Singapore Math in Rotterdam 2 Opleiding Singapore rekenspecialist Review of Day 1 What are some features of Singapore Math and its theoretical underpinnings. On Day 2, we look at the focus on visualization and the model method.
Dec 23, 2014
Singapore Math in Rotterdam 2Opleiding Singapore rekenspecialist
Review of Day 1What are some features of Singapore Math and its theoretical underpinnings.
On Day 2, we look at the focus on visualization and the model method.
Variations
Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.
Math in Focus 2A
Math in Focus 2A
Math in Focus 2A
Zoltan Dienes
The three lessons include mathematical variations within the same grade.
This is referred to as a spiral approach.
It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation.
The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons.
Place Value Chart Expanded Notation
Numerals WordsTens and Ones Notation Primary Mathematics
Zoltan Dienes
This lesson include perceptual variations. This is Dienes’ idea of multiple embodiment. The
mathematical concept is constant while the materials used to embody it are varied.
Jerome Bruner
Bruner advised teachers to use the CPA Approach in teaching mathematics.
Richard SkempSkemp distinguished between instrumental
understanding from relational understanding to encourage teachers to teach for conceptual
understanding.
conceptual
Bina Bangsa School, Semarang, Indonesia
skemp’s
understandingtheory
Example 2
Division in Other Grade Levels
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
My Pals Are Here! Mathematics 3A
Keys Grade School, Manila, The Philippines
Keys Grade School, Manila, The Philippines
The Bar Model Methodde strookmodel
Yeap Ban Har, Ph.D.
Marshall Cavendish InstituteSingapore
Mathematics Curriculum Framework
Mathematical Problem
Solving
Attitudes
Metacognition
Proc
esse
s
Concepts
SkillsNumericalAlgebraic
GeometricalStatistical
ProbabilisticAnalytical
Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling
Numerical calculationAlgebraic
manipulationSpatial visualization
Data analysisMeasurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
Wellington Primary School
visualization
Primary Mathematics Standards Edition
John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?
19 cm x 5 = 95 cm
150 cm – 95 cm = 105 cm
There was an interesting discussion on this problem. There was an explanation that a + b + c = 19 cm. Then there was an assumption that a : b : c = 4 : 2 : 1 which was met with rebuttals such as there is no need to know a : b : c as well as the point that a : b : c can be determined by measuring or folding.
The Bar Model Methodde strookmodel
Yeap Ban Har, Ph.D.
Marshall Cavendish InstituteSingapore
Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?
Ali
Billy
Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?
Ali
Billy
Introduction
The focus is on the bar model method.
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Summary
The three basic situations are part-whole, comparison and before-after situations.
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
The class decided that this was
impossible. The teacher asked the class to change this to another
number to make the situation possible. We
discussed when it is 3, 4 and 5
times.
A student gave an incorrect solution
for the second part. The teacher asked students to write a question
for which this would be a correct
solution.
Summary
We discussed how to use students’ responses to make the lesson focus on depth. We also saw how a
problem can be modified to challenge learners.
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
School Assessment
women
men
School Assessment
women
men 12
45
School Assessment
women
men 12
45
6 6
?
women
men
Further Practice for Model Method
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping
Materials developed by Poon Yain Ping