Object],54,[object Object]
3 x 7 = 21,[object Object],21 girls wear goggles.,[object Object]
Beliefs,[object Object],Interest,[object Object],Appreciation,[object Object],Confidence,[object Object],Perseverance,[object Object],Monitoring of one’s own thinking,[object Object],Self-regulation of learning,[object Object],Attitudes,[object Object],Metacognition,[object Object],Numerical calculation,[object Object],Algebraic manipulation,[object Object],Spatial visualization,[object Object],Data analysis,[object Object],Measurement,[object Object],Use of mathematical tools,[object Object],Estimation,[object Object],Mathematical Problem Solving,[object Object],Reasoning, communication & connections,[object Object],Thinking skills & heuristics,[object Object],Application & modelling,[object Object],Skills,[object Object],Processes,[object Object],Concepts,[object Object],Numerical,[object Object],Algebraic,[object Object],Geometrical,[object Object],Statistical,[object Object],Probabilistic,[object Object],Analytical,[object Object],Mathematics Curriculum Framework,[object Object]
Philosophy of the Education System,[object Object],thinking schools,[object Object],learning nation,[object Object],Ministry of Education 1997,[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],Trends in,[object Object],Mathematics,[object Object],This  whole shape stands for 1.,[object Object],& Science Studies,[object Object],What does this stand for?,[object Object],apply,[object Object],their understanding,[object Object],and knowledge,[object Object],in a variety of,[object Object],complex situations,[object Object]
Trends in,[object Object],Mathematics,[object Object],& ScienceStudy,[object Object],explain,[object Object],their reasoning,[object Object],mathz4kidz Learning Centre, Penang, Malaysia,[object Object]
mathematical,[object Object],literacy,[object Object],… capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life …,[object Object],OECD Program for International Student Assessment (PISA),[object Object]
effective,[object Object],mathematics,[object Object],teaching,[object Object],BinaBangsa School, Indonesia,[object Object]
Primary Mathematics 1A,[object Object],Pedagogical Principle:,[object Object],Bruner,[object Object]
Number Bonds,[object Object],PCF Kindergarten TelokBlangah,[object Object]
Number Bonds,[object Object],PCF Kindergarten TelokBlangah,[object Object]
Bruner,[object Object],The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. ,[object Object],Division,[object Object],National Institute of Education,[object Object]
Division,[object Object],Princess Elizabeth Primary School,[object Object]
Catholic High School (Primary),[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],bruner’s theory,[object Object],concrete,[object Object],A lesson from Earlybird Kindergarten Mathematics,[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],concrete,[object Object],experiences,[object Object]
from,[object Object],concrete,[object Object],to,[object Object],pictorial,[object Object],mathz4kidz Learning Centre, Penang, Malaysia,[object Object]
from,[object Object],pictorial,[object Object],to,[object Object],abstract,[object Object],All Kids Are Intelligent Series,[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],symbols,[object Object]
using,[object Object],concrete,[object Object],materials,[object Object],Professional Development in AteneoGrade School, Manila, The Philippines,[object Object],Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile,[object Object]
Primary Mathematics (Standards Edition) 2A,[object Object],Pictorial Before Abstract,[object Object]
     bruner,[object Object],Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile,[object Object]
skemp’s,[object Object],theory,[object Object],conceptual,[object Object],understanding,[object Object],BinaBangsa School, Semarang, Indonesia,[object Object]
Keys Grade School, Manila, The Philippines,[object Object]
Keys Grade School, Manila, The Philippines,[object Object]
Skemp,[object Object],Understanding in mathematics  ,[object Object], relational,[object Object],  (conceptual) ,[object Object], instrumental  ,[object Object],  (procedural),[object Object], conventional  ,[object Object],Teaching for conceptual understanding is given emphasis in Singapore Math.,[object Object],Pedagogical Principle:,[object Object],Skemp,[object Object],Primary Mathematics Standards Edition Grade 6,[object Object]
Fraction Division,[object Object],Primary Mathematics Standards Edition Grade 6,[object Object]
skemp,[object Object],Scarsdale Middle School New York,[object Object]
Dienes,[object Object],Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. ,[object Object],Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition ,[object Object],Primary Mathematics Standards Edition Grade 1,[object Object]
Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition Grade 1,[object Object]
Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition Grade 2,[object Object]
How is Task 4 different from Task 5?,[object Object],16,[object Object],Primary Mathematics Standards Edition Grade 5,[object Object]
16,[object Object],What is the given in Task 5? What is the given in Task 6? Are these different?,[object Object],30,[object Object],Primary Mathematics Standards Edition Grade 5,[object Object]
Earlybird Kindergarten  Mathematics ,[object Object],Standards Edition ,[object Object],Can you see how Dienes’ idea is used in designing these tasks?,[object Object],diene’s,[object Object],theory,[object Object],of,[object Object],variation,[object Object]
  dienes,[object Object],Princess Elizabeth Primary School, Singapore,[object Object]
thinking,[object Object],problem solving,[object Object],bruner’scpa approach,[object Object],conceptual understanding,[object Object],diene’s variations,[object Object]
Emphasis on pictorial representation and systematic variation to enhance conceptual understanding,[object Object]
conclusion,[object Object],PCF Kindergarten PasirRis,[object Object]
Instructional Models,[object Object],[object Object]
 Modeling
 Providing
ExplaningDaQiao Primary School,[object Object]
“Children are trulythe future of our nation. “,[object Object],Irving Harris,[object Object]

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St Edward's School, Florida

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