WEBVTT

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Hi, good afternoon parents.

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Welcome to our 2021
Parent Empowerment Workshop Series.

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My name is [Name]

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I am a senior manager for student
and corporate affairs.

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Now before we start,

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I know a lot of parents are still coming in

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so let me just go through some of the
housekeeping rules.

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I think for many of you who have already
used zoom

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you will know that upon entry

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participants will be muted and their
video function will been disabled.

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Please ensure that your devices
speakers are enabled

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and for best audio experience
you may wish to use your earphones.

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If you have technical issues, please use
the chat function to alert us

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and to encourage interaction
for this workshop series

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you can ask questions
throughout the session.

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Please use the QNA function below

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and please do not use the chat function
because we will not be monitoring that.

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We will be monitoring the QNA function
for the questions asked

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And doctor Yip, our workshop facilitator

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will be answering the questions
as they come along.

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And just a reminder

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strictly no recording
by participants is allowed

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This workshop series will be put up
on Learn for Life eCampus

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to enable parents who have
missed this session

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or if you wish to revisit some of the
highlights of the workshop.

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Many of you with children
in mainstream schools

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you'll be very familiar with
Parents Support Group (PSG).

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In Pathlight we don't have PSG

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we have what we call

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Parent-School Collaboration Teams

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and we have five of them.

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So basically we have one PSCT for short
on safety

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and this safety is when parent volunteers
can come in and

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accompany our students when they go for
external learning journeys.

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We also have a PSCT for work opportunities

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so some of you who are highly placed
in your organisation

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and are able to open doors for us for

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FAM tours or even internships

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please volunteer in this PSCT.

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We also have a PSCT for family bonding

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to organise activities for the families
to enjoy family time together.

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And there's also a PSCT for greening

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so we have a group of enthusiastic parents
who usually come

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and help to contribute
to make the school beautiful.

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And then of course I head the PSCT
for parent empowerment.

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So it has been more than a year since we

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suspended all PSCT activities
due to COVID.

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So this year, I think we are very pleased
to bring back this

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Math workshop series

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conducted by Doctor Dr Yeap Ban Har.

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It's a very very popular series

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we always get more than 95% approval rates

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from parents who attended our workshops.

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Let me give you a short introduction
of Dr Yeap.

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Dr Yeap is our director of curriculum and

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teacher development at Pathlight School.

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He usually conducts paid 
math education courses around the world

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and he told me he has covered close to 40
countries to date.

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He is an author of math textbooks
and consultant

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and his books have been translated
to seven languages.

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So don't play play ah!

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he's a very accomplished and

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learn-et??? educator.

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He holds a Master of Education and
Ph.D. in math education.

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So without much further ado

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let me pass the floor to Dr Yeap.

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Lets welcome Dr Yeap please.

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Good evening parents

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thank you for joining me this evening

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My name is Ban Har

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and I'll be conducting this webinar.

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The focus of today’s webinar

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is on helping children

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process information in Mathematics.

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In this webinar

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I will help all of us understand

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the kind of information that students...

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need to process...

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whenever they do mathematics.

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And I will suggest
some ways of helping them

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ways that adults including parents

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will be able to use quite easily

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whenever we engage them
with their mathematics at home.

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So that's our plan this evening.

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Through examples,

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we are going to be looking at

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the kind of information

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that students need to handle
in Mathematics

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and I will suggest some ways

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to help students
become more proficient in this.

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But before we get into the content

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let me give a brief introduction.

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Whenever we help students with anything

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we are always helping them with
not only the skills

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but also the mindset.

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Without the corresponding lens

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without the corresponding mindset

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students sometimes cannot use the skill
that they have acquired.

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In other words,

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skills...

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without the right mindset...

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sometimes are still not useful.

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Do you sometimes see your children
able to do something

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but then...

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on their own...

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they don't seem to be able to do it?

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That will be symptomatic of having skills

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without the corresponding mindset.

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What do I mean by that?

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Some students...

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think that Mathematics is a subject
where they remember stuff.

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That mindset...

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is counterproductive.

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Research has shown us that

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children who think of Mathematics

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as a subject where they remember things,

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they do less well...

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than children...

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who understand the exact nature
of mathematics.

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So what is the exact nature
of mathematics?

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Mathematics is a language.

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Children who understand mathematics
as a language

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and learn mathematics as a language

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they do far better...

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than children who think that

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mathematics is a subject where you
remember things

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where you memories things.

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Secondly,

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children sometimes accidentally think that

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mathematics is a subject
where you answer questions.

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They perceive mathematics as

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a subject where people ask you question

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and you answer it.

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mathematics is not like that.

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Mathematics is a subject 
where you figure things out

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it's not a subject where you are
answering a question all the time.

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So sometimes as adults,
parents, and teachers alike

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we have made children perceive mathematics

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with a incorrect mindset.

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In summary,

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children who are successful...

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highly successful in mathematics

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they see mathematics as

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1. A language

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2. A subject where they think

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a subject where they figure things out.

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Mathematics as a language.

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Do you know that mathematics
is a language?

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Yes it is

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it is a language to describe
things around us.

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When you see things around you,

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you try to describe it.

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Example:

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you might try to say

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"4 groups of children"

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and in mathematics we have multiplication

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to describe that.

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Or sometimes you try to put

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a tray of 60 cookies

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you try to pack them into

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maybe...

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containers of 24's

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and I wonder whether
there is enough cookies

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to give you full containers or not

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or there might be some leftover...
some remainder.

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So putting 60 cookies into
containers of 24

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can be described quite precisely

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in this case using the concept
of division.

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Mathematics as a language
is a productive way

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for children to think about the subject.

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And like in any language
there are different alphabet systems

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so to speak.

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There are different grammars

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there are different rules.

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In mathematics,

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there are three alphabet systems

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so when we say that
"oh I understand mathematics"

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as in I understand Spanish
or I understand Japanese

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or I understand whatever language

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what does it mean?

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It means 3 things:

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Firstly,

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it means we can read
and comprehend visuals

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we might see,

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1 row of 3

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2 rows of 3

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3 rows of 3

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4 rows of 3

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5 rows of 3

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and so on...

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6 rows of 3

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7 rows of 3.

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Of course it's written like so

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7 rows of 3

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I know as adults sometimes you get lazy

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and we don't read

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we spell.

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Spelling is making sounds of the symbols

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so we say 7 times 3

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that means you are spelling out
that expression.

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In what language do we spell out
every single word?

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Can you imagine reading a book

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and spelling every single word
in the book?

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How much of it
will you actually understand?

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and how much of it
will you actually enjoy?

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quite little right?

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Do children know how to read mathematics?

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Or are they spelling out
every single expression?

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When we say that children
understand mathematics,

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it means that they look at the visual

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and they can read it,

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they can comprehend it,

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they can make use of it.

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This is one kind of information
that children need to process

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meaning: Read, Comprehend, Make use of it.

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I can make use of this. For example,

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let's say I forget my times table

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and I need to know 7 groups of 3

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7 rows of 3.

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I can say "well I know 7 rows of 3
is actually...

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5 rows of 3...

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that's 15

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and also 2 rows of 3
that's 6.

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so 7 rows of 3 is simply
15 and 6

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15 and 6,

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6 is really 5 and 1

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15 and 5 is simply 20

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20 and 1 is 21.

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Do children read when they do mathematics?

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The way I just demonstrated it.

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So that is what I mean parents

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by mathematics is a language.

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And this is the first type of information

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that out children need to be good at

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Visual information:

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how to read,

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how to comprehend,

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how to make use of it.

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Other than visuals,

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they also need to be able to comprehend...

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symbols

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they must be able to read symbols.

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So when they see things like

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this...

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they know what that means

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they know it's five 10's and one 1

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so they know that it actually represents

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5 of the blues

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and 1 of the yellow

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so when they see the symbol 51

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they know the 5 refer to one item,
the blues

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which is actually 10

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and the 1 refers to the yellows
which refer to 1.

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So this is a highly efficient
way of saying

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5 of this and 1 of that

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which if you say in plain language
is quite lengthy

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you have just heard that

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five of 10 and one of 1

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but in mathematics we have a short and

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a highly precise way, highly encoded way

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of symbols to describe the same thing.

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So when children look at symbols,

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they understand what it means.

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51

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share equally among 3.

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So just like what I said earlier

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do children read mathematics?

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They must.

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If they say 51 divided by 3

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they may not get the full meaning of it.

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in this case as sharing among 3.

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So parents,

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Mathematics is a language

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and it's a language that comprises of

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not just visual,

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but also symbols.

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What else?

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Words

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a verbal language.

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In our case English.

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English or Spanish or Japanese or Chinese

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whatever language the children are
learning mathematics in

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in that society.

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For ours it is English language.

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A verbal language like English language
is part of mathematical language.

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In summary, mathematical language

00:16:22.973 --> 00:16:25.113
comprises of

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visuals, diagrams,
pictures, graphs,

00:16:31.781 --> 00:16:32.873
tables,

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it also includes symbols,

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notations,

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finally it also includes a verbal language

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example, English.

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So children need to be able to understand

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when I write a sentence

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Spiky... has

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more... coins

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than Curly,

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they must be able to read this

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and make sense of it,

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they must know who has more

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and who has fewer coins.

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Spiky has more coins than Curly.

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3 more.

00:17:25.417 --> 00:17:26.237
Spiky...

00:17:28.292 --> 00:17:30.171
has ten coins.

00:17:33.067 --> 00:17:36.096
So if Spiky has ten coins

00:17:36.620 --> 00:17:40.407
and he has more coins than Curly

00:17:40.832 --> 00:17:45.417
then obviously Curly's number of coins
will be less than ten.

00:17:47.835 --> 00:17:51.149
Because Spiky has more
and Spiky has ten

00:17:51.772 --> 00:17:56.518
so obviously, Curly
whatever number she has

00:17:57.373 --> 00:18:00.764
that number is less than ten.

00:18:01.205 --> 00:18:05.669
So Curly has fewer than ten coins

00:18:06.823 --> 00:18:07.587
isn't it?

00:18:07.920 --> 00:18:13.825
So in this case, we can obtain the answer
by doing a subtraction.

00:18:14.186 --> 00:18:15.064
Isn't it?

00:18:15.988 --> 00:18:16.749
So...

00:18:18.844 --> 00:18:19.956
if you do this

00:18:19.956 --> 00:18:21.851
please stop doing it from now on.

00:18:21.870 --> 00:18:23.350
Please don't tell your children

00:18:23.350 --> 00:18:24.472
"eh ah boy ah

00:18:24.636 --> 00:18:26.473
you see the word more you add okay?"

00:18:27.160 --> 00:18:28.590
parents please don't do that.

00:18:29.127 --> 00:18:29.834
Why?

00:18:30.323 --> 00:18:31.124
It's wrong

00:18:31.232 --> 00:18:32.087
obviously.

00:18:32.504 --> 00:18:33.833
It could be anything,

00:18:34.385 --> 00:18:36.156
the word more does not mean add,

00:18:36.298 --> 00:18:38.005
it could be anything really,

00:18:38.231 --> 00:18:39.800
in this case subtraction.

00:18:40.489 --> 00:18:42.208
There is no shortcut,

00:18:42.649 --> 00:18:44.840
there is no tricks

00:18:45.378 --> 00:18:48.654
tricks are not for children,
tricks are for circus animals.

00:18:49.078 --> 00:18:51.116
There are no tricks in mathematics,

00:18:51.275 --> 00:18:53.214
mathematics is a language

00:18:53.418 --> 00:18:57.438
and we use words, we use symbols,
we use visuals

00:18:57.575 --> 00:19:00.032
to describe whatever we want to describe.

00:19:00.074 --> 00:19:02.102
Alright so parents

00:19:02.197 --> 00:19:04.746
those are the three kinds of information

00:19:05.418 --> 00:19:07.611
that children have to encounter

00:19:08.269 --> 00:19:10.092
when they learn mathematics.

00:19:11.179 --> 00:19:15.069
I will illustrate with some examples
after I attend to some questions.

00:19:15.383 --> 00:19:17.046
Parents, if you have questions

00:19:17.046 --> 00:19:18.863
some of you already have done so

00:19:18.943 --> 00:19:22.099
please put them in the Q&A function.

00:19:22.885 --> 00:19:26.126
Please do not use the chat function
for asking questions,

00:19:26.280 --> 00:19:29.379
you can use the chat function
to chat with the other participants.

00:19:29.635 --> 00:19:31.768
Feel free to use the chat function

00:19:31.984 --> 00:19:34.015
to share ideas, to talk

00:19:34.215 --> 00:19:35.512
among yourselves.

00:19:35.610 --> 00:19:38.415
This is a maths lesson

00:19:38.644 --> 00:19:41.236
maths lesson's are supposed
to be a little bit noisy.

00:19:41.342 --> 00:19:44.010
Have you been to a Maths class
and it's very quiet?

00:19:44.708 --> 00:19:47.793
A quiet mathematics class is suspicious.

00:19:48.619 --> 00:19:52.856
One of the ways of learning a language
is to speak.

00:19:53.011 --> 00:19:54.002
We all know

00:19:54.195 --> 00:19:57.476
learning a language includes oral skills

00:19:58.013 --> 00:20:00.250
speaking but also listening.

00:20:00.797 --> 00:20:03.911
It also includes reading and writing.

00:20:04.692 --> 00:20:07.280
When children do not have the
full experience

00:20:08.017 --> 00:20:10.365
in learning mathematics as a language

00:20:10.575 --> 00:20:11.812
not talking,

00:20:12.393 --> 00:20:16.421
rarely listening to another person
other than the teacher,

00:20:17.858 --> 00:20:19.979
writing but not reading,

00:20:21.124 --> 00:20:25.222
then often they will have
some kind of difficulties.

00:20:25.658 --> 00:20:27.304
Let me take some questions.

00:20:35.250 --> 00:20:39.489
So far all the questions are problems that
you want me to solve for you.

00:20:39.663 --> 00:20:41.017
But I have one here,

00:20:42.775 --> 00:20:44.995
this parent mentioned this...

00:20:46.167 --> 00:20:50.723
"my son always write answers
without working

00:20:52.284 --> 00:20:54.917
how can I help him on this

00:20:55.152 --> 00:20:56.806
he does mental sums"

00:21:06.066 --> 00:21:07.675
So that's the question.

00:21:09.393 --> 00:21:12.358
I think many parents encounter
the same situation

00:21:12.945 --> 00:21:13.689
Yeah?

00:21:14.193 --> 00:21:15.513
Children

00:21:17.037 --> 00:21:19.366
writing answers without working.

00:21:19.805 --> 00:21:20.804
Example,

00:21:21.830 --> 00:21:23.124
In primary one

00:21:24.329 --> 00:21:26.247
they say nine, ten, eleven

00:21:26.486 --> 00:21:27.616
write it down.

00:21:28.173 --> 00:21:29.746
Did the child do working?

00:21:29.839 --> 00:21:30.630
Yes

00:21:31.237 --> 00:21:33.738
when the child thinks
that's working.

00:21:34.275 --> 00:21:36.686
Thinking is working, parents

00:21:38.394 --> 00:21:41.207
working is not always writing things down.

00:21:43.306 --> 00:21:44.866
Some children do this:

00:21:45.141 --> 00:21:46.426
9 and 6

00:21:47.935 --> 00:21:50.856
oh 6 is one and 5

00:21:51.181 --> 00:21:53.703
9 go with the 1 makes 10

00:21:54.222 --> 00:21:56.496
10 and 5, 5 and 10

00:21:57.118 --> 00:21:57.930
15

00:21:59.558 --> 00:22:01.023
is that acceptable?

00:22:01.883 --> 00:22:04.243
Yes, that is acceptable.

00:22:06.464 --> 00:22:08.808
Thinking is working

00:22:10.928 --> 00:22:15.896
this is acceptable if they are doing
basic skills.

00:22:17.612 --> 00:22:19.447
Mathematics is a language

00:22:20.116 --> 00:22:21.846
just like in all languages

00:22:22.358 --> 00:22:27.154
if I say something very difficult
for other people to understand

00:22:27.544 --> 00:22:29.475
I need to explain myself.

00:22:30.426 --> 00:22:32.489
But if I say something obvious

00:22:33.135 --> 00:22:34.608
I will just say it.

00:22:35.296 --> 00:22:40.472
If I try to elaborate on a simple point
you will think I am long-winded.

00:22:41.543 --> 00:22:43.319
Mathematics is a language.

00:22:44.425 --> 00:22:46.197
Just like all languages

00:22:46.515 --> 00:22:49.590
when children want to tell you something
straight forward

00:22:49.908 --> 00:22:51.578
5 groups, sorry...

00:22:51.718 --> 00:22:54.228
3 groups of 5
for example

00:22:55.974 --> 00:22:58.609
they will just say
"I know it it's 15"

00:22:59.325 --> 00:23:01.811
I know it's easy for a lot of people

00:23:02.072 --> 00:23:04.018
so I will not elaborate it.

00:23:06.138 --> 00:23:08.200
But if they say something difficult

00:23:08.283 --> 00:23:11.136
afterwards you are going to see
some examples of those

00:23:11.890 --> 00:23:16.016
Those require them to
articulate their thinking

00:23:18.244 --> 00:23:20.571
in adult language we call that working.

00:23:21.762 --> 00:23:24.022
Parents let me say clearly now

00:23:24.991 --> 00:23:26.466
When is working required?

00:23:27.528 --> 00:23:32.411
Working is required when they are
solving a challenging problem.

00:23:32.887 --> 00:23:34.571
When they are solving problems.

00:23:34.661 --> 00:23:36.621
Because when they solve problems

00:23:36.891 --> 00:23:38.671
even though they are so smart

00:23:38.744 --> 00:23:40.791
and they know the answer by thinking

00:23:41.567 --> 00:23:43.188
they are not allowed to just

00:23:43.477 --> 00:23:45.176
say the final answer.

00:23:45.517 --> 00:23:48.977
Can you imagine when Albert Einstein

00:23:50.172 --> 00:23:52.974
discovered E equals to the square

00:23:53.228 --> 00:23:56.868
you know energy equals to the
product of mass

00:23:56.999 --> 00:23:59.106
and the square of speed of light

00:23:59.230 --> 00:24:01.907
or the well known E = mc^2.

00:24:02.835 --> 00:24:05.217
Can you imagine Einstein
went to the lecture hall

00:24:05.538 --> 00:24:07.888
and said "guys trust me

00:24:08.943 --> 00:24:11.998
this is how energy is related to mass

00:24:12.901 --> 00:24:15.037
this is the final equation

00:24:15.192 --> 00:24:17.116
bye end of lecture".

00:24:17.353 --> 00:24:19.023
Can you imagine that

00:24:19.848 --> 00:24:22.398
no one will believe that

00:24:22.735 --> 00:24:25.435
Einstein was correct

00:24:25.542 --> 00:24:30.643
because back then people think that
energy and mass were not related.

00:24:32.054 --> 00:24:35.056
But he has to slowly convince people

00:24:35.496 --> 00:24:37.032
that energy and mass

00:24:38.338 --> 00:24:39.784
are actually related.

00:24:40.146 --> 00:24:44.173
So whenever your children
are solving a difficult problem

00:24:44.493 --> 00:24:46.084
a challenging problem

00:24:46.721 --> 00:24:48.737
they must explain themselves

00:24:49.327 --> 00:24:53.756
even if...
they know the answer by eyeballing.

00:24:54.568 --> 00:24:57.407
Even if they know the answer
just by looking at the problem

00:24:58.697 --> 00:25:02.895
They still must explain things
to other people.

00:25:03.878 --> 00:25:05.886
But if they are saying something simple

00:25:06.267 --> 00:25:07.064
like...

00:25:09.898 --> 00:25:11.547
2 less than 11

00:25:12.639 --> 00:25:14.504
oh two less than 11 is 9.

00:25:14.504 --> 00:25:16.021
Why? because I know it.

00:25:16.184 --> 00:25:19.704
Or 2 less than 11
I just count back

00:25:21.740 --> 00:25:25.216
in my mind 11, 10, 9
and write it down.

00:25:25.309 --> 00:25:26.946
Must I explain myself?

00:25:27.577 --> 00:25:28.994
I don't have to.

00:25:29.450 --> 00:25:31.761
Can I explain myself?

00:25:31.933 --> 00:25:33.701
Sure, if I want to.

00:25:34.622 --> 00:25:37.836
If a teacher or my parent
ask me to explain myself

00:25:37.900 --> 00:25:39.506
I should be able to do it.

00:25:40.046 --> 00:25:41.195
So parents...

00:25:42.660 --> 00:25:43.954
what must we do?

00:25:44.037 --> 00:25:48.529
so this is the part where
I want to share with you strategies.

00:25:50.360 --> 00:25:53.860
What must we do
when the kids are still young

00:25:54.488 --> 00:25:56.430
and we can mold their thinking

00:25:56.430 --> 00:25:57.679
what must we do?

00:25:58.477 --> 00:25:59.530
We ask them

00:25:59.923 --> 00:26:02.139
"Do you think this is easy
for other people?"

00:26:04.734 --> 00:26:07.322
"Do you think this is obvious
to other people?"

00:26:07.636 --> 00:26:08.739
so if they

00:26:11.150 --> 00:26:12.476
they write it down

00:26:13.800 --> 00:26:15.048
the answer

00:26:15.053 --> 00:26:15.904
You ask them

00:26:15.904 --> 00:26:18.298
"Do you think this is easy
to a lot of people?"

00:26:18.686 --> 00:26:20.046
If it is easy...

00:26:21.020 --> 00:26:22.020
that's alright.

00:26:22.178 --> 00:26:23.885
Don't have to explain yourself.

00:26:24.220 --> 00:26:26.738
Don't have to draw pictures.

00:26:29.564 --> 00:26:31.872
Don't have to draw pictures of 12

00:26:33.191 --> 00:26:37.317
and then show them how to
put into groups of 3's.

00:26:38.808 --> 00:26:40.622
If you want to you can...

00:26:42.702 --> 00:26:44.195
but you don't have to.

00:26:45.693 --> 00:26:48.192
Do you think this is easy to other people?

00:26:48.685 --> 00:26:50.911
If it is not easy to other people...

00:26:51.202 --> 00:26:55.032
even if you know the answer,
you must explain yourself

00:26:55.364 --> 00:26:56.942
you must show your working.

00:26:57.749 --> 00:26:58.669
Parents,

00:26:59.222 --> 00:27:03.709
this is strategy number one
I want to share with you this evening.

00:27:05.727 --> 00:27:07.510
Always ask this question:

00:27:07.733 --> 00:27:09.620
Is this easy to other people?

00:27:11.051 --> 00:27:11.924
If yes,

00:27:12.142 --> 00:27:13.319
no need working.

00:27:13.960 --> 00:27:15.040
If no,

00:27:16.195 --> 00:27:17.861
you have to show working.

00:27:17.982 --> 00:27:20.375
Even if you know the answer

00:27:21.537 --> 00:27:22.783
just by looking.

00:27:23.278 --> 00:27:25.916
Alright parents, if you do this often

00:27:25.971 --> 00:27:28.558
your children will develop
self-awareness.

00:27:29.832 --> 00:27:33.043
Your children will develop
meta-cognitive ability.

00:27:33.599 --> 00:27:34.797
That well...

00:27:34.856 --> 00:27:36.530
This is very easy for me

00:27:36.618 --> 00:27:38.092
I know the answer

00:27:38.131 --> 00:27:39.799
but actually it's a difficult thing

00:27:40.034 --> 00:27:41.863
so I should be proud of myself.

00:27:42.193 --> 00:27:44.836
I know the answer
to a very difficult thing

00:27:45.160 --> 00:27:49.748
but I am still responsible
to explain it to my teacher

00:27:50.358 --> 00:27:51.655
or to a friend

00:27:51.920 --> 00:27:54.957
to the friend with specs
who sits beside me.

00:27:55.946 --> 00:28:00.100
So parents, try to use this strategy more
whenever you are guiding your child.

00:28:00.244 --> 00:28:02.234
Don't just tell your child
"Eh you'll la

00:28:02.385 --> 00:28:03.842
show your working please

00:28:03.995 --> 00:28:05.400
otherwise you'll lose marks".

00:28:06.187 --> 00:28:07.504
That's not very helpful

00:28:07.611 --> 00:28:09.129
it doesn't tell them anything.

00:28:09.448 --> 00:28:12.818
It's a rather useless thing
to say actually.

00:28:13.811 --> 00:28:16.257
They have no idea why
they are showing their working

00:28:17.734 --> 00:28:21.089
because losing marks
is a artificial indicator.

00:28:22.224 --> 00:28:26.702
It is, I have to show working
to explain to other people

00:28:26.952 --> 00:28:28.506
is the actual explanation.

00:28:29.214 --> 00:28:32.067
And I have to explain to other people
because it's difficult.

00:28:33.403 --> 00:28:35.166
Or I don't have to explain to people.

00:28:35.301 --> 00:28:37.140
Why? Because it's obvious.

00:28:38.032 --> 00:28:39.617
Let me take perhaps

00:28:40.100 --> 00:28:41.242
another question.

00:28:47.487 --> 00:28:49.883
Is it a must to draw a model?

00:28:52.712 --> 00:28:55.503
In a way I have answered the question.

00:28:57.717 --> 00:28:59.571
I have to draw the model

00:29:00.246 --> 00:29:01.058
if...

00:29:02.520 --> 00:29:04.448
other people cannot understand me.

00:29:06.284 --> 00:29:08.489
And I want them to understand me.

00:29:08.876 --> 00:29:10.862
And I am quite good at drawing

00:29:11.024 --> 00:29:15.510
so I draw a model
to help them understand me.

00:29:16.898 --> 00:29:18.775
But if the problem is very easy

00:29:19.652 --> 00:29:21.447
then I won't draw a model because

00:29:21.841 --> 00:29:23.484
I can just tell them the answer.

00:29:23.683 --> 00:29:25.871
Example, if the question is

00:29:26.921 --> 00:29:30.174
I have 12 lollipops

00:29:30.720 --> 00:29:34.405
that's really too many but
for some reason I have 12 lollipops.

00:29:35.332 --> 00:29:40.245
and my friend kindly
gave me another 2

00:29:42.645 --> 00:29:47.451
so I had 12 lollipops
and she gave me another 2.

00:29:47.659 --> 00:29:50.736
I know the answer is obvious
now I have 14

00:29:51.234 --> 00:29:52.276
it's obvious.

00:29:52.523 --> 00:29:57.892
I don't think I need to draw a model
to tell people how I got 14.

00:29:58.491 --> 00:30:01.809
Maybe, I should tell them
how I get 14

00:30:02.362 --> 00:30:04.490
by showing them the calculation

00:30:04.717 --> 00:30:05.520
maybe...

00:30:06.099 --> 00:30:08.402
Maybe they don't know how I get 14

00:30:08.472 --> 00:30:12.373
so at least I show a little bit
of explanation to them.

00:30:12.702 --> 00:30:14.290
But actually I can just tell you

00:30:14.451 --> 00:30:16.608
in the end I had 14 lollipops

00:30:16.709 --> 00:30:18.429
that's perfectly fine actually.

00:30:20.629 --> 00:30:23.378
So must my child draw a model?

00:30:24.414 --> 00:30:27.175
No, if they already know the answer

00:30:28.742 --> 00:30:31.696
and no if the problem is a simple one.

00:30:33.719 --> 00:30:36.521
So the second reason why
children draw a model...

00:30:37.862 --> 00:30:40.134
is because they don't know the answer.

00:30:41.071 --> 00:30:43.734
For example, 
the problem I gave you earlier.

00:30:44.791 --> 00:30:48.716
Spiky has more coins that Curly.

00:30:48.981 --> 00:30:50.697
So lets say a child doesn't know

00:30:50.835 --> 00:30:52.246
the child might draw,

00:30:52.391 --> 00:30:56.406
Spiky had more coins than Curly.

00:30:57.517 --> 00:30:59.294
So the diagram might look like that

00:31:00.061 --> 00:31:03.493
with Spiky having more coins than Curly

00:31:05.435 --> 00:31:06.170
and...

00:31:06.742 --> 00:31:08.353
Spiky has ten

00:31:10.277 --> 00:31:13.258
Spiky has 3 more coins

00:31:14.735 --> 00:31:16.776
than what Curly has.

00:31:17.411 --> 00:31:20.741
From here I can see
to obtain this value

00:31:21.062 --> 00:31:24.856
my calculation is taking
3 away from 10

00:31:25.463 --> 00:31:26.837
giving me 7

00:31:26.904 --> 00:31:30.803
so I know that Curly has 7 coins.

00:31:31.068 --> 00:31:33.252
So must my child draw a model?

00:31:34.529 --> 00:31:36.932
Yes, if they don't know the answer.

00:31:37.439 --> 00:31:39.391
If they don't know the operation.

00:31:40.170 --> 00:31:43.931
Model is a good bridge to the operation

00:31:44.869 --> 00:31:48.339
They will learn whether to add,
to subtract, to multiply, or to divide.

00:31:48.656 --> 00:31:50.721
So if they don't know the operation.

00:31:51.711 --> 00:31:54.440
So if they know the operation
must they draw the model?

00:31:54.440 --> 00:31:55.791
No, they don't have to.

00:31:57.562 --> 00:31:58.925
Second answer,

00:31:59.524 --> 00:32:00.749
must they draw the model?

00:32:01.897 --> 00:32:03.947
Yes, if the problem is difficult

00:32:04.162 --> 00:32:06.542
and they need to explain it
to another person.

00:32:07.820 --> 00:32:10.240
No, if the problem straightforward.

00:32:12.266 --> 00:32:14.716
Finally, I want to add one more comment.

00:32:15.380 --> 00:32:17.871
When your child is first learning model

00:32:18.000 --> 00:32:21.678
sometimes the teacher will insist
they draw it

00:32:22.994 --> 00:32:24.981
just because they are learning it.

00:32:25.155 --> 00:32:27.682
So if today's lesson is about
drawing model's

00:32:27.951 --> 00:32:30.118
then of course you must
practice drawing it.

00:32:30.487 --> 00:32:31.951
So that's a third answer

00:32:32.049 --> 00:32:33.782
must my child draw model?

00:32:33.832 --> 00:32:36.218
Yes, if that is the lesson itself.

00:32:37.304 --> 00:32:40.232
So if the teacher is teaching
model drawing that day

00:32:40.232 --> 00:32:43.003
obviously the teacher will expect
them to practice it.

00:32:43.346 --> 00:32:47.019
So those are the three answers to
"must my child draw model".

00:32:48.001 --> 00:32:51.481
I'll take on more question
before I continue to the next part.

00:32:58.102 --> 00:33:00.694
My child feel's that mathematics is boring

00:33:01.317 --> 00:33:03.492
any tips to make it interesting?

00:33:04.276 --> 00:33:07.873
I will answer this question and then
I'll continue with some examples.

00:33:09.567 --> 00:33:12.139
Why do children find mathematics boring?

00:33:13.516 --> 00:33:20.309
1. If we portray mathematics as a subject
where they have to memorise things.

00:33:24.159 --> 00:33:28.358
Memorising... is rarely exciting

00:33:28.820 --> 00:33:30.441
to most children anyway.

00:33:33.196 --> 00:33:35.403
In some subjects,

00:33:36.107 --> 00:33:39.337
In some domains
memorising is necessary.

00:33:39.588 --> 00:33:41.497
Example, learning the Quran

00:33:42.196 --> 00:33:45.823
If you are learning the Quran
we have to memorise.

00:33:46.633 --> 00:33:51.905
I have seen children, friends learning
the Quran when I was very young.

00:33:52.085 --> 00:33:54.324
And they kinda memorised the whole thing.

00:33:55.109 --> 00:33:56.726
It's just necessary I think.

00:33:59.436 --> 00:34:03.470
But mathematics is not a subject
where you memorise everything.

00:34:03.660 --> 00:34:07.266
You won't remember stuff, but you
don't have to memorise them.

00:34:07.710 --> 00:34:09.335
Like the times table.

00:34:09.530 --> 00:34:12.202
You forget 7 groups of 3?
Just figure it out.

00:34:12.697 --> 00:34:16.288
Use your 5 and use your 2
you can get your 7 times table.

00:34:16.610 --> 00:34:18.547
You forget your 9 groups of 8?

00:34:19.300 --> 00:34:23.072
Start from 9 groups of 2
double that 9 groups of 4

00:34:23.464 --> 00:34:25.630
double that 9 groups of 8.

00:34:25.777 --> 00:34:27.745
Or you can start with 10 groups of 8

00:34:28.500 --> 00:34:30.070
and take away 1 group

00:34:30.891 --> 00:34:32.295
80 take away 8

00:34:33.081 --> 00:34:34.612
to get whatever you need to get.

00:34:39.513 --> 00:34:42.969
So memorising is rarely exciting.

00:34:44.005 --> 00:34:45.768
What is exciting?

00:34:46.583 --> 00:34:48.014
Figuring things out.

00:34:48.424 --> 00:34:50.463
Children are by nature curious

00:34:51.120 --> 00:34:53.531
they LIKE to figure things out.

00:34:54.016 --> 00:34:56.998
They feel proud, they feel empowered

00:34:57.443 --> 00:35:00.491
that they have the ability
to figure things out.

00:35:00.758 --> 00:35:03.994
And trust me,
every child can figure things out

00:35:05.960 --> 00:35:07.633
If only we allow them to.

00:35:08.836 --> 00:35:13.475
If only we make them understand that
in Mathematics, we figure things out.

00:35:14.463 --> 00:35:16.972
If I do not know how to do long division

00:35:17.589 --> 00:35:21.513
and 51 share among 3 mess me up

00:35:22.274 --> 00:35:24.405
that's alright, I can figure it out.

00:35:25.581 --> 00:35:28.322
I know that 51 is 30 and 21.

00:35:30.115 --> 00:35:31.731
So 30 share by 3

00:35:32.808 --> 00:35:33.932
that's not too hard

00:35:34.085 --> 00:35:35.560
so I take out the 30

00:35:35.560 --> 00:35:37.001
I know that leaves me 10.

00:35:38.274 --> 00:35:40.681
So the thirty is not too hard, gets me 10

00:35:41.501 --> 00:35:42.866
and the 21

00:35:43.096 --> 00:35:45.166
when I share among 3

00:35:46.765 --> 00:35:50.111
the 21 that I have
if I take it out to be considered

00:35:52.134 --> 00:35:54.427
share among 3, that gives me...

00:35:54.735 --> 00:35:55.863
that gives me 7.

00:35:57.204 --> 00:35:59.404
Resulting in 10 and 7

00:35:59.824 --> 00:36:01.575
which of course we write as 17.

00:36:02.230 --> 00:36:04.435
And let me check
if there is anything else left

00:36:04.435 --> 00:36:05.662
oh nothing else left

00:36:05.740 --> 00:36:08.627
everything is accounted for
nothing is leftover.

00:36:09.442 --> 00:36:12.749
So, how to make mathematics
more interesting?

00:36:12.811 --> 00:36:16.422
Avoid portraying mathematics
as a subject of memorising

00:36:16.870 --> 00:36:19.297
but as a subject of figuring things out.

00:36:19.884 --> 00:36:20.746
Secondly

00:36:21.630 --> 00:36:24.622
portray mathematics as a subject
where you do things.

00:36:25.525 --> 00:36:26.691
Use your hands.

00:36:27.219 --> 00:36:30.290
In school, they use concrete materials
all the time.

00:36:30.629 --> 00:36:32.131
They use their iPad,

00:36:32.229 --> 00:36:34.328
the teacher let them play on apps

00:36:35.304 --> 00:36:37.479
they use concrete materials all the time.

00:36:38.326 --> 00:36:42.366
So let your child learn Mathematics
by doing

00:36:43.161 --> 00:36:45.027
When they learn counting,

00:36:45.219 --> 00:36:47.177
When they learn adding subtracting,

00:36:47.681 --> 00:36:49.245
use concrete materials.

00:36:49.669 --> 00:36:53.214
You can use the application,
including the one I shared with you.

00:36:53.296 --> 00:36:56.511
Later I will share with you
the names of the applications as well.

00:36:59.367 --> 00:37:00.736
Throughout this workshop,

00:37:00.818 --> 00:37:01.878
this webinar,

00:37:01.938 --> 00:37:04.147
you might pick up other ideas

00:37:04.243 --> 00:37:06.969
on how to make mathematics
more interesting for your child

00:37:07.011 --> 00:37:09.376
but for a start, I share with you two.

00:37:10.339 --> 00:37:11.978
Use concrete materials

00:37:13.023 --> 00:37:13.729
and...

00:37:15.465 --> 00:37:19.243
portray mathematics
not as a subject of memorising,

00:37:19.407 --> 00:37:21.784
but as a subject of figuring things out.

00:37:21.933 --> 00:37:23.605
Let me now move on.

00:37:26.369 --> 00:37:28.824
So mathematics include visuals.

00:37:30.614 --> 00:37:32.222
Let me show you some examples.

00:37:33.803 --> 00:37:37.030
All the examples
I've taken from Pathlight school

00:37:37.620 --> 00:37:39.810
mid-year examination paper

00:37:40.602 --> 00:37:41.852
for Primary 4

00:37:42.321 --> 00:37:45.274
so that you can see
where your child is moving to.

00:37:45.372 --> 00:37:50.383
I know some of you have children in
Primary 1, Primary 2, also Primary 3.

00:37:50.928 --> 00:37:54.320
So you kind of see
where they are heading to.

00:37:54.665 --> 00:37:57.193
And you can see they
also do similar things

00:37:58.018 --> 00:38:00.138
in the current level.

00:38:01.624 --> 00:38:03.678
So they are expected

00:38:03.939 --> 00:38:06.899
to be able to handle visuals.

00:38:09.113 --> 00:38:10.397
Visuals like that.

00:38:10.883 --> 00:38:13.655
Things they might encounter
in their everyday life.

00:38:14.245 --> 00:38:17.003
So if I go to Whampoa market

00:38:17.534 --> 00:38:18.713
there's a bakery

00:38:18.811 --> 00:38:20.522
and at that bakery

00:38:20.707 --> 00:38:24.474
sometimes I see the lady
putting up signs like that

00:38:24.931 --> 00:38:28.420
telling me how much the cupcakes are,

00:38:28.420 --> 00:38:31.740
and I think she was eager
to promote cupcakes that week.

00:38:31.954 --> 00:38:32.709
So she's

00:38:33.082 --> 00:38:34.740
having a little promotion

00:38:35.424 --> 00:38:36.750
she's having a little sale.

00:38:37.186 --> 00:38:38.813
Cupcakes for sale.

00:38:39.943 --> 00:38:41.542
One for two dollars

00:38:41.798 --> 00:38:43.492
oh I think she meant one cupcake

00:38:43.693 --> 00:38:46.213
you know people don't write
everything out clearly

00:38:46.213 --> 00:38:49.003
but it's understood isn't it
even when they say one

00:38:49.003 --> 00:38:50.399
when they meant one cupcake.

00:38:50.827 --> 00:38:52.231
Not one...

00:38:52.782 --> 00:38:54.240
tray of cupcakes

00:38:54.494 --> 00:38:56.979
not one short of cupcakes

00:38:57.172 --> 00:38:58.584
but one cupcake.

00:38:58.801 --> 00:39:01.216
But they don't write it out
we try to understand it

00:39:01.216 --> 00:39:02.787
from our daily experience.

00:39:03.052 --> 00:39:04.499
So 1 for 2 dollars

00:39:04.736 --> 00:39:06.466
and 3 for 5 dollars.

00:39:07.675 --> 00:39:10.412
??? we mean by understanding visuals,

00:39:10.434 --> 00:39:12.373
visuals in everyday life.

00:39:12.579 --> 00:39:15.322
That's a third way to make
mathematics interesting.

00:39:15.659 --> 00:39:17.633
Don't have to sit down and do worksheet

00:39:18.054 --> 00:39:19.686
when you take your children out

00:39:19.929 --> 00:39:21.046
nowadays that's not a good idea

00:39:21.046 --> 00:39:22.647
with the heightened alert.

00:39:22.647 --> 00:39:24.171
But in normal times

00:39:24.224 --> 00:39:26.172
when you have your children out with you

00:39:26.192 --> 00:39:29.035
at the NTUC, at the neighborhood market

00:39:30.237 --> 00:39:31.648
wherever you go,

00:39:31.977 --> 00:39:34.974
you can make use of
small opportunities like that

00:39:35.170 --> 00:39:37.147
just to engage your child

00:39:37.534 --> 00:39:38.646
in mathematics

00:39:38.830 --> 00:39:41.910
in a rather informal way

00:39:41.923 --> 00:39:43.398
like "oh you know

00:39:43.865 --> 00:39:45.700
I think we need to buy 10

00:39:46.384 --> 00:39:48.770
is it a good idea to buy 10 cupcakes?"

00:39:49.504 --> 00:39:50.944
and see what your child says.

00:39:51.411 --> 00:39:53.719
That is as good as
if not better than

00:39:54.063 --> 00:39:55.199
doing a worksheet.

00:39:56.231 --> 00:39:58.052
So in examination

00:39:58.213 --> 00:40:00.531
they are expected to be able to handle

00:40:00.598 --> 00:40:06.485
visuals that's common place
in their everyday experience.

00:40:09.360 --> 00:40:11.423
And in this case there are also some words

00:40:12.694 --> 00:40:14.892
Matthew has some money

00:40:16.354 --> 00:40:19.180
Matthew has $32

00:40:20.063 --> 00:40:21.656
oh $32

00:40:22.203 --> 00:40:27.587
I wonder... the $32
come in what denominations?

00:40:27.812 --> 00:40:32.080
I wonder what he has in his hand
or in his pockets?

00:40:32.303 --> 00:40:33.427
$32

00:40:34.351 --> 00:40:37.585
and the child may say
"Maybe three $10 notes

00:40:38.380 --> 00:40:40.191
and a $2 note?"

00:40:42.336 --> 00:40:44.515
Matthew has some money

00:40:44.823 --> 00:40:46.092
$32

00:40:47.576 --> 00:40:49.156
what is the greatest

00:40:49.251 --> 00:40:51.485
oh greatest means the biggest

00:40:51.635 --> 00:40:54.770
what is the greatest
number of cupcakes he can buy?

00:40:56.247 --> 00:40:58.402
Oh what does that mean?
You can ask your child

00:40:58.558 --> 00:41:00.902
and let your child paraphrase the question

00:41:00.998 --> 00:41:03.411
"oh it means the most"

00:41:04.056 --> 00:41:05.888
some children know the word maximum

00:41:05.888 --> 00:41:08.041
"it means the maximum number"

00:41:08.869 --> 00:41:12.448
and then if your child is quite advance
you can also engage them further.

00:41:12.795 --> 00:41:16.114
"Why are they asking us for the maximum?"

00:41:17.541 --> 00:41:19.553
Maybe the child will laugh
at you probably.

00:41:19.584 --> 00:41:24.432
"Of course you know he got $32
he can just buy $2.

00:41:25.941 --> 00:41:27.313
He can just but one cupcake

00:41:27.678 --> 00:41:29.829
doesn't mean must spend
all your money right?"

00:41:29.829 --> 00:41:32.483
So some children are smart that way
they will like

00:41:32.729 --> 00:41:35.563
"doesn't mean you got $32
you spend all on cupcakes

00:41:35.699 --> 00:41:37.452
who actually does that right?

00:41:37.452 --> 00:41:38.429
very few people"

00:41:38.469 --> 00:41:40.226
but in this case we want to know

00:41:40.226 --> 00:41:43.315
if Matthew wants
as many cupcakes as possible,

00:41:43.661 --> 00:41:47.136
what is the greatest number of cupcakes
he can buy?

00:41:47.797 --> 00:41:50.516
The fourth way to make
mathematics interesting,

00:41:52.072 --> 00:41:54.120
engage your child in conversation.

00:41:54.818 --> 00:41:56.897
Don't always just answer the question

00:41:56.897 --> 00:41:57.598
and then say

00:41:57.598 --> 00:42:00.312
"boy quickly go to the next one
no time already".

00:42:01.273 --> 00:42:02.533
There is a lot of time

00:42:03.883 --> 00:42:05.088
we must take time

00:42:05.512 --> 00:42:06.446
otherwise

00:42:06.557 --> 00:42:10.111
you will get children
who don't enjoy mathematics

00:42:10.481 --> 00:42:14.416
and also don't do too well
in mathematics subsequently.

00:42:14.672 --> 00:42:17.376
Do not think of learning mathematics
as sitting down

00:42:17.690 --> 00:42:19.921
doing worksheets all the time.

00:42:20.487 --> 00:42:22.077
That's actually the final step.

00:42:23.246 --> 00:42:26.577
Early stages of learning is quite informal,

00:42:27.517 --> 00:42:29.039
you can engage your child

00:42:29.488 --> 00:42:31.548
in the everyday experience they have.

00:42:32.089 --> 00:42:34.657
It is then that they are able
to do the worksheet.

00:42:35.399 --> 00:42:38.640
Children who never encounter this
in their everyday life

00:42:39.260 --> 00:42:41.717
and the conversation that
I just had with you

00:42:42.501 --> 00:42:47.226
will find it quite difficult
to do the examination afterwards

00:42:48.456 --> 00:42:50.102
example, a question like this.

00:42:50.566 --> 00:42:52.049
Anyway

00:42:53.124 --> 00:42:58.346
then the child might then be
asked to solve a problem like that.

00:42:59.796 --> 00:43:01.439
So they should also appreciate that

00:43:01.752 --> 00:43:07.441
"eh actually buying three is a good deal
because you pay $5".

00:43:07.609 --> 00:43:12.010
Normally you buy three
it would have cost us $6.

00:43:12.676 --> 00:43:14.725
You see parents, I don't do any working

00:43:15.499 --> 00:43:17.107
I do the working in my mind.

00:43:17.299 --> 00:43:18.867
And that's perfectly normal

00:43:18.973 --> 00:43:20.460
and of course it's allowed

00:43:20.954 --> 00:43:22.872
that's what we do in real life.

00:43:23.390 --> 00:43:25.924
Mathematics is a extension of real life

00:43:26.827 --> 00:43:30.121
it's not like sometime different

00:43:30.490 --> 00:43:31.998
to what we normally do.

00:43:31.998 --> 00:43:34.395
So normally we will say
"one cupcake" $2

00:43:34.395 --> 00:43:35.656
"three cupcake" $6

00:43:36.387 --> 00:43:38.464
then people ask, "how come $6?"

00:43:38.612 --> 00:43:39.468
then you tell them

00:43:39.468 --> 00:43:43.713
oh you know $2 + $2 + $2 = $6
or 3 x $2

00:43:43.868 --> 00:43:44.860
If they ask.

00:43:44.860 --> 00:43:47.765
If they don't ask I just like
"okay $6 , they nod their head".

00:43:48.639 --> 00:00:02.889
So in exams

99:59:59.999 --> 99:59:59.999
for questions like this

99:59:59.999 --> 99:59:59.999
they can just give the answer.

99:59:59.999 --> 99:59:59.999
Example, at PSLE this kind of question
answers are given

99:59:59.999 --> 99:59:59.999
the marks are given

99:59:59.999 --> 99:59:59.999
for the answers.

99:59:59.999 --> 99:59:59.999
If they show working it's fine.

99:59:59.999 --> 99:59:59.999
If they don't show it's also fine because
all the marks are given for the answer.

99:59:59.999 --> 99:59:59.999
Okay?

99:59:59.999 --> 99:59:59.999
So they said
"Okay so try to buy three"

99:59:59.999 --> 99:59:59.999
Yeah? Try to buy three.

99:59:59.999 --> 99:59:59.999
So $5, and I know that

99:59:59.999 --> 99:59:59.999
oh now I need to write because
I cannot remember so many things.

99:59:59.999 --> 99:59:59.999
I know that I got a lot of $5 in $30

99:59:59.999 --> 99:59:59.999
in face I got six of them.

99:59:59.999 --> 99:59:59.999
Because six times $5 dollars gets $30

99:59:59.999 --> 99:59:59.999
and then I got $2 more.

99:59:59.999 --> 99:59:59.999
So this $30
there are six $5

99:59:59.999 --> 99:59:59.999
and every $5 gets me three

99:59:59.999 --> 99:59:59.999
so I can get six of three cupcakes
that's eighteen cupcakes.

99:59:59.999 --> 99:59:59.999
But then the $2 I can get more

99:59:59.999 --> 99:59:59.999
so I get whatever I can get
and give a final answer.

99:59:59.999 --> 99:59:59.999
Parents,

99:59:59.999 --> 99:59:59.999
I have illustrated what I mean by

99:59:59.999 --> 99:59:59.999
Mathematical language include visuals.

99:59:59.999 --> 99:59:59.999
In this first example

99:59:59.999 --> 99:59:59.999
I demonstrated visuals
that are common place

99:59:59.999 --> 99:59:59.999
in our everyday life.

99:59:59.999 --> 99:59:59.999
Let me move on.

99:59:59.999 --> 99:59:59.999
Sometimes, at a higher grade level

99:59:59.999 --> 99:59:59.999
the visual dissapears

99:59:59.999 --> 99:59:59.999
like this problem.

99:59:59.999 --> 99:59:59.999
If you read it

99:59:59.999 --> 99:59:59.999
you'll realise that it's the
same kind of Mathematics involved.

99:59:59.999 --> 99:59:59.999
It's what we call division with remainder

99:59:59.999 --> 99:59:59.999
like just now the division remainder.

99:59:59.999 --> 99:59:59.999
The visual disappeared.

99:59:59.999 --> 99:59:59.999
So what is the learning progression?

99:59:59.999 --> 99:59:59.999
First is you let them see the visual

99:59:59.999 --> 99:59:59.999
in the actual context.

99:59:59.999 --> 99:59:59.999
In the bakery in Whampoa market

99:59:59.999 --> 99:59:59.999
for example

99:59:59.999 --> 99:59:59.999
then they come to school

99:59:59.999 --> 99:59:59.999
they will see this.

99:59:59.999 --> 99:59:59.999
The same visual or similar visuals

99:59:59.999 --> 99:59:59.999
but printed on paper.

99:59:59.999 --> 99:59:59.999
Finally, the visual disappears.

99:59:59.999 --> 99:59:59.999
So parents, we can help the teachers

99:59:59.999 --> 99:59:59.999
by alerting our children
to visuals around them.

99:59:59.999 --> 99:59:59.999
That one is harder for teachers to do

99:59:59.999 --> 99:59:59.999
because the teachers
only see them at school

99:59:59.999 --> 99:59:59.999
and not taking them out to the market

99:59:59.999 --> 99:59:59.999
or just engaging them
with everyday experiences

99:59:59.999 --> 99:59:59.999
that one I think parents can do
and can do quite well.

99:59:59.999 --> 99:59:59.999
So do alert your children
to visuals around them

99:59:59.999 --> 99:59:59.999
and engage them with a bit of Mathematics

99:59:59.999 --> 99:59:59.999
don't have to use worksheets.

99:59:59.999 --> 99:59:59.999
So that's a strategy

99:59:59.999 --> 99:59:59.999
a strategy to help them process
information better.

99:59:59.999 --> 99:59:59.999
In this case visual information.

99:59:59.999 --> 99:59:59.999
That is commonplace.

99:59:59.999 --> 99:59:59.999
Oh we have a question here!

99:59:59.999 --> 99:59:59.999
Lets look at what the question
is all about.

99:59:59.999 --> 99:59:59.999
Crate...

99:59:59.999 --> 99:59:59.999
oh what is a crate?

99:59:59.999 --> 99:59:59.999
Ask your child that.

99:59:59.999 --> 99:59:59.999
Give me other words
that's similar to crate.

99:59:59.999 --> 99:59:59.999
If they don't know,

99:59:59.999 --> 99:59:59.999
just Google

99:59:59.999 --> 99:59:59.999
and then they can see
a picture of a crate

99:59:59.999 --> 99:59:59.999
as simple as that actually.

99:59:59.999 --> 99:59:59.999
Use technology

99:59:59.999 --> 99:59:59.999
that we already have.

99:59:59.999 --> 99:59:59.999
Don't complain

99:59:59.999 --> 99:59:59.999
"oh is this Maths or is this English ah

99:59:59.999 --> 99:59:59.999
how come they use words like that"

99:59:59.999 --> 99:59:59.999
there is no question whether
this is Maths or English

99:59:59.999 --> 99:59:59.999
English is part of Maths.

99:59:59.999 --> 99:59:59.999
So remember,
Mathematical language include:

99:59:59.999 --> 99:59:59.999
symbols, visual, and English

99:59:59.999 --> 99:59:59.999
English is part of Maths.

99:59:59.999 --> 99:59:59.999
If the don't know the word,

99:59:59.999 --> 99:59:59.999
just do what we normally do,
Google it.

99:59:59.999 --> 99:59:59.999
And then "oh that's a crate!"

99:59:59.999 --> 99:59:59.999
then your child will give you other words
like box or whatever they want to say.

99:59:59.999 --> 99:59:59.999
A crate can hold milk bottles,

99:59:59.999 --> 99:59:59.999
okay a crate can hold milk bottles.

99:59:59.999 --> 99:59:59.999
Actually I haven't seen milk bottles
in a very long time.

99:59:59.999 --> 99:59:59.999
Once upon a time when I was a child

99:59:59.999 --> 99:59:59.999
wow that's a long time ago
50 years ago.

99:59:59.999 --> 99:59:59.999
You know the milkman who goes round

99:59:59.999 --> 99:59:59.999
and they give you the milk in a bottle

99:59:59.999 --> 99:59:59.999
F & N bottle
with a little...

99:59:59.999 --> 99:59:59.999
banana leaf stopper.

99:59:59.999 --> 99:59:59.999
Okay, most of you are too young
to even know this.

99:59:59.999 --> 99:59:59.999
So sometimes, children
are asked to read stories

99:59:59.999 --> 99:59:59.999
that are so alien to them.

99:59:59.999 --> 99:59:59.999
But that's... that's life

99:59:59.999 --> 99:59:59.999
we also read stories that's alien to us.

99:59:59.999 --> 99:59:59.999
Harry Potter, you mean you grew up
like Harry potter?

99:59:59.999 --> 99:59:59.999
No right? but you still enjoy it.

99:59:59.999 --> 99:59:59.999
Right?

99:59:59.999 --> 99:59:59.999
So, that's normal in a language

99:59:59.999 --> 99:59:59.999
we sometimes read things familiar to us
like the bakery, selling the cupcakes.

99:59:59.999 --> 99:59:59.999
But sometimes we also read things
that are not so familiar to us

99:59:59.999 --> 99:59:59.999
and some of us enjoy it
some of us don't, that's life.

99:59:59.999 --> 99:59:59.999
We cannot expect everyone to find
the same thing exciting.

99:59:59.999 --> 99:59:59.999
You cannot expect every child to find
milk bottles exciting.

99:59:59.999 --> 99:59:59.999
Okay, some of them do but...

99:59:59.999 --> 99:59:59.999
most of them don't.

99:59:59.999 --> 99:59:59.999
But they will still learn
to imagine it.

99:59:59.999 --> 99:59:59.999
And we, as adults can help them.

99:59:59.999 --> 99:59:59.999
We can Google, we can show them that

99:59:59.999 --> 99:59:59.999
"oh you know, in some countries,
they actually sell milk in bottles".

99:59:59.999 --> 99:59:59.999
"in some countries, they bring
milk bottles to the shop

99:59:59.999 --> 99:59:59.999
and then they get their milk".

99:59:59.999 --> 99:59:59.999
But for us we go NTUC
it comes in a box

99:59:59.999 --> 99:59:59.999
sometimes plastic.

99:59:59.999 --> 99:59:59.999
We are not very green in that way.

99:59:59.999 --> 99:59:59.999
So engage them
in that kind of conversation

99:59:59.999 --> 99:59:59.999
that's very important.

99:59:59.999 --> 99:59:59.999
Very often parents ask,
"how do I prepare my child for Mathematics"

99:59:59.999 --> 99:59:59.999
and they think the answer will be

99:59:59.999 --> 99:59:59.999
buy more workbooks,
by more assessment books

99:59:59.999 --> 99:59:59.999
It not.

99:59:59.999 --> 99:59:59.999
It's doing things that
parents do very well.

99:59:59.999 --> 99:59:59.999
Engaging children with things around them

99:59:59.999 --> 99:59:59.999
both familiar, but also unfamiliar.

99:59:59.999 --> 99:59:59.999
So these are some kind of images

99:59:59.999 --> 99:59:59.999
children need to encounter.

99:59:59.999 --> 99:59:59.999
So one more example on visuals,

99:59:59.999 --> 99:59:59.999
Farah, okay probably somebody

99:59:59.999 --> 99:59:59.999
a girl

99:59:59.999 --> 99:59:59.999
I see the word she, so it must be a girl.

99:59:59.999 --> 99:59:59.999
I don't have a friend called Farah
so I don't know whether it's a boy or girl.

99:59:59.999 --> 99:59:59.999
And I am not so familiar with this name

99:59:59.999 --> 99:59:59.999
but I saw the word she,
must be a girl.

99:59:59.999 --> 99:59:59.999
But shouldn't matter right?
whether it's a boy or a girl.

99:59:59.999 --> 99:59:59.999
Farah has some cards

99:59:59.999 --> 99:59:59.999
okay I understand that.

99:59:59.999 --> 99:59:59.999
Rectangular cards...

99:59:59.999 --> 99:59:59.999
oh so the cards are rectangle

99:59:59.999 --> 99:59:59.999
I know what rectangles are
we learned that in primary 1.

99:59:59.999 --> 99:59:59.999
Farah has some rectangular cards

99:59:59.999 --> 99:59:59.999
okay I understand that.

99:59:59.999 --> 99:59:59.999
Measuring 10 centimeter by 6 centimeter 
oh I can see that.

99:59:59.999 --> 99:59:59.999
So this is what we mean by children

99:59:59.999 --> 99:59:59.999
using visual to support
their reading comprehension.

99:59:59.999 --> 99:59:59.999
So some children struggle with language

99:59:59.999 --> 99:59:59.999
for example, I have one question like this.

99:59:59.999 --> 99:59:59.999
How can I improve my sons language
or Mathematical language capability?

99:59:59.999 --> 99:59:59.999
He has delayed language processing.

99:59:59.999 --> 99:59:59.999
So that's the answer actually,
use visuals

99:59:59.999 --> 99:59:59.999
use visuals.

99:59:59.999 --> 99:59:59.999
And very often even in examinations,

99:59:59.999 --> 99:59:59.999
there are some items
where visual support is provided

99:59:59.999 --> 99:59:59.999
whether or not you have delayed processing

99:59:59.999 --> 99:59:59.999
it is just something
they support children with.

99:59:59.999 --> 99:59:59.999
So even if a child doesn't have
any issues with language

99:59:59.999 --> 99:59:59.999
often, a visual can help them
with comprehension.

99:59:59.999 --> 99:59:59.999
So I see, 10 centimeter by 6 centimeter

99:59:59.999 --> 99:59:59.999
now parents, try not to be...

99:59:59.999 --> 99:59:59.999
try not to be lazy

99:59:59.999 --> 99:59:59.999
don't say 10 cm

99:59:59.999 --> 99:59:59.999
it is actually called centimeters

99:59:59.999 --> 99:59:59.999
say in full
so children hear it

99:59:59.999 --> 99:59:59.999
if we use truncated language,
lazy language too early...

99:59:59.999 --> 99:59:59.999
Children doesn't get the full meaning
eventually

99:59:59.999 --> 99:59:59.999
don't say three times five,

99:59:59.999 --> 99:59:59.999
say three rows of five,
three groups of five

99:59:59.999 --> 99:59:59.999
especially in the beginning

99:59:59.999 --> 99:59:59.999
once they understanding it
you can be lazy

99:59:59.999 --> 99:59:59.999
but in the beginning,
try to say it completely.

99:59:59.999 --> 99:59:59.999
So that they know
that cm is a symbol for centimeters

99:59:59.999 --> 99:59:59.999
otherwise some of them may not know

99:59:59.999 --> 99:59:59.999
and they will be wondering what is this

99:59:59.999 --> 99:59:59.999
and then in exam, whether it is millimeter
or centimeter they don't really care.

99:59:59.999 --> 99:59:59.999
??? sometimes you see that
amongst your children also

99:59:59.999 --> 99:59:59.999
they don't really care what the unit is
and they do very strange things to it.

99:59:59.999 --> 99:59:59.999
So do read it in full.

99:59:59.999 --> 99:59:59.999
And the question is what is the smallest
number of cards she needs

99:59:59.999 --> 99:59:59.999
to form a square

99:59:59.999 --> 99:59:59.999
without overlapping the cards.

99:59:59.999 --> 99:59:59.999
So let your children try,
give them papers like that

99:59:59.999 --> 99:59:59.999
let them try.

99:59:59.999 --> 99:59:59.999
If you are hardworking you can
go and get the exact measurement

99:59:59.999 --> 99:59:59.999
but it's not necessary
but if you want to

99:59:59.999 --> 99:59:59.999
And let them try.

99:59:59.999 --> 99:59:59.999
That's how you make
Mathematics interesting.

99:59:59.999 --> 99:59:59.999
Mathematics is initially
a hands on experience

99:59:59.999 --> 99:59:59.999
in Singapore we call that (CPA)
Concrete, Pictorial, Abstract.

99:59:59.999 --> 99:59:59.999
You first learn it by experiencing

99:59:59.999 --> 99:59:59.999
you take a paper, you take a rectangle
and you try to make a square

99:59:59.999 --> 99:59:59.999
like a puzzle
like a jigsaw puzzle.

99:59:59.999 --> 99:59:59.999
Use the rectangular parts to form a square

99:59:59.999 --> 99:59:59.999
without overlapping.

99:59:59.999 --> 99:59:59.999
You do it,

99:59:59.999 --> 99:59:59.999
once you have done it
you can understand the visual.

99:59:59.999 --> 99:59:59.999
So how does your child learn
and process a visual like that

99:59:59.999 --> 99:59:59.999
in the exams?

99:59:59.999 --> 99:59:59.999
In P4

99:59:59.999 --> 99:59:59.999
it's because in P1, P2, P3
you let them use concrete materials.

99:59:59.999 --> 99:59:59.999
Even in P4 of course I will let them
use concrete materials still.

99:59:59.999 --> 99:59:59.999
But because they are exposed to doing

99:59:59.999 --> 99:59:59.999
when they see a picture
of what they have done

99:59:59.999 --> 99:59:59.999
obviously, they understand it better.

99:59:59.999 --> 99:59:59.999
And when they read and they have a
picture to support the reading

99:59:59.999 --> 99:59:59.999
That's where comprehension
of the word problem

99:59:59.999 --> 99:59:59.999
becomes possible.

99:59:59.999 --> 99:59:59.999
Let me take a couple more questions
before I move on.

99:59:59.999 --> 99:59:59.999
Quite a few have similar questions

99:59:59.999 --> 99:59:59.999
like my son has problems
with English language,

99:59:59.999 --> 99:59:59.999
part of problem sums,
word problems

99:59:59.999 --> 99:59:59.999
so we cannot understand the question

99:59:59.999 --> 99:59:59.999
and therefore cannot apply
the Mathematics principle.

99:59:59.999 --> 99:59:59.999
How can I help him?

99:59:59.999 --> 99:59:59.999
So a lot of questions along this line
I'll be demonstrating that further

99:59:59.999 --> 99:59:59.999
I have demonstrated some strategies
you can use

99:59:59.999 --> 99:59:59.999
Yeah, my child is still catching up

99:59:59.999 --> 99:59:59.999
on his language skills how can we best
translate Maths problems to visuals

99:59:59.999 --> 99:59:59.999
for his better understanding.

99:59:59.999 --> 99:59:59.999
And how do we slowly get him to be
less dependent on visual.

99:59:59.999 --> 99:59:59.999
A very important question.

99:59:59.999 --> 99:59:59.999
Whatever help we give children,
is with the goal of not helping eventually

99:59:59.999 --> 99:59:59.999
less dependent.

99:59:59.999 --> 99:59:59.999
Let me answer those
questions about language.

99:59:59.999 --> 99:59:59.999
Parents, up to this point

99:59:59.999 --> 99:59:59.999
I have shared with you that
Mathematics is a language

99:59:59.999 --> 99:59:59.999
comprising of:

99:59:59.999 --> 99:59:59.999
visuals, pictures, diagrams, even graphs

99:59:59.999 --> 99:59:59.999
but also symbols

99:59:59.999 --> 99:59:59.999
and of course words.

99:59:59.999 --> 99:59:59.999
In our case, English language.

99:59:59.999 --> 99:59:59.999
I will now focus
on the question just asked

99:59:59.999 --> 99:59:59.999
how do I help with the language part

99:59:59.999 --> 99:59:59.999
of word problems.

99:59:59.999 --> 99:59:59.999
How do I help them with language
that's embedded in Mathematics?

99:59:59.999 --> 99:59:59.999
Oh let's look at this story

99:59:59.999 --> 99:59:59.999
not a very long story right?

99:59:59.999 --> 99:59:59.999
Just two sentences
short story.

99:59:59.999 --> 99:59:59.999
Who is in the story?

99:59:59.999 --> 99:59:59.999
Hmm... how interesting

99:59:59.999 --> 99:59:59.999
Pierre, I don't know how to pronounce it
I cannot speak french

99:59:59.999 --> 99:59:59.999
Is it Pierre?
Yeah maybe it's Pierre

99:59:59.999 --> 99:59:59.999
doesn't matter.

99:59:59.999 --> 99:59:59.999
Oh he's a boy
okay doesn't matter either

99:59:59.999 --> 99:59:59.999
but well...

99:59:59.999 --> 99:59:59.999
Pierre had marbles

99:59:59.999 --> 99:59:59.999
you know marbles right?

99:59:59.999 --> 99:59:59.999
Yeah the one you see at aquariums

99:59:59.999 --> 99:59:59.999
actually marbles are for playing

99:59:59.999 --> 99:59:59.999
I don't know why it is put in
aquariums nowadays

99:59:59.999 --> 99:59:59.999
and plants.

99:59:59.999 --> 99:59:59.999
But anyway, Pierre had marbles
i hope he's not losing any.

99:59:59.999 --> 99:59:59.999
So children learn language

99:59:59.999 --> 99:59:59.999
right?

99:59:59.999 --> 99:59:59.999
So they learned that

99:59:59.999 --> 99:59:59.999
oh you know in English language,
very funny language,

99:59:59.999 --> 99:59:59.999
when people say you lose your marbles
it means something.

99:59:59.999 --> 99:59:59.999
It means like

99:59:59.999 --> 99:59:59.999
You are going a bit crazy
you are not getting it all together.

99:59:59.999 --> 99:59:59.999
Anyway,

99:59:59.999 --> 99:59:59.999
let's not get distracted

99:59:59.999 --> 99:59:59.999
let's come back to the story.

99:59:59.999 --> 99:59:59.999
So Parents, you've engaged your child
in what might happen to them

99:59:59.999 --> 99:59:59.999
don't be so straitjacket
I am quite sure you are quite fun parents

99:59:59.999 --> 99:59:59.999
but when it comes to Math suddenly you
become a different animal altogether.

99:59:59.999 --> 99:59:59.999
Don't be like that,

99:59:59.999 --> 99:59:59.999
make it fun.

99:59:59.999 --> 99:59:59.999
make it informal

99:59:59.999 --> 99:59:59.999
just engage your child
in what might happen to them.

99:59:59.999 --> 99:59:59.999
when children read stories
their brain go in all directions

99:59:59.999 --> 99:59:59.999
I'm sure you know that.

99:59:59.999 --> 99:59:59.999
Don't scold them

99:59:59.999 --> 99:59:59.999
because they are just being themselves

99:59:59.999 --> 99:59:59.999
nothing wrong with being themselves

99:59:59.999 --> 99:59:59.999
what they need is guidance.

99:59:59.999 --> 99:59:59.999
How to refocus

99:59:59.999 --> 99:59:59.999
so I was just demonstrating
that awhile ago.

99:59:59.999 --> 99:59:59.999
Pierre has some marbles,
okay that's easy to understand.

99:59:59.999 --> 99:59:59.999
We know how many right?

99:59:59.999 --> 99:59:59.999
There are 315.

99:59:59.999 --> 99:59:59.999
He divided them

99:59:59.999 --> 99:59:59.999
equally

99:59:59.999 --> 99:59:59.999
into 3 boxes.

99:59:59.999 --> 99:59:59.999
Oh, what does that mean?

99:59:59.999 --> 99:59:59.999
So you ask your child that

99:59:59.999 --> 99:59:59.999
and your child
will tell you in his own words.

99:59:59.999 --> 99:59:59.999
Parents, I have so far demonstrated
three strategies,

99:59:59.999 --> 99:59:59.999
if you missed them let me
articulate them one by one.

99:59:59.999 --> 99:59:59.999
What strategy did I use?

99:59:59.999 --> 99:59:59.999
Strategy number 1:
To help them with language

99:59:59.999 --> 99:59:59.999
I deleted the question

99:59:59.999 --> 99:59:59.999
the question is there

99:59:59.999 --> 99:59:59.999
but I deleted it.

99:59:59.999 --> 99:59:59.999
I deleted the question

99:59:59.999 --> 99:59:59.999
why?

99:59:59.999 --> 99:59:59.999
When you give a child a question
what will they do?

99:59:59.999 --> 99:59:59.999
They answer it.

99:59:59.999 --> 99:59:59.999
But I don't want them to
answer the question just yet

99:59:59.999 --> 99:59:59.999
I want them to learn to comprehend,

99:59:59.999 --> 99:59:59.999
I want them to learn to understand.

99:59:59.999 --> 99:59:59.999
So because my goal for them is to learn,
to understand things

99:59:59.999 --> 99:59:59.999
I removed the answering point first.

99:59:59.999 --> 99:59:59.999
So try to cultivate that habit.

99:59:59.999 --> 99:59:59.999
Many children have the bad habit

99:59:59.999 --> 99:59:59.999
of trying to answer the question

99:59:59.999 --> 99:59:59.999
before they understand it,

99:59:59.999 --> 99:59:59.999
that's how they make mistakes.

99:59:59.999 --> 99:59:59.999
if you don't understand the story
how can you answer the question.

99:59:59.999 --> 99:59:59.999
You cannot.

99:59:59.999 --> 99:59:59.999
So to cultivate the good mindset, a good ???

99:59:59.999 --> 99:59:59.999
Mathematics is not answering questions

99:59:59.999 --> 99:59:59.999
Mathematics is understanding stuff.

99:59:59.999 --> 99:59:59.999
Once you understand stuff

99:59:59.999 --> 99:59:59.999
you can answer whatever question
they ask you.

99:59:59.999 --> 99:59:59.999
That's the truth right?

99:59:59.999 --> 99:59:59.999
So focus on understanding,

99:59:59.999 --> 99:59:59.999
how do you help them
focus on understanding?

99:59:59.999 --> 99:59:59.999
Remove the distractions,
remove the question.

99:59:59.999 --> 99:59:59.999
Question is the distraction

99:59:59.999 --> 99:59:59.999
because they try to answer
they do strange things.

99:59:59.999 --> 99:59:59.999
Second strategy I demonstrated:

99:59:59.999 --> 99:59:59.999
I did not read the question

99:59:59.999 --> 99:59:59.999
sorry... I did not read the numbers

99:59:59.999 --> 99:59:59.999
Second strategy:
I did not read the numbers.

99:59:59.999 --> 99:59:59.999
I'm sure you saw me
doing that earlier already

99:59:59.999 --> 99:59:59.999
remember the more, less problem?

99:59:59.999 --> 99:59:59.999
In face all the questions so far.

99:59:59.999 --> 99:59:59.999
So you might notice I said
Pierre had marbles

99:59:59.999 --> 99:59:59.999
Pierre had some marbles.

99:59:59.999 --> 99:59:59.999
I replaced the number
with a qualitative word.

99:59:59.999 --> 99:59:59.999
Pierre had some marbles.

99:59:59.999 --> 99:59:59.999
There is ample research to say that

99:59:59.999 --> 99:59:59.999
numerical information breaks a sentence up

99:59:59.999 --> 99:59:59.999
and decreases comprehension

99:59:59.999 --> 99:59:59.999
so that is well documented.

99:59:59.999 --> 99:59:59.999
Especially for those children
with language issues

99:59:59.999 --> 99:59:59.999
try to help them

99:59:59.999 --> 99:59:59.999
try to help them by letting them

99:59:59.999 --> 99:59:59.999
not have that problem

99:59:59.999 --> 99:59:59.999
so avoid reading the numbers.

99:59:59.999 --> 99:59:59.999
Pierre had some marbles

99:59:59.999 --> 99:59:59.999
oh how many? 315.

99:59:59.999 --> 99:59:59.999
So you read the sentences to understand it
then you put in the numbers later on.

99:59:59.999 --> 99:59:59.999
Third strategy: ask your child to paraphrase
some lengthy cumbersome sentences:

99:59:59.999 --> 99:59:59.999
Oh he divided them equally
into three boxes

99:59:59.999 --> 99:59:59.999
so hard for me to understand

99:59:59.999 --> 99:59:59.999
can you explain to me?

99:59:59.999 --> 99:59:59.999
Or if the child is not very good
in explaining,

99:59:59.999 --> 99:59:59.999
can you draw for me?

99:59:59.999 --> 99:59:59.999
So let your child have a choice,

99:59:59.999 --> 99:59:59.999
to draw or to tell.

99:59:59.999 --> 99:59:59.999
So you might even have that as a routine

99:59:59.999 --> 99:59:59.999
"do you want to tell?
or do you want to draw?"

99:59:59.999 --> 99:59:59.999
draw or tell,

99:59:59.999 --> 99:59:59.999
then those who like to draw will say draw

99:59:59.999 --> 99:59:59.999
then those who like to tell or
lazy to draw will say yeah I want to tell.

99:59:59.999 --> 99:59:59.999
But sometimes you don't give them a choice

99:59:59.999 --> 99:59:59.999
okay you've been drawing a lot

99:59:59.999 --> 99:59:59.999
next one I choose

99:59:59.999 --> 99:59:59.999
tell me

99:59:59.999 --> 99:59:59.999
then you force them a little bit
out of their comfort zone

99:59:59.999 --> 99:59:59.999
so they learn something more.

99:59:59.999 --> 99:59:59.999
So those are three strategies
quite well documented,

99:59:59.999 --> 99:59:59.999
letting children paraphrase sentences
by drawing or in their own words,

99:59:59.999 --> 99:59:59.999
leaving our numbers,

99:59:59.999 --> 99:59:59.999
and then the other one
that I mentioned earlier

99:59:59.999 --> 99:59:59.999
the three strategies.

99:59:59.999 --> 99:59:59.999
Anyway, once they have their ???
they will answer the question

99:59:59.999 --> 99:59:59.999
and they will say "ok".

99:59:59.999 --> 99:59:59.999
Pierre had three boxes

99:59:59.999 --> 99:59:59.999
and they are equal in size

99:59:59.999 --> 99:59:59.999
and he had 315 marbles

99:59:59.999 --> 99:59:59.999
and he put them equally

99:59:59.999 --> 99:59:59.999
I can replace divided with put right?

99:59:59.999 --> 99:59:59.999
He put them equally into three boxes

99:59:59.999 --> 99:59:59.999
so the 300 is quite easy to do

99:59:59.999 --> 99:59:59.999
100 each

99:59:59.999 --> 99:59:59.999
and the 15

99:59:59.999 --> 99:59:59.999
I think can

99:59:59.999 --> 99:59:59.999
5 each

99:59:59.999 --> 99:59:59.999
and together is 105.

99:59:59.999 --> 99:59:59.999
So 315 put equally into three boxes
result in... 105

99:59:59.999 --> 99:59:59.999
and then write a sentence if you want

99:59:59.999 --> 99:59:59.999
or if your teacher say you
write a sentence to answer the question.

99:59:59.999 --> 99:59:59.999
Let me demonstrate with another example.

99:59:59.999 --> 99:59:59.999
Oh who is in the question?
Who is in the story?

99:59:59.999 --> 99:59:59.999
Oh in this case it is nobody

99:59:59.999 --> 99:59:59.999
just now was a boy named Pierre
but here it is nobody.

99:59:59.999 --> 99:59:59.999
What is it about?

99:59:59.999 --> 99:59:59.999
Oh it's about COVID-19

99:59:59.999 --> 99:59:59.999
when else did we talk about masks

99:59:59.999 --> 99:59:59.999
and hand sanitisers.

99:59:59.999 --> 99:59:59.999
Oh it's about a factory
do you know what a factory is?

99:59:59.999 --> 99:59:59.999
Okay, let's see what the story is about.

99:59:59.999 --> 99:59:59.999
A factory produced some masks
and hand sanitisers.

99:59:59.999 --> 99:59:59.999
Quite a lot right?

99:59:59.999 --> 99:59:59.999
You can see the number

99:59:59.999 --> 99:59:59.999
the factory produced

99:59:59.999 --> 99:59:59.999
some masks and hand sanitisers.

99:59:59.999 --> 99:59:59.999
Can I calculate already?

99:59:59.999 --> 99:59:59.999
Probably not yet.

99:59:59.999 --> 99:59:59.999
Can I draw a diagram?

99:59:59.999 --> 99:59:59.999
Not sure

99:59:59.999 --> 99:59:59.999
never mind lets read the next sentence.

99:59:59.999 --> 99:59:59.999
It produced fewer
hand sanitisers than masks.

99:59:59.999 --> 99:59:59.999
Whats "it"?

99:59:59.999 --> 99:59:59.999
Oh the factory ,okay

99:59:59.999 --> 99:59:59.999
the factory produced fewer
hand sanitisers than masks

99:59:59.999 --> 99:59:59.999
so hand sanitisers

99:59:59.999 --> 99:59:59.999
so many

99:59:59.999 --> 99:59:59.999
masks

99:59:59.999 --> 99:59:59.999
oh mask more is it?

99:59:59.999 --> 99:59:59.999
So fewer hand sanitiser.

99:59:59.999 --> 99:59:59.999
Is my diagram showing
what the story shows?

99:59:59.999 --> 99:59:59.999
The factory produced fewer hand sanitisers
than masks.

99:59:59.999 --> 99:59:59.999
Okay I can draw
so I will draw.

99:59:59.999 --> 99:59:59.999
What information I have?

99:59:59.999 --> 99:59:59.999
Oh 2821...
where should I put that?

99:59:59.999 --> 99:59:59.999
It produced 2821 fewer hand sanitisers
than masks.

99:59:59.999 --> 99:59:59.999
When children first learn this
comparison thing,

99:59:59.999 --> 99:59:59.999
pieces of paper like that is quite useful

99:59:59.999 --> 99:59:59.999
let them use paper strips

99:59:59.999 --> 99:59:59.999
or you can go to

99:59:59.999 --> 99:59:59.999
shops and buy paper strips
the longish one

99:59:59.999 --> 99:59:59.999
or just cut your own,
make your own.

99:59:59.999 --> 99:59:59.999
Color is quite useful,
also quite interesting

99:59:59.999 --> 99:59:59.999
when you overlap
the colors will show up also

99:59:59.999 --> 99:59:59.999
then they can se
"oh that's where the 2821 is"

99:59:59.999 --> 99:59:59.999
oh we also know 5743

99:59:59.999 --> 99:59:59.999
do you know where that is?

99:59:59.999 --> 99:59:59.999
And if the child understands the story...

99:59:59.999 --> 99:59:59.999
they will know that this is the total
number of hand sanitisers and masks.

99:59:59.999 --> 99:59:59.999
Then ask your child...
what do we do next?

99:59:59.999 --> 99:59:59.999
And

99:59:59.999 --> 99:59:59.999
hopefully the child will say

99:59:59.999 --> 99:59:59.999
"I need to take
this number off that number"

99:59:59.999 --> 99:59:59.999
that's another strategy.

99:59:59.999 --> 99:59:59.999
Talk about what to do,

99:59:59.999 --> 99:59:59.999
don't always like...

99:59:59.999 --> 99:59:59.999
write down the working
write down the working

99:59:59.999 --> 99:59:59.999
get them to talk about it.

99:59:59.999 --> 99:59:59.999
So you know "oh my child knows,

99:59:59.999 --> 99:59:59.999
my child knows the first step
is subtraction".

99:59:59.999 --> 99:59:59.999
The idea that we subtract is more
important than the actual subtraction

99:59:59.999 --> 99:59:59.999
by the time they take PSLE, the
subtraction itself is done by calculator

99:59:59.999 --> 99:59:59.999
but they must know to subtract
otherwise it is pointless.

99:59:59.999 --> 99:59:59.999
If the children cannot identify
the right operation: that I subtract first

99:59:59.999 --> 99:59:59.999
then the result we divide by 2,

99:59:59.999 --> 99:59:59.999
the calculator is still useless.

99:59:59.999 --> 99:59:59.999
So from a young age

99:59:59.999 --> 99:59:59.999
engage them in telling you
what operation.

99:59:59.999 --> 99:59:59.999
Children are children,
they are not very good at multitasking.

99:59:59.999 --> 99:59:59.999
Sometimes when they

99:59:59.999 --> 99:59:59.999
identify the operation

99:59:59.999 --> 99:59:59.999
and do the operation,

99:59:59.999 --> 99:59:59.999
they don't realise that
these are two separate things.

99:59:59.999 --> 99:59:59.999
So it's not
clear in their mind.

99:59:59.999 --> 99:59:59.999
Meta-cognitively speaking,

99:59:59.999 --> 99:59:59.999
they are not learning somethings useful
for years to come.

99:59:59.999 --> 99:59:59.999
So do engage your child
in telling you the operation

99:59:59.999 --> 99:59:59.999
Don't bother them with the actual
calculation which is quite boring

99:59:59.999 --> 99:59:59.999
to be honest.

99:59:59.999 --> 99:59:59.999
The actual calculation 5000
you know like whatever we normally do

99:59:59.999 --> 99:59:59.999
that one is quite boring

99:59:59.999 --> 99:59:59.999
there's nothing exciting about doing this

99:59:59.999 --> 99:59:59.999
nothing exciting about doing this

99:59:59.999 --> 99:59:59.999
but they will do it
and they can do it.

99:59:59.999 --> 99:59:59.999
In this case they'll probably say

99:59:59.999 --> 99:59:59.999
"okay, this one is easy"

99:59:59.999 --> 99:59:59.999
yeah the 43 and 21 part is easy

99:59:59.999 --> 99:59:59.999
oh the 5728 part is slightly harder

99:59:59.999 --> 99:59:59.999
but that's okay

99:59:59.999 --> 99:59:59.999
I can rename it 4170.

99:59:59.999 --> 99:59:59.999
But anyways... that's another strategy.

99:59:59.999 --> 99:59:59.999
ask them to tell you that operation.

99:59:59.999 --> 99:59:59.999
And if they identify the operation,

99:59:59.999 --> 99:59:59.999
at least you are assured that
they know what they are doing.

99:59:59.999 --> 99:59:59.999
??? to the actual calculation.

99:59:59.999 --> 99:59:59.999
And then even in the event
they cannot get calculation

99:59:59.999 --> 99:59:59.999
or don't like to do the calculation
or cannot do the calculation,

99:59:59.999 --> 99:59:59.999
at least you know that they're okay.

99:59:59.999 --> 99:59:59.999
Identification of the Mathematics
is more important than the computation.

99:59:59.999 --> 99:59:59.999
The computation, eventually they are
going to use some calculator

99:59:59.999 --> 99:59:59.999
to actually get the answer

99:59:59.999 --> 99:59:59.999
for example: in the PSLE

99:59:59.999 --> 99:59:59.999
for numbers that are tedious.

99:59:59.999 --> 99:59:59.999
Let me take some questions now.

99:59:59.999 --> 99:59:59.999
My son always dream away
in the middle of his work,

99:59:59.999 --> 99:59:59.999
how do I get him to concentrate?

99:59:59.999 --> 99:59:59.999
I think... we must first understand
why he is dreaming away.

99:59:59.999 --> 99:59:59.999
Some children dream away
because the work is meaningless to them.

99:59:59.999 --> 99:59:59.999
So that's what I have been talking about
the whole of this evening,

99:59:59.999 --> 99:59:59.999
we must make Mathematics
meaningful to them.

99:59:59.999 --> 99:59:59.999
How?

99:59:59.999 --> 99:59:59.999
By being able to read the language.

99:59:59.999 --> 99:59:59.999
Some children cannot read the language

99:59:59.999 --> 99:59:59.999
they cannot read the language

99:59:59.999 --> 99:59:59.999
for example in P2, P3

99:59:59.999 --> 99:59:59.999
they cannot read this

99:59:59.999 --> 99:59:59.999
correctly.

99:59:59.999 --> 99:59:59.999
They cannot read this as one half

99:59:59.999 --> 99:59:59.999
but that's what it is.

99:59:59.999 --> 99:59:59.999
The denominator tells you
what the thing is... hal

99:59:59.999 --> 99:59:59.999
the numerator tells you how many

99:59:59.999 --> 99:59:59.999
or three-fifths.

99:59:59.999 --> 99:59:59.999
They say three upon five

99:59:59.999 --> 99:59:59.999
nobody talks like that,

99:59:59.999 --> 99:59:59.999
maybe once upon a time

99:59:59.999 --> 99:59:59.999
somebody tlaked like that.

99:59:59.999 --> 99:59:59.999
In modern day language
we say one apple

99:59:59.999 --> 99:59:59.999
we say three slices.

99:59:59.999 --> 99:59:59.999
In modern English language
we don't say once upon a time,

99:59:59.999 --> 99:59:59.999
in modern day language
we use number plus the noun.

99:59:59.999 --> 99:59:59.999
We say three slices
we say three children

99:59:59.999 --> 99:59:59.999
we say three apples.

99:59:59.999 --> 99:59:59.999
In modern English,
we put number followed by a noun

99:59:59.999 --> 99:59:59.999
this is what they are familiar with

99:59:59.999 --> 99:59:59.999
number plus noun

99:59:59.999 --> 99:59:59.999
which is what they are reading.

99:59:59.999 --> 99:59:59.999
Three and the noun

99:59:59.999 --> 99:59:59.999
fifth is a noun
it's a name of that slice

99:59:59.999 --> 99:59:59.999
it's a name of that ???
that you get out of one.

99:59:59.999 --> 99:59:59.999
When out cut one in to five equal slices,
that slice has a name... fifth

99:59:59.999 --> 99:59:59.999
and then we write fifth using that symbol.

99:59:59.999 --> 99:59:59.999
So, three fifths..

99:59:59.999 --> 99:59:59.999
but for some reason
we prefer to put it just underneath

99:59:59.999 --> 99:59:59.999
so it's three fifths

99:59:59.999 --> 99:59:59.999
It's like that right?

99:59:59.999 --> 99:59:59.999
So many children cannot read it

99:59:59.999 --> 99:59:59.999
that's why they think
thing's are meaning to them

99:59:59.999 --> 99:59:59.999
but actually it is quite meaningful.

99:59:59.999 --> 99:59:59.999
So by P3, P4, P5
they learn things like this

99:59:59.999 --> 99:59:59.999
like half and one-fourth.

99:59:59.999 --> 99:59:59.999
They know even as a child,

99:59:59.999 --> 99:59:59.999
one apple and one orange
what do you get?

99:59:59.999 --> 99:59:59.999
you don't get two

99:59:59.999 --> 99:59:59.999
you don't get two apples
of course not

99:59:59.999 --> 99:59:59.999
you don't get two oranges
any child can understand that right?

99:59:59.999 --> 99:59:59.999
One apple and one orange
is not two apples it's not two oranges

99:59:59.999 --> 99:59:59.999
They know from a very young age

99:59:59.999 --> 99:59:59.999
when the nouns are different,
you cannot add.

99:59:59.999 --> 99:59:59.999
Like three boys and two girls

99:59:59.999 --> 99:59:59.999
you should be horrified to get five boys

99:59:59.999 --> 99:59:59.999
you don't, so no need to panic
you don't

99:59:59.999 --> 99:59:59.999
And any child knows

99:59:59.999 --> 99:59:59.999
that three boys and two girls
don't give me five boys nor five girls.

99:59:59.999 --> 99:59:59.999
What? Different type what.
Different noun what.

99:59:59.999 --> 99:59:59.999
And if I can change the noun
then I can add,

99:59:59.999 --> 99:59:59.999
three children and two more children
ah business as usual, five children.

99:59:59.999 --> 99:59:59.999
One apple and one orange,

99:59:59.999 --> 99:59:59.999
one piece of fruit
and another piece of fruit

99:59:59.999 --> 99:59:59.999
that gives me two pieces of fruit.

99:59:59.999 --> 99:59:59.999
So one-half and one-fourth

99:59:59.999 --> 99:59:59.999
different kind, cannot add
just yet.

99:59:59.999 --> 99:59:59.999
Can I change the half into fourth?

99:59:59.999 --> 99:59:59.999
Not so convenient or okay?

99:59:59.999 --> 99:59:59.999
It's okay right?

99:59:59.999 --> 99:59:59.999
Half is two fourths
they learned that in P3 right?

99:59:59.999 --> 99:59:59.999
Oh so now two fourths and fourth

99:59:59.999 --> 99:59:59.999
business as usual
same kind.

99:59:59.999 --> 99:59:59.999
Children dream off because they
cannot make sense of the gibberish

99:59:59.999 --> 99:59:59.999
that is in front of them.

99:59:59.999 --> 99:59:59.999
But when they can

99:59:59.999 --> 99:59:59.999
when they can

99:59:59.999 --> 99:59:59.999
they can do the work.

99:59:59.999 --> 99:59:59.999
Like most of us are

99:59:59.999 --> 99:59:59.999
probably not able to function
if I give you something in Russian

99:59:59.999 --> 99:59:59.999
if you don't understand Russian.

99:59:59.999 --> 99:59:59.999
It'll be that exciting
I ask you to read a page in Russian.

99:59:59.999 --> 99:59:59.999
No matter now exciting
or engaging the story is

99:59:59.999 --> 99:59:59.999
you surely dream off
and definitely give up

99:59:59.999 --> 99:59:59.999
because you don't even
understand the first thing about it.

99:59:59.999 --> 99:59:59.999
This is the main reason why children
cannot focus and they dream off.

99:59:59.999 --> 99:59:59.999
So the big answer is
make things meaningful to them

99:59:59.999 --> 99:59:59.999
and earlier today I've also said
"make things interesting for them".

99:59:59.999 --> 99:59:59.999
A third answer to that is

99:59:59.999 --> 99:59:59.999
remember these are children

99:59:59.999 --> 99:59:59.999
and some of the children we have Pathlight

99:59:59.999 --> 99:59:59.999
they do have attention issues
you know that

99:59:59.999 --> 99:59:59.999
your own children you know that.

99:59:59.999 --> 99:59:59.999
Break things down for them

99:59:59.999 --> 99:59:59.999
frame them up slowly

99:59:59.999 --> 99:59:59.999
start with 10 minutes,
go on to 15, go on to 30 minutes

99:59:59.999 --> 99:59:59.999
don't expect them to be able to sit
there for an entire hour

99:59:59.999 --> 99:59:59.999
it's not possible.

99:59:59.999 --> 99:59:59.999
Even for adults we do struggle with it
let alone children.

99:59:59.999 --> 99:59:59.999
So if your children dream off,

99:59:59.999 --> 99:59:59.999
Two strategies.

99:59:59.999 --> 99:59:59.999
The practical one: 
Just write things down for them.

99:59:59.999 --> 99:59:59.999
Llet them do things in small
bits and pieces

99:59:59.999 --> 99:59:59.999
and that will train up
their ability to focus.

99:59:59.999 --> 99:59:59.999
But the bigger answer
is make things meaningful for them.

99:59:59.999 --> 99:59:59.999
I am sure you know your children can
be engaged for a very long time

99:59:59.999 --> 99:59:59.999
if it is something
they are very interested in.

99:59:59.999 --> 99:59:59.999
Like some of the children
who loves dinosaurs

99:59:59.999 --> 99:59:59.999
they will spend hours

99:59:59.999 --> 99:59:59.999
watching YouTube
or reading about dinosaurs.

99:59:59.999 --> 99:59:59.999
Some of them like transports

99:59:59.999 --> 99:59:59.999
and they will spend enormous
amounts of resources, cognitive resources

99:59:59.999 --> 99:59:59.999
learning what bus goes where,
this bus goes through which route

99:59:59.999 --> 99:59:59.999
I am sure you know that.

99:59:59.999 --> 99:59:59.999
It's not that they cannot engage,
it's not that they cannot focus,

99:59:59.999 --> 99:59:59.999
it's just that the material
is not meaningful for them.

99:59:59.999 --> 99:59:59.999
So that's a bigger answer actually
make things meaningful for them.

99:59:59.999 --> 99:59:59.999
Let me illustrate a little bit more.

99:59:59.999 --> 99:59:59.999
Bby now I think you know
some strategies already

99:59:59.999 --> 99:59:59.999
to tell how children process information

99:59:59.999 --> 99:59:59.999
I use them all the time
in every single example.

99:59:59.999 --> 99:59:59.999
Here is the story
never mind the question.

99:59:59.999 --> 99:59:59.999
Important is to understand the story

99:59:59.999 --> 99:59:59.999
once we understand the stories
we can answer any question.

99:59:59.999 --> 99:59:59.999
My strategy of removing questions.

99:59:59.999 --> 99:59:59.999
Who is in the story?

99:59:59.999 --> 99:59:59.999
This story has nobody.

99:59:59.999 --> 99:59:59.999
What is it about?

99:59:59.999 --> 99:59:59.999
Beads, what are beads?
Do you know beads?

99:59:59.999 --> 99:59:59.999
If you know them great
if not we Google.

99:59:59.999 --> 99:59:59.999
There are some beads in a box
can you imagine that?

99:59:59.999 --> 99:59:59.999
There are five times

99:59:59.999 --> 99:59:59.999
five times

99:59:59.999 --> 99:59:59.999
if I use this to be one time
can you show me twice?

99:59:59.999 --> 99:59:59.999
If this is one time,
can you show me three times?

99:59:59.999 --> 99:59:59.999
Or what Singaporeans call thrice.

99:59:59.999 --> 99:59:59.999
Can you show me four times?
Can you show me five times?

99:59:59.999 --> 99:59:59.999
Engage your child using pieces of paper.

99:59:59.999 --> 99:59:59.999
Tf they don't want to draw the model
don't force them

99:59:59.999 --> 99:59:59.999
let them use paper.

99:59:59.999 --> 99:59:59.999
The purpose of drawing
is to create the ability to visualise

99:59:59.999 --> 99:59:59.999
so that they know the operation to use.

99:59:59.999 --> 99:59:59.999
Pieces of paper for building the model
serve the same purpose.

99:59:59.999 --> 99:59:59.999
If they don't want to draw,
this is your option

99:59:59.999 --> 99:59:59.999
let them use paper like that
to build the model.

99:59:59.999 --> 99:59:59.999
The goal is to get the right operation

99:59:59.999 --> 99:59:59.999
that's the goal.

99:59:59.999 --> 99:59:59.999
And to get to the right operation,
either you know it

99:59:59.999 --> 99:59:59.999
for easy cases

99:59:59.999 --> 99:59:59.999
or you use a diagram, a model
to get to it.

99:59:59.999 --> 99:59:59.999
So model drawing is to
tell you the right operation

99:59:59.999 --> 99:59:59.999
that's the purpose of model drawing.

99:59:59.999 --> 99:59:59.999
It's not because they lose marks in PSLE.

99:59:59.999 --> 99:59:59.999
Examiners don't care about your model

99:59:59.999 --> 99:59:59.999
they don't even give marks to your model

99:59:59.999 --> 99:59:59.999
they give marks to your equation.

99:59:59.999 --> 99:59:59.999
So when they are young
let them do those things as well.

99:59:59.999 --> 99:59:59.999
Anyway, there are five times

99:59:59.999 --> 99:59:59.999
what a long sentence

99:59:59.999 --> 99:59:59.999
let's read it carefully.

99:59:59.999 --> 99:59:59.999
There are five times

99:59:59.999 --> 99:59:59.999
five times? I use five pieces
compared to the other one.

99:59:59.999 --> 99:59:59.999
There are five times

99:59:59.999 --> 99:59:59.999
five times as many green as red beads
in the box that is very long.

99:59:59.999 --> 99:59:59.999
Okay, don't want the box
ignore the box thing.

99:59:59.999 --> 99:59:59.999
There are five times

99:59:59.999 --> 99:59:59.999
as many green

99:59:59.999 --> 99:59:59.999
don't want the beads

99:59:59.999 --> 99:59:59.999
there are five times as many green as red

99:59:59.999 --> 99:59:59.999
ah I understand already!

99:59:59.999 --> 99:59:59.999
There are five times
as many green as there are red

99:59:59.999 --> 99:59:59.999
oh so this is green
five units

99:59:59.999 --> 99:59:59.999
and this is red
one unit.

99:59:59.999 --> 99:59:59.999
There are five times as many green as red

99:59:59.999 --> 99:59:59.999
oh I understand already

99:59:59.999 --> 99:59:59.999
there are five times as many
green beads as red beads

99:59:59.999 --> 99:59:59.999
understand already.

99:59:59.999 --> 99:59:59.999
There are five times as many
green beads as red beads in the box

99:59:59.999 --> 99:59:59.999
understand already.

99:59:59.999 --> 99:59:59.999
If I want to drawn,
I can draw

99:59:59.999 --> 99:59:59.999
if not I can use the paper just now

99:59:59.999 --> 99:59:59.999
to say that green I use five pieces

99:59:59.999 --> 99:59:59.999
and red I use one piece of paper
to represent it.

99:59:59.999 --> 99:59:59.999
Okay I understand that already
I can draw.

99:59:59.999 --> 99:59:59.999
Can I calculate?

99:59:59.999 --> 99:59:59.999
Oh I can, but I got information like 78,
where does the 78 go?

99:59:59.999 --> 99:59:59.999
There are 78 beads in a box, okay

99:59:59.999 --> 99:59:59.999
it must be all the beads
the red and the green ones.

99:59:59.999 --> 99:59:59.999
So the 78 must put into 1, 2, 3, 4, 5, 6

99:59:59.999 --> 99:59:59.999
78 put equally into 6 boxes.

99:59:59.999 --> 99:59:59.999
Parents, I hope you are seeing me applying

99:59:59.999 --> 99:59:59.999
the various things I suggested earlier.

99:59:59.999 --> 99:59:59.999
Always read as you write,

99:59:59.999 --> 99:59:59.999
putting 78 equally into 6 boxes

99:59:59.999 --> 99:59:59.999
I didn't say 78 divided by 6

99:59:59.999 --> 99:59:59.999
that doesn't give them the meaning
of whatever they are doing.

99:59:59.999 --> 99:59:59.999
Many children eventually

99:59:59.999 --> 99:59:59.999
does not became good enough
in Mathematics when they get to PSLE

99:59:59.999 --> 99:59:59.999
because they kind of
wasted their six years

99:59:59.999 --> 99:59:59.999
trying to understand gibberish.

99:59:59.999 --> 99:59:59.999
It is really gibberish to them

99:59:59.999 --> 99:59:59.999
they have no clue

99:59:59.999 --> 99:59:59.999
what all these squiggles actually mean

99:59:59.999 --> 99:59:59.999
so sometimes by luck they get it right

99:59:59.999 --> 99:59:59.999
and often they get it wrong

99:59:59.999 --> 99:59:59.999
and they struggle

99:59:59.999 --> 99:59:59.999
they struggle because
it's Martian to them.

99:59:59.999 --> 99:59:59.999
But it doesn't have to be

99:59:59.999 --> 99:59:59.999
and we adults, both parents and teachers

99:59:59.999 --> 99:59:59.999
can really help them

99:59:59.999 --> 99:59:59.999
especially for most of you
your kids are in Primary 1, 2,3

99:59:59.999 --> 99:59:59.999
still plenty of time
to put all these into practice

99:59:59.999 --> 99:59:59.999
in a more regular basis.

99:59:59.999 --> 99:59:59.999
The teachers have spoken to them
over the years

99:59:59.999 --> 99:59:59.999
we have constant professional development

99:59:59.999 --> 99:59:59.999
and they try to do this.

99:59:59.999 --> 99:59:59.999
The information we share
with you this evening

99:59:59.999 --> 99:59:59.999
is for you to have the
same consistent practice

99:59:59.999 --> 99:59:59.999
so that your child can learn Mathematics

99:59:59.999 --> 99:59:59.999
in a rather easy way.

99:59:59.999 --> 99:59:59.999
So from there they will do
whatever they...

99:59:59.999 --> 99:59:59.999
This is a calculation for Primary 3

99:59:59.999 --> 99:59:59.999
so 78 is too hard
for me anyway

99:59:59.999 --> 99:59:59.999
but I think I can take out

99:59:59.999 --> 99:59:59.999
I think I can take out 60

99:59:59.999 --> 99:59:59.999
60 is quite easy, I get 10

99:59:59.999 --> 99:59:59.999
and then left with 18

99:59:59.999 --> 99:59:59.999
18 put into 6
that one is okay, I get 3.

99:59:59.999 --> 99:59:59.999
So 10 and 3, I get 13 as
the value for 1 unit.

99:59:59.999 --> 99:59:59.999
Can they do this mentally?

99:59:59.999 --> 99:59:59.999
Yes.

99:59:59.999 --> 99:59:59.999
For those of you with children
who can do Mathematics mentally

99:59:59.999 --> 99:59:59.999
sorry

99:59:59.999 --> 99:59:59.999
For those of you with children
who can do calculation mentally

99:59:59.999 --> 99:59:59.999
encourage them to do so.

99:59:59.999 --> 99:59:59.999
That is the end goal of
learning calculation anyway

99:59:59.999 --> 99:59:59.999
you learn calculation by writing it down

99:59:59.999 --> 99:59:59.999
so that one fine day
you no longer have to write it down.

99:59:59.999 --> 99:59:59.999
Mental calculation.

99:59:59.999 --> 99:59:59.999
Mental calculation is a pinnacle
to learning computation.

99:59:59.999 --> 99:59:59.999
By the way computation is arithmetic
it's not Mathematics.

99:59:59.999 --> 99:59:59.999
it's part of Mathematics.

99:59:59.999 --> 99:59:59.999
Mathematics is a thinking part

99:59:59.999 --> 99:59:59.999
the arithmetic is the computation part.

99:59:59.999 --> 99:59:59.999
Some of your children like
to do mental calculation?

99:59:59.999 --> 99:59:59.999
That's perfect, that's alright.

99:59:59.999 --> 99:59:59.999
In fact, those who are over reliant on
paper all the time to do simple things

99:59:59.999 --> 99:59:59.999
example, things like

99:59:59.999 --> 99:59:59.999
things like 11 minus 9

99:59:59.999 --> 99:59:59.999
it break my heart to see P6's do this

99:59:59.999 --> 99:59:59.999
11 minus 9
what has happened?

99:59:59.999 --> 99:59:59.999
really what has happened?

99:59:59.999 --> 99:59:59.999
if you still do 11 minus 9 like that.

99:59:59.999 --> 99:59:59.999
Then the best part is then they will do
what the teacher taught them to do.

99:59:59.999 --> 99:59:59.999
Like why?!
You are still doing 11 minus 9 right?

99:59:59.999 --> 99:59:59.999
So can't you like

99:59:59.999 --> 99:59:59.999
oh what's the difference between
11 and 9.

99:59:59.999 --> 99:59:59.999
So if they only read it,
what's the difference between 11 and 9?

99:59:59.999 --> 99:59:59.999
Oh the difference, so the gap between them
9 to 11, only two steps

99:59:59.999 --> 99:59:59.999
So this will all translate into better
things when they deal with bigger numbers.

99:59:59.999 --> 99:59:59.999
When they have to do 401

99:59:59.999 --> 99:59:59.999
then they will say

99:59:59.999 --> 99:59:59.999
"oh what's the difference between
the two numbers?

99:59:59.999 --> 99:59:59.999
oh the two numbers are quite close
399 is only one step to 400

99:59:59.999 --> 99:59:59.999
400 to 401 only one step

99:59:59.999 --> 99:59:59.999
the difference is two.

99:59:59.999 --> 99:59:59.999
Like that.

99:59:59.999 --> 99:59:59.999
When you can read,

99:59:59.999 --> 99:59:59.999
difficult things

99:59:59.999 --> 99:59:59.999
become quite easy you know.

99:59:59.999 --> 99:59:59.999
Let me just show you
when your kids get older

99:59:59.999 --> 99:59:59.999
when they get to P5

99:59:59.999 --> 99:59:59.999
they do things like three-fifth
share among 3

99:59:59.999 --> 99:59:59.999
so when they can read this
as three slices,

99:59:59.999 --> 99:59:59.999
three whatever, three nouns,
three-fifths

99:59:59.999 --> 99:59:59.999
they will say

99:59:59.999 --> 99:59:59.999
"oh three share among three
is easy, it's one"

99:59:59.999 --> 99:59:59.999
and the item is fifth
so the answer is one-fifth.

99:59:59.999 --> 99:59:59.999
For this case,
it's so straight forward

99:59:59.999 --> 99:59:59.999
but then I see P5 who does this
because they do what adults tell them.

99:59:59.999 --> 99:59:59.999
Maybe some of us tell out older children

99:59:59.999 --> 99:59:59.999
"eh boy ah, remember ah
dividing fraction very easy one

99:59:59.999 --> 99:59:59.999
got formula. just remember ah

99:59:59.999 --> 99:59:59.999
you change divide to multiply

99:59:59.999 --> 99:59:59.999
and then this one you write
as three upon one

99:59:59.999 --> 99:59:59.999
and then this one you terbalik
the thing lah."

99:59:59.999 --> 99:59:59.999
Terbalik is Singlish for invert
invert the thing

99:59:59.999 --> 99:59:59.999
then you cancel your life away lah

99:59:59.999 --> 99:59:59.999
then you get the answer right?

99:59:59.999 --> 99:59:59.999
All that hassle for something
that quiet simple

99:59:59.999 --> 99:59:59.999
three whatever share by three
the answer is one.

99:59:59.999 --> 99:59:59.999
No need all that
nuts and bolts and

99:59:59.999 --> 99:59:59.999
all those nonsense

99:59:59.999 --> 99:59:59.999
to just get to the same answer.

99:59:59.999 --> 99:59:59.999
Just to illustrate that once you can read

99:59:59.999 --> 99:59:59.999
a lot of things are actually
quite straightforward.

99:59:59.999 --> 99:59:59.999
Now let me take a couple more question's 
as we wrap things up.

99:59:59.999 --> 99:59:59.999
Some of you are quite lucky

99:59:59.999 --> 99:59:59.999
because your children seem to be
doing really alright

99:59:59.999 --> 99:59:59.999
better than alright.

99:59:59.999 --> 99:59:59.999
How can I bring out the best of the child

99:59:59.999 --> 99:59:59.999
which Is in primary 1
but he's able to do primary 4 Mathematics.

99:59:59.999 --> 99:59:59.999
Any advise besides volunteered training?

99:59:59.999 --> 99:59:59.999
Five things I would suggest

99:59:59.999 --> 99:59:59.999
for those of us
who have children

99:59:59.999 --> 99:59:59.999
who seems to be quite
capable in Mathematics.

99:59:59.999 --> 99:59:59.999
How do you push them further?

99:59:59.999 --> 99:59:59.999
I think part of the answer is this:

99:59:59.999 --> 99:59:59.999
let them choose what to learn.

99:59:59.999 --> 99:59:59.999
Since they already can learn
what they are supposed to learn

99:59:59.999 --> 99:59:59.999
let them decide.

99:59:59.999 --> 99:59:59.999
Like okay you know there is
this thing called prime numbers

99:59:59.999 --> 99:59:59.999
and let them find out

99:59:59.999 --> 99:59:59.999
if they are interested,
they will pursue it

99:59:59.999 --> 99:59:59.999
if they don't like it,
they will ignore it

99:59:59.999 --> 99:59:59.999
it's fine.

99:59:59.999 --> 99:59:59.999
So that's my global answer

99:59:59.999 --> 99:59:59.999
let them choose
to do whatever they want to do.

99:59:59.999 --> 99:59:59.999
No need to go to primary 2, primary 3,
primary 4, primary 5 but let them choose.

99:59:59.999 --> 99:59:59.999
Oh you know, your brother in P4
learned about factors and multiples

99:59:59.999 --> 99:59:59.999
do you want to find out more about it?

99:59:59.999 --> 99:59:59.999
Go to this website or watch this video
or whatever.

99:59:59.999 --> 99:59:59.999
So that's my answer actually

99:59:59.999 --> 99:59:59.999
expose them to some things
but let them choose

99:59:59.999 --> 99:59:59.999
let them choose.

99:59:59.999 --> 99:59:59.999
So that is more liberating

99:59:59.999 --> 99:59:59.999
than sending them to cookie-cutter
kind of enrichment activities.

99:59:59.999 --> 99:59:59.999
What else can you do

99:59:59.999 --> 99:59:59.999
if they are not ready
for higher level content.

99:59:59.999 --> 99:59:59.999
So some children are quite good

99:59:59.999 --> 99:59:59.999
and these strategies can be applicable
to all children actually.

99:59:59.999 --> 99:59:59.999
If they are quite good,

99:59:59.999 --> 99:59:59.999
and they can do their Mathematics
quite easily

99:59:59.999 --> 99:59:59.999
like they know their timetable
in primary 2, primary 3 quite readily

99:59:59.999 --> 99:59:59.999
what else can they do?

99:59:59.999 --> 99:59:59.999
You can ask them to write a story

99:59:59.999 --> 99:59:59.999
if they don't want to write
you can always ask them to draw it.

99:59:59.999 --> 99:59:59.999
Anyone can do this,
not just the advance children.

99:59:59.999 --> 99:59:59.999
But if they're advance, these are
some things that are quite helpful

99:59:59.999 --> 99:59:59.999
to further their understanding
of Mathematics.

99:59:59.999 --> 99:59:59.999
You can also ask them to explain

99:59:59.999 --> 99:59:59.999
can be oral, can be written form.

99:59:59.999 --> 99:59:59.999
So keeping a Math journal
is quite useful also

99:59:59.999 --> 99:59:59.999
a little diary where they record stuff.

99:59:59.999 --> 99:59:59.999
I believe most of your children
have a Math journal anyway in school

99:59:59.999 --> 99:59:59.999
you can also have a Math journal at home.

99:59:59.999 --> 99:59:59.999
I don't understand how come
9 groups of 7 the answer is whatever

99:59:59.999 --> 99:59:59.999
why is it like that
why is it like less than 70

99:59:59.999 --> 99:59:59.999
and see what your child say.

99:59:59.999 --> 99:59:59.999
And maybe they will say

99:59:59.999 --> 99:59:59.999
"oh you see, 10 groups of 7 is 70 already"

99:59:59.999 --> 99:59:59.999
oh course ah

99:59:59.999 --> 99:59:59.999
if 10 groups is 70 then 9 groups
must be less than 70.

99:59:59.999 --> 99:59:59.999
In fact it should be 7 less than 70.

99:59:59.999 --> 99:59:59.999
So if a child is fully advanced
they usually can do this

99:59:59.999 --> 99:59:59.999
they can explain orally

99:59:59.999 --> 99:59:59.999
or if they have enough writing skills they
can write it or draw it in their journal.

99:59:59.999 --> 99:59:59.999
Finally,

99:59:59.999 --> 99:59:59.999
they can challenge themselves

99:59:59.999 --> 99:59:59.999
children when advanced
will find avenues

99:59:59.999 --> 99:59:59.999
to challenge themselves

99:59:59.999 --> 99:59:59.999
and you can help them in that.

99:59:59.999 --> 99:59:59.999
Example, maybe they do
a lot of calculation

99:59:59.999 --> 99:59:59.999
they do a lot of calculation in P3
when they are asked to multiply

99:59:59.999 --> 99:59:59.999
a two digit number by a one digit number.

99:59:59.999 --> 99:59:59.999
Like in a worksheet, 
quite boring actually.

99:59:59.999 --> 99:59:59.999
you can say
"eh, why don't we challenge ourselves".

99:59:59.999 --> 99:59:59.999
We notice that the answer is two digit

99:59:59.999 --> 99:59:59.999
but this one the answer is three digit.

99:59:59.999 --> 99:59:59.999
and this one the answer
is also three digit.

99:59:59.999 --> 99:59:59.999
I wonder if it is possible

99:59:59.999 --> 99:59:59.999
for two digit number
multiply by one digit

99:59:59.999 --> 99:59:59.999
and the answer is two digit

99:59:59.999 --> 99:59:59.999
we know it's possible already
we have one example.

99:59:59.999 --> 99:59:59.999
But this one

99:59:59.999 --> 99:59:59.999
this one the answer is 26
so the digit 2 is repeated.

99:59:59.999 --> 99:59:59.999
I wonder if it's possible
all the five digits

99:59:59.999 --> 99:59:59.999
all the five digits are different

99:59:59.999 --> 99:59:59.999
you know?

99:59:59.999 --> 99:59:59.999
Let's find if it is possible.

99:59:59.999 --> 99:59:59.999
So children who are quite advance
will challenge themselves

99:59:59.999 --> 99:59:59.999
but when they are younger
they don't know what to do

99:59:59.999 --> 99:59:59.999
so you can expose them to some examples
and over time you should see them

99:59:59.999 --> 99:59:59.999
you should see then challenging themselves
rather independently.

99:59:59.999 --> 99:59:59.999
Let me conclude now

99:59:59.999 --> 99:59:59.999
with one final example.

99:59:59.999 --> 99:59:59.999
Let's look at something that's more

99:59:59.999 --> 99:59:59.999
involved.

99:59:59.999 --> 99:59:59.999
In today's webinar,

99:59:59.999 --> 99:59:59.999
the topic is helping children
process information in Mathematics

99:59:59.999 --> 99:59:59.999
So we need to know

99:59:59.999 --> 99:59:59.999
the different types of information.

99:59:59.999 --> 99:59:59.999
What are they?

99:59:59.999 --> 99:59:59.999
Visuals, yes visuals

99:59:59.999 --> 99:59:59.999
pictures, diagrams, graphs

99:59:59.999 --> 99:59:59.999
some are from daily life,.
some are more formal

99:59:59.999 --> 99:59:59.999
What else?

99:59:59.999 --> 99:59:59.999
Language, words, English

99:59:59.999 --> 99:59:59.999
some are familiar
like stories about bakery

99:59:59.999 --> 99:59:59.999
some are quite strange
about milk bottles.

99:59:59.999 --> 99:59:59.999
What else?

99:59:59.999 --> 99:59:59.999
Symbols.

99:59:59.999 --> 99:59:59.999
So today we learned that
these are the kind of information

99:59:59.999 --> 99:59:59.999
children deal with in Mathematics

99:59:59.999 --> 99:59:59.999
language, symbols, and visuals

99:59:59.999 --> 99:59:59.999
and I have suggested some strategies

99:59:59.999 --> 99:59:59.999
on how we can help them become better
in processing those information.

99:59:59.999 --> 99:59:59.999
Those are mere suggestions,

99:59:59.999 --> 99:59:59.999
I am sure you can come up
with other ways

99:59:59.999 --> 99:59:59.999
which are equally effective
or engaging for your children.

99:59:59.999 --> 99:59:59.999
The webinar this afternoon
is just to give you a starting point

99:59:59.999 --> 99:59:59.999
to inspire you to try to make
Mathematics more palatable

99:59:59.999 --> 99:59:59.999
hopefully more exciting, more interesting
for your children.

99:59:59.999 --> 99:59:59.999
But if not at least meaningful

99:59:59.999 --> 99:59:59.999
because Mathematics is a language

99:59:59.999 --> 99:59:59.999
once we cannot read the symbols

99:59:59.999 --> 99:59:59.999
everything falls blank.

99:59:59.999 --> 99:59:59.999
Once we cannot read the English language
with comprehension

99:59:59.999 --> 99:59:59.999
everything cannot happen.

99:59:59.999 --> 99:59:59.999
Symbols sometimes they really cannot read

99:59:59.999 --> 99:59:59.999
like I said, children say three over five
three upon five

99:59:59.999 --> 99:59:59.999
that's really, 
cannot speak proper Mathematical language.

99:59:59.999 --> 99:59:59.999
So it's like in English,
the child only knows Singlish

99:59:59.999 --> 99:59:59.999
sure fail PSLE English
confirm

99:59:59.999 --> 99:59:59.999
If all you know is Singlish
and no understanding of standard English.

99:59:59.999 --> 99:59:59.999
Likewise in Mathematics
some children cannot read symbols

99:59:59.999 --> 99:59:59.999
do help them

99:59:59.999 --> 99:59:59.999
do help them by reading,
don't by lazy and say three times five

99:59:59.999 --> 99:59:59.999
say three rows of five
three groups of five

99:59:59.999 --> 99:59:59.999
fifty-one share among three
twelve put into groups of four.

99:59:59.999 --> 99:59:59.999
There are many ways to read

99:59:59.999 --> 99:59:59.999
important thing is read, don't spell.

99:59:59.999 --> 99:59:59.999
Let me demonstrate this final example

99:59:59.999 --> 99:59:59.999
and you'll be able to see the various
strategies addressing language difficulty.

99:59:59.999 --> 99:59:59.999
Many of you raise questions

99:59:59.999 --> 99:59:59.999
so many I cannot answer
every single one of them live.

99:59:59.999 --> 99:59:59.999
There are some important questions
that I would still want to answer

99:59:59.999 --> 99:59:59.999
so we are going to put this
as a eCampus course

99:59:59.999 --> 99:59:59.999
so some of your questions that are not
addressed will be featured on the course

99:59:59.999 --> 99:59:59.999
so do visit eCampus
to revisit today's topic

99:59:59.999 --> 99:59:59.999
and you might get other insights
from the answers to

99:59:59.999 --> 99:59:59.999
some important questions that were
also raised

99:59:59.999 --> 99:59:59.999
just that you know we only have
less than two hours

99:59:59.999 --> 99:59:59.999
there is only so much we can cover anway

99:59:59.999 --> 99:59:59.999
but do go to eCampus to
continue to get more ideas,

99:59:59.999 --> 99:59:59.999
more information about this topic.

99:59:59.999 --> 99:59:59.999
Oh never mind the question
let's look at the story

99:59:59.999 --> 99:59:59.999
notice the question is not there yet.

99:59:59.999 --> 99:59:59.999
Who is in the story?

99:59:59.999 --> 99:59:59.999
Oh finally we have someone in the story

99:59:59.999 --> 99:59:59.999
Mrs Baey and Mrs Chia

99:59:59.999 --> 99:59:59.999
I don't really know them
but that's alright.

99:59:59.999 --> 99:59:59.999
What are they doing?

99:59:59.999 --> 99:59:59.999
They went shopping.

99:59:59.999 --> 99:59:59.999
Quite a long story

99:59:59.999 --> 99:59:59.999
one sentence...

99:59:59.999 --> 99:59:59.999
two sentences...

99:59:59.999 --> 99:59:59.999
three sentences
alright it's a long story

99:59:59.999 --> 99:59:59.999
but never mind
one by one ,one at a time.

99:59:59.999 --> 99:59:59.999
They went shopping

99:59:59.999 --> 99:59:59.999
alright I can understand that

99:59:59.999 --> 99:59:59.999
with the same amount of money

99:59:59.999 --> 99:59:59.999
okay not too hard.

99:59:59.999 --> 99:59:59.999
Can I calculate.

99:59:59.999 --> 99:59:59.999
Can I calculate?

99:59:59.999 --> 99:59:59.999
Probably not yet

99:59:59.999 --> 99:59:59.999
no numbers.

99:59:59.999 --> 99:59:59.999
Can I draw?

99:59:59.999 --> 99:59:59.999
In this case I can,
same amount.

99:59:59.999 --> 99:59:59.999
So I can draw model
that will make my teacher happy.

99:59:59.999 --> 99:59:59.999
I can draw this

99:59:59.999 --> 99:59:59.999
but sometimes I don't want to draw

99:59:59.999 --> 99:59:59.999
it's okay, I said wait
I want to read more.

99:59:59.999 --> 99:59:59.999
So it's up to you

99:59:59.999 --> 99:59:59.999
sometimes you want to do it straight away

99:59:59.999 --> 99:59:59.999
sometimes you decide to wait
maybe another sentence

99:59:59.999 --> 99:59:59.999
it's better to draw
or better to calculate

99:59:59.999 --> 99:59:59.999
so you decide.

99:59:59.999 --> 99:59:59.999
Parents, the final thing
I want to share with you is

99:59:59.999 --> 99:59:59.999
do teach children to make decisions

99:59:59.999 --> 99:59:59.999
don't decide everything for them.

99:59:59.999 --> 99:59:59.999
When you help them with Mathematics,
don't always tell them what to do

99:59:59.999 --> 99:59:59.999
that's not helpful.

99:59:59.999 --> 99:59:59.999
Children that become successful
in Mathematics eventually

99:59:59.999 --> 99:59:59.999
are independent

99:59:59.999 --> 99:59:59.999
it is a characteristic.

99:59:59.999 --> 99:59:59.999
You cannot be not independent
and be highly successful.

99:59:59.999 --> 99:59:59.999
You may be artificially successful
that means you get AL1 for PSLE

99:59:59.999 --> 99:59:59.999
A-Star for PSLE

99:59:59.999 --> 99:59:59.999
but my O-Level not so good anymore.

99:59:59.999 --> 99:59:59.999
Some of them still quite okay
for O-Level

99:59:59.999 --> 99:59:59.999
but by A-Level, Polytechnic
not very good anymore.

99:59:59.999 --> 99:59:59.999
So at some point,
they will become not very good.

99:59:59.999 --> 99:59:59.999
They'll be found out.

99:59:59.999 --> 99:59:59.999
So independence is a
very important characteristic

99:59:59.999 --> 99:59:59.999
do let children learn to make decisions.

99:59:59.999 --> 99:59:59.999
"Do you want to draw now?

99:59:59.999 --> 99:59:59.999
okay go on

99:59:59.999 --> 99:59:59.999
don't want is okay

99:59:59.999 --> 99:59:59.999
you decided".

99:59:59.999 --> 99:59:59.999
If it's a bad decision it's fine

99:59:59.999 --> 99:59:59.999
later we just correct ourselves.

99:59:59.999 --> 99:59:59.999
"Do you want to calculate?
Do you want to draw?"

99:59:59.999 --> 99:59:59.999
it's a simple question
you can ask all the time.

99:59:59.999 --> 99:59:59.999
Alright, that is done.

99:59:59.999 --> 99:59:59.999
They went shopping with th.e
same amount of money

99:59:59.999 --> 99:59:59.999
One of them spend so much

99:59:59.999 --> 99:59:59.999
the other one spend so much.

99:59:59.999 --> 99:59:59.999
Mrs Baey spent $480

99:59:59.999 --> 99:59:59.999
so Mrs Baey...

99:59:59.999 --> 99:59:59.999
spent $480

99:59:59.999 --> 99:59:59.999
can I draw?

99:59:59.999 --> 99:59:59.999
Yeah I can, I put in $480 somewhere
but I want to wait.

99:59:59.999 --> 99:59:59.999
I don't know how to calculate
so cannot calculate anyway.

99:59:59.999 --> 99:59:59.999
Mrs Chia spent $620

99:59:59.999 --> 99:59:59.999
Can I draw?

99:59:59.999 --> 99:59:59.999
Yeah, just draw
Put $620 in.

99:59:59.999 --> 99:59:59.999
that's what she had

99:59:59.999 --> 99:59:59.999
she spent so much
so that's what she had left.

99:59:59.999 --> 99:59:59.999
I can do that, but I don't want
to do it yet.

99:59:59.999 --> 99:59:59.999
Sometimes I don't it straight away,
sometimes I want to wait

99:59:59.999 --> 99:59:59.999
I can decide.

99:59:59.999 --> 99:59:59.999
Anyway,

99:59:59.999 --> 99:59:59.999
Mrs Baey spent $480 and 
Mrs Chia spent $620.

99:59:59.999 --> 99:59:59.999
In the end

99:59:59.999 --> 99:59:59.999
Mrs Baey had 3 times

99:59:59.999 --> 99:59:59.999
oh I can draw

99:59:59.999 --> 99:59:59.999
I can draw how much they spent

99:59:59.999 --> 99:59:59.999
and how much is left.

99:59:59.999 --> 99:59:59.999
Do I want to draw how much they spent?

99:59:59.999 --> 99:59:59.999
Or do I want to draw how much is left?

99:59:59.999 --> 99:59:59.999
I can decide.

99:59:59.999 --> 99:59:59.999
Whichever that is easier to do.

99:59:59.999 --> 99:59:59.999
For me,

99:59:59.999 --> 99:59:59.999
I think it is easier for me to draw

99:59:59.999 --> 99:59:59.999
how much is left

99:59:59.999 --> 99:59:59.999
because 3 times is easy to draw

99:59:59.999 --> 99:59:59.999
3 times is like use the paper right?

99:59:59.999 --> 99:59:59.999
It gives 1 time

99:59:59.999 --> 99:59:59.999
this is 3 times

99:59:59.999 --> 99:59:59.999
so 3 times is easy to draw.

99:59:59.999 --> 99:59:59.999
In the end, Mrs Baey has 3 times

99:59:59.999 --> 99:59:59.999
so I can draw that one

99:59:59.999 --> 99:59:59.999
Mrs Baey has 3 times

99:59:59.999 --> 99:59:59.999
So if Mrs Chia has this left,

99:59:59.999 --> 99:59:59.999
Mrs Baey will be 3 times

99:59:59.999 --> 99:59:59.999
one, two three.

99:59:59.999 --> 99:59:59.999
So this is what...

99:59:59.999 --> 99:59:59.999
what is left.

99:59:59.999 --> 99:59:59.999
If I am afraid people don't understand me
I can write, this is what is left.

99:59:59.999 --> 99:59:59.999
So that means,

99:59:59.999 --> 99:59:59.999
this is what they spent.

99:59:59.999 --> 99:59:59.999
For Mrs Baey, it was $480

99:59:59.999 --> 99:59:59.999
and for Mrs Chia it is $620.

99:59:59.999 --> 99:59:59.999
Parents,

99:59:59.999 --> 99:59:59.999
if they can understand all that

99:59:59.999 --> 99:59:59.999
whatever question that is asked of them,
they can answer

99:59:59.999 --> 99:59:59.999
because from here,
they will notice that well...

99:59:59.999 --> 99:59:59.999
they do know the values

99:59:59.999 --> 99:59:59.999
they do know the values of

99:59:59.999 --> 99:59:59.999
of these two units
isn't it?

99:59:59.999 --> 99:59:59.999
I leave the Mathematics to you

99:59:59.999 --> 99:59:59.999
but you can find the value
of these two units

99:59:59.999 --> 99:59:59.999
because you know the whole thing
is $620

99:59:59.999 --> 99:59:59.999
the whole thing as in
the whole thing I have just drawn.

99:59:59.999 --> 99:59:59.999
And this little bit here is $480

99:59:59.999 --> 99:59:59.999
so I think we can find out
the value of these two units

99:59:59.999 --> 99:59:59.999
and the rest is pedestrian
just a bit more of calculation.

99:59:59.999 --> 99:59:59.999
And then when they are done...
for those children who are more advance...

99:59:59.999 --> 99:59:59.999
you can ask them to critique the diagram.

99:59:59.999 --> 99:59:59.999
like "do you think this diagram is good?"

99:59:59.999 --> 99:59:59.999
so they may say
"oh it's not good"

99:59:59.999 --> 99:59:59.999
or whatever reason they will say.

99:59:59.999 --> 99:59:59.999
Say "oh look, the proportion is not right"

99:59:59.999 --> 99:59:59.999
then they may want to draw
a better one.

99:59:59.999 --> 99:59:59.999
Right?

99:59:59.999 --> 99:59:59.999
So that's my concluding example

99:59:59.999 --> 99:59:59.999
for me to make two additional points
about individual independence

99:59:59.999 --> 99:59:59.999
but also inviting them
to critique solution.

99:59:59.999 --> 99:59:59.999
Parents, this webinar is about
helping children process information

99:59:59.999 --> 99:59:59.999
and we want to help them.

99:59:59.999 --> 99:59:59.999
We can only help them if...

99:59:59.999 --> 99:59:59.999
we ourselves portray
Mathematics as a language

99:59:59.999 --> 99:59:59.999
comprising of information
given as visuals,

99:59:59.999 --> 99:59:59.999
given in words,
sometimes given in symbols.

99:59:59.999 --> 99:59:59.999
Throughout today, in answering
some of your questions

99:59:59.999 --> 99:59:59.999
I have demonstrated some strategies
that we parents, adults, teachers

99:59:59.999 --> 99:59:59.999
we can use with children

99:59:59.999 --> 99:59:59.999
to help them become better

99:59:59.999 --> 99:59:59.999
in reading comprehension,
making use of diagrams, pictures

99:59:59.999 --> 99:59:59.999
words, phrases, sentences,
symbols, expressions.

99:59:59.999 --> 99:59:59.999
Right?

99:59:59.999 --> 99:59:59.999
I want to thank all of you
for spending your precious evening with me

99:59:59.999 --> 99:59:59.999
and hope to see you again

99:59:59.999 --> 99:59:59.999
hopefully in person

99:59:59.999 --> 99:59:59.999
in the next seminar that we have.