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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
-
and to encourage interaction
for this workshop series
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you can ask questions
throughout the session.
-
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.
-
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
-
please volunteer in this PSCT.
-
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
-
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.
-
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...
-
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...
-
than children...
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who understand the exact nature
of mathematics.
-
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
-
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
-
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.
-
mathematics is not like that.
-
Mathematics is a subject
where you figure things out
-
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
-
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
-
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?
-
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.
-
Other than visuals,
-
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.
-
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.
-
In summary, mathematical language
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comprises of
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visuals, diagrams,
pictures, graphs,
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tables,
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it also includes symbols,
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notations,
-
finally it also includes a verbal language
-
example, English.
-
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.
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Spiky...
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has ten coins.
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So if Spiky has ten coins
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and he has more coins than Curly
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then obviously Curly's number of coins
will be less than ten.
-
Because Spiky has more
and Spiky has ten
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so obviously, Curly
whatever number she has
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that number is less than ten.
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So Curly has fewer than ten coins
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isn't it?
-
So in this case, we can obtain the answer
by doing a subtraction.
-
Isn't it?
-
So...
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if you do this
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please stop doing it from now on.
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Please don't tell your children
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"eh ah boy ah
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you see the word more you add okay?"
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parents please don't do that.
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Why?
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It's wrong
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obviously.
-
It could be anything,
-
the word more does not mean add,
-
it could be anything really,
-
in this case subtraction.
-
There is no shortcut,
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there is no tricks
-
tricks are not for children,
tricks are for circus animals.
-
There are no tricks in mathematics,
-
mathematics is a language
-
and we use words, we use symbols,
we use visuals
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to describe whatever we want to describe.
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Alright so parents
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those are the three kinds of information
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that children have to encounter
-
when they learn mathematics.
-
I will illustrate with some examples
after I attend to some questions.
-
Parents, if you have questions
-
some of you already have done so
-
please put them in the Q&A function.
-
Please do not use the chat function
for asking questions,
-
you can use the chat function
to chat with the other participants.
-
Feel free to use the chat function
-
to share ideas, to talk
-
among yourselves.
-
This is a maths lesson
-
maths lesson's are supposed
to be a little bit noisy.
-
Have you been to a Maths class
and it's very quiet?
-
A quiet mathematics class is suspicious.
-
One of the ways of learning a language
is to speak.
-
We all know
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learning a language includes oral skills
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speaking but also listening.
-
It also includes reading and writing.
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When children do not have the
full experience
-
in learning mathematics as a language
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not talking,
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rarely listening to another person
other than the teacher,
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writing but not reading,
-
then often they will have
some kind of difficulties.
-
Let me take some questions.
-
So far all the questions are problems that
you want me to solve for you.
-
But I have one here,
-
this parent mentioned this...
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"my son always write answers
without working
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how can I help him on this
-
he does mental sums"
-
So that's the question.
-
I think many parents encounter
the same situation
-
Yeah?
-
Children
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writing answers without working.
-
Example,
-
In primary one
-
they say nine, ten, eleven
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write it down.
-
Did the child do working?
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Yes
-
when the child thinks
that's working.
-
Thinking is working, parents
-
working is not always writing things down.
-
Some children do this:
-
9 and 6
-
oh 6 is one and 5
-
9 go with the 1 makes 10
-
10 and 5, 5 and 10
-
15
-
is that acceptable?
-
Yes, that is acceptable.
-
Thinking is working
-
this is acceptable if they are doing
basic skills.
-
Mathematics is a language
-
just like in all languages
-
if I say something very difficult
for other people to understand
-
I need to explain myself.
-
But if I say something obvious
-
I will just say it.
-
If I try to elaborate on a simple point
you will think I am long-winded.
-
Mathematics is a language.
-
Just like all languages
-
when children want to tell you something
straight forward
-
5 groups, sorry...
-
3 groups of 5
for example
-
they will just say
"I know it it's 15"
-
I know it's easy for a lot of people
-
so I will not elaborate it.
-
But if they say something difficult
-
afterwards you are going to see
some examples of those
-
Those require them to
articulate their thinking
-
in adult language we call that working.
-
Parents let me say clearly now
-
When is working required?
-
Working is required when they are
solving a challenging problem.
-
When they are solving problems.
-
Because when they solve problems
-
even though they are so smart
-
and they know the answer by thinking
-
they are not allowed to just
-
say the final answer.
-
Can you imagine when Albert Einstein
-
discovered E equals to the square
-
you know energy equals to the
product of mass
-
and the square of speed of light
-
or the well known E = mc^2.
-
Can you imagine Einstein
went to the lecture hall
-
and said "guys trust me
-
this is how energy is related to mass
-
this is the final equation
-
bye end of lecture".
-
Can you imagine that
-
no one will believe that
-
Einstein was correct
-
because back then people think that
energy and mass were not related.
-
But he has to slowly convince people
-
that energy and mass
-
are actually related.
-
So whenever your children
are solving a difficult problem
-
a challenging problem
-
they must explain themselves
-
even if...
they know the answer by eyeballing.
-
Even if they know the answer
just by looking at the problem
-
They still must explain things
to other people.
-
But if they are saying something simple
-
like...
-
2 less than 11
-
oh two less than 11 is 9.
-
Why? because I know it.
-
Or 2 less than 11
I just count back
-
in my mind 11, 10, 9
and write it down.
-
Must I explain myself?
-
I don't have to.
-
Can I explain myself?
-
Sure, if I want to.
-
If a teacher or my parent
ask me to explain myself
-
I should be able to do it.
-
So parents...
-
what must we do?
-
so this is the part where
I want to share with you strategies.
-
What must we do
when the kids are still young
-
and we can mold their thinking
-
what must we do?
-
We ask them
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"Do you think this is easy
for other people?"
-
"Do you think this is obvious
to other people?"
-
so if they
-
they write it down
-
the answer
-
You ask them
-
"Do you think this is easy
to a lot of people?"
-
If it is easy...
-
that's alright.
-
Don't have to explain yourself.
-
Don't have to draw pictures.
-
Don't have to draw pictures of 12
-
and then show them how to
put into groups of 3's.
-
If you want to you can...
-
but you don't have to.
-
Do you think this is easy to other people?
-
If it is not easy to other people...
-
even if you know the answer,
you must explain yourself
-
you must show your working.
-
Parents,
-
this is strategy number one
I want to share with you this evening.
-
Always ask this question:
-
Is this easy to other people?
-
If yes,
-
no need working.
-
If no,
-
you have to show working.
-
Even if you know the answer
-
just by looking.
-
Alright parents, if you do this often
-
your children will develop
self-awareness.
-
Your children will develop
meta-cognitive ability.
-
That well...
-
This is very easy for me
-
I know the answer
-
but actually it's a difficult thing
-
so I should be proud of myself.
-
I know the answer
to a very difficult thing
-
but I am still responsible
to explain it to my teacher
-
or to a friend
-
to the friend with specs
who sits beside me.
-
So parents, try to use this strategy more
whenever you are guiding your child.
-
Don't just tell your child
"Eh you'll la
-
show your working please
-
otherwise you'll lose marks".
-
That's not very helpful
-
it doesn't tell them anything.
-
It's a rather useless thing
to say actually.
-
They have no idea why
they are showing their working
-
because losing marks
is a artificial indicator.
-
It is, I have to show working
to explain to other people
-
is the actual explanation.
-
And I have to explain to other people
because it's difficult.
-
Or I don't have to explain to people.
-
Why? Because it's obvious.
-
Let me take perhaps
-
another question.
-
Is it a must to draw a model?
-
In a way I have answered the question.
-
I have to draw the model
-
if...
-
other people cannot understand me.
-
And I want them to understand me.
-
And I am quite good at drawing
-
so I draw a model
to help them understand me.
-
But if the problem is very easy
-
then I won't draw a model because
-
I can just tell them the answer.
-
Example, if the question is
-
I have 12 lollipops
-
that's really too many but
for some reason I have 12 lollipops.
-
and my friend kindly
gave me another 2
-
so I had 12 lollipops
and she gave me another 2.
-
I know the answer is obvious
now I have 14
-
it's obvious.
-
I don't think I need to draw a model
to tell people how I got 14.
-
Maybe, I should tell them
how I get 14
-
by showing them the calculation
-
maybe...
-
Maybe they don't know how I get 14
-
so at least I show a little bit
of explanation to them.
-
But actually I can just tell you
-
in the end I had 14 lollipops
-
that's perfectly fine actually.
-
So must my child draw a model?
-
No, if they already know the answer
-
and no if the problem is a simple one.
-
So the second reason why
children draw a model...
-
is because they don't know the answer.
-
For example,
the problem I gave you earlier.
-
Spiky has more coins that Curly.
-
So lets say a child doesn't know
-
the child might draw,
-
Spiky had more coins than Curly.
-
So the diagram might look like that
-
with Spiky having more coins than Curly
-
and...
-
Spiky has ten
-
Spiky has 3 more coins
-
than what Curly has.
-
From here I can see
to obtain this value
-
my calculation is taking
3 away from 10
-
giving me 7
-
so I know that Curly has 7 coins.
-
So must my child draw a model?
-
Yes, if they don't know the answer.
-
If they don't know the operation.
-
Model is a good bridge to the operation
-
They will learn whether to add,
to subtract, to multiply, or to divide.
-
So if they don't know the operation.
-
So if they know the operation
must they draw the model?
-
No, they don't have to.
-
Second answer,
-
must they draw the model?
-
Yes, if the problem is difficult
-
and they need to explain it
to another person.
-
No, if the problem straightforward.
-
Finally, I want to add one more comment.
-
When your child is first learning model
-
sometimes the teacher will insist
they draw it
-
just because they are learning it.
-
So if today's lesson is about
drawing model's
-
then of course you must
practice drawing it.
-
So that's a third answer
-
must my child draw model?
-
Yes, if that is the lesson itself.
-
So if the teacher is teaching
model drawing that day
-
obviously the teacher will expect
them to practice it.
-
So those are the three answers to
"must my child draw model".
-
I'll take on more question
before I continue to the next part.
-
My child feel's that mathematics is boring
-
any tips to make it interesting?
-
I will answer this question and then
I'll continue with some examples.
-
Why do children find mathematics boring?
-
1. If we portray mathematics as a subject
where they have to memorise things.
-
Memorising... is rarely exciting
-
to most children anyway.
-
In some subjects,
-
In some domains
memorising is necessary.
-
Example, learning the Quran
-
If you are learning the Quran
we have to memorise.
-
I have seen children, friends learning
the Quran when I was very young.
-
And they kinda memorised the whole thing.
-
It's just necessary I think.
-
But mathematics is not a subject
where you memorise everything.
-
You won't remember stuff, but you
don't have to memorise them.
-
Like the times table.
-
You forget 7 groups of 3?
Just figure it out.
-
Use your 5 and use your 2
you can get your 7 times table.
-
You forget your 9 groups of 8?
-
Start from 9 groups of 2
double that 9 groups of 4
-
double that 9 groups of 8.
-
Or you can start with 10 groups of 8
-
and take away 1 group
-
80 take away 8
-
to get whatever you need to get.
-
So memorising is rarely exciting.
-
What is exciting?
-
Figuring things out.
-
Children are by nature curious
-
they LIKE to figure things out.
-
They feel proud, they feel empowered
-
that they have the ability
to figure things out.
-
And trust me,
every child can figure things out
-
If only we allow them to.
-
If only we make them understand that
in Mathematics, we figure things out.
-
If I do not know how to do long division
-
and 51 share among 3 mess me up
-
that's alright, I can figure it out.
-
I know that 51 is 30 and 21.
-
So 30 share by 3
-
that's not too hard
-
so I take out the 30
-
I know that leaves me 10.
-
So the thirty is not too hard, gets me 10
-
and the 21
-
when I share among 3
-
the 21 that I have
if I take it out to be considered
-
share among 3, that gives me...
-
that gives me 7.
-
Resulting in 10 and 7
-
which of course we write as 17.
-
And let me check
if there is anything else left
-
oh nothing else left
-
everything is accounted for
nothing is leftover.
-
So, how to make mathematics
more interesting?
-
Avoid portraying mathematics
as a subject of memorising
-
but as a subject of figuring things out.
-
Secondly
-
portray mathematics as a subject
where you do things.
-
Use your hands.
-
In school, they use concrete materials
all the time.
-
They use their iPad,
-
the teacher let them play on apps
-
they use concrete materials all the time.
-
So let your child learn Mathematics
by doing
-
When they learn counting,
-
When they learn adding subtracting,
-
use concrete materials.
-
You can use the application,
including the one I shared with you.
-
Later I will share with you
the names of the applications as well.
-
Throughout this workshop,
-
this webinar,
-
you might pick up other ideas
-
on how to make mathematics
more interesting for your child
-
but for a start, I share with you two.
-
Use concrete materials
-
and...
-
portray mathematics
not as a subject of memorising,
-
but as a subject of figuring things out.
-
Let me now move on.
-
So mathematics include visuals.
-
Let me show you some examples.
-
All the examples
I've taken from Pathlight school
-
mid-year examination paper
-
for Primary 4
-
so that you can see
where your child is moving to.
-
I know some of you have children in
Primary 1, Primary 2, also Primary 3.
-
So you kind of see
where they are heading to.
-
And you can see they
also do similar things
-
in the current level.
-
So they are expected
-
to be able to handle visuals.
-
Visuals like that.
-
Things they might encounter
in their everyday life.
-
So if I go to Whampoa market
-
there's a bakery
-
and at that bakery
-
sometimes I see the lady
putting up signs like that
-
telling me how much the cupcakes are,
-
and I think she was eager
to promote cupcakes that week.
-
So she's
-
having a little promotion
-
she's having a little sale.
-
Cupcakes for sale.
-
One for two dollars
-
oh I think she meant one cupcake
-
you know people don't write
everything out clearly
-
but it's understood isn't it
even when they say one
-
when they meant one cupcake.
-
Not one...
-
tray of cupcakes
-
not one short of cupcakes
-
but one cupcake.
-
But they don't write it out
we try to understand it
-
from our daily experience.
-
So 1 for 2 dollars
-
and 3 for 5 dollars.
-
??? we mean by understanding visuals,
-
visuals in everyday life.
-
That's a third way to make
mathematics interesting.
-
Don't have to sit down and do worksheet
-
when you take your children out
-
nowadays that's not a good idea
-
with the heightened alert.
-
But in normal times
-
when you have your children out with you
-
at the NTUC, at the neighborhood market
-
wherever you go,
-
you can make use of
small opportunities like that
-
just to engage your child
-
in mathematics
-
in a rather informal way
-
like "oh you know
-
I think we need to buy 10
-
is it a good idea to buy 10 cupcakes?"
-
and see what your child says.
-
That is as good as
if not better than
-
doing a worksheet.
-
So in examination
-
they are expected to be able to handle
-
visuals that's common place
in their everyday experience.
-
And in this case there are also some words
-
Matthew has some money
-
Matthew has $32
-
oh $32
-
I wonder... the $32
come in what denominations?
-
I wonder what he has in his hand
or in his pockets?
-
$32
-
and the child may say
"Maybe three $10 notes
-
and a $2 note?"
-
Matthew has some money
-
$32
-
what is the greatest
-
oh greatest means the biggest
-
what is the greatest
number of cupcakes he can buy?
-
Oh what does that mean?
You can ask your child
-
and let your child paraphrase the question
-
"oh it means the most"
-
some children know the word maximum
-
"it means the maximum number"
-
and then if your child is quite advance
you can also engage them further.
-
"Why are they asking us for the maximum?"
-
Maybe the child will laugh
at you probably.
-
"Of course you know he got $32
he can just buy $2.
-
He can just but one cupcake
-
doesn't mean must spend
all your money right?"
-
So some children are smart that way
they will like
-
"doesn't mean you got $32
you spend all on cupcakes
-
who actually does that right?
-
very few people"
-
but in this case we want to know
-
if Matthew wants
as many cupcakes as possible,
-
what is the greatest number of cupcakes
he can buy?
-
The fourth way to make
mathematics interesting,
-
engage your child in conversation.
-
Don't always just answer the question
-
and then say
-
"boy quickly go to the next one
no time already".
-
There is a lot of time
-
we must take time
-
otherwise
-
you will get children
who don't enjoy mathematics
-
and also don't do too well
in mathematics subsequently.
-
Do not think of learning mathematics
as sitting down
-
doing worksheets all the time.
-
That's actually the final step.
-
Early stages of learning is quite informal,
-
you can engage your child
-
in the everyday experience they have.
-
It is then that they are able
to do the worksheet.
-
Children who never encounter this
in their everyday life
-
and the conversation that
I just had with you
-
will find it quite difficult
to do the examination afterwards
-
example, a question like this.
-
Anyway
-
then the child might then be
asked to solve a problem like that.
-
So they should also appreciate that
-
"eh actually buying three is a good deal
because you pay $5".
-
Normally you buy three
it would have cost us $6.
-
You see parents, I don't do any working
-
I do the working in my mind.
-
And that's perfectly normal
-
and of course it's allowed
-
that's what we do in real life.
-
Mathematics is a extension of real life
-
it's not like sometime different
-
to what we normally do.
-
So normally we will say
"one cupcake" $2
-
"three cupcake" $6
-
then people ask, "how come $6?"
-
then you tell them
-
oh you know $2 + $2 + $2 = $6
or 3 x $2
-
If they ask.
-
If they don't ask I just like
"okay $6 , they nod their head".
-
So in exams
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for questions like this
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they can just give the answer.
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Example, at PSLE this kind of question
answers are given
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the marks are given
-
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for the answers.
-
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If they show working it's fine.
-
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If they don't show it's also fine because
all the marks are given for the answer.
-
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Okay?
-
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So they said
"Okay so try to buy three"
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Yeah? Try to buy three.
-
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So $5, and I know that
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oh now I need to write because
I cannot remember so many things.
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I know that I got a lot of $5 in $30
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in face I got six of them.
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Because six times $5 dollars gets $30
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and then I got $2 more.
-
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So this $30
there are six $5
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and every $5 gets me three
-
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so I can get six of three cupcakes
that's eighteen cupcakes.
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But then the $2 I can get more
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so I get whatever I can get
and give a final answer.
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Parents,
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I have illustrated what I mean by
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Mathematical language include visuals.
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In this first example
-
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I demonstrated visuals
that are common place
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in our everyday life.
-
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Let me move on.
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Sometimes, at a higher grade level
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the visual dissapears
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like this problem.
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If you read it
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you'll realise that it's the
same kind of Mathematics involved.
-
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It's what we call division with remainder
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like just now the division remainder.
-
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The visual disappeared.
-
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So what is the learning progression?
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First is you let them see the visual
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in the actual context.
-
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In the bakery in Whampoa market
-
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for example
-
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then they come to school
-
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they will see this.
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The same visual or similar visuals
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but printed on paper.
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Finally, the visual disappears.
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So parents, we can help the teachers
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by alerting our children
to visuals around them.
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That one is harder for teachers to do
-
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because the teachers
only see them at school
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and not taking them out to the market
-
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or just engaging them
with everyday experiences
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that one I think parents can do
and can do quite well.
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So do alert your children
to visuals around them
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and engage them with a bit of Mathematics
-
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don't have to use worksheets.
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So that's a strategy
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a strategy to help them process
information better.
-
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In this case visual information.
-
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That is commonplace.
-
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Oh we have a question here!
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Lets look at what the question
is all about.
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Crate...
-
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oh what is a crate?
-
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Ask your child that.
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Give me other words
that's similar to crate.
-
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If they don't know,
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just Google
-
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and then they can see
a picture of a crate
-
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as simple as that actually.
-
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Use technology
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that we already have.
-
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Don't complain
-
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"oh is this Maths or is this English ah
-
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how come they use words like that"
-
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there is no question whether
this is Maths or English
-
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English is part of Maths.
-
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So remember,
Mathematical language include:
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symbols, visual, and English
-
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English is part of Maths.
-
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If the don't know the word,
-
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just do what we normally do,
Google it.
-
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And then "oh that's a crate!"
-
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then your child will give you other words
like box or whatever they want to say.
-
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A crate can hold milk bottles,
-
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okay a crate can hold milk bottles.
-
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Actually I haven't seen milk bottles
in a very long time.
-
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Once upon a time when I was a child
-
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wow that's a long time ago
50 years ago.
-
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You know the milkman who goes round
-
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and they give you the milk in a bottle
-
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F & N bottle
with a little...
-
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banana leaf stopper.
-
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Okay, most of you are too young
to even know this.
-
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So sometimes, children
are asked to read stories
-
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that are so alien to them.
-
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But that's... that's life
-
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we also read stories that's alien to us.
-
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Harry Potter, you mean you grew up
like Harry potter?
-
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No right? but you still enjoy it.
-
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Right?
-
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So, that's normal in a language
-
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we sometimes read things familiar to us
like the bakery, selling the cupcakes.
-
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But sometimes we also read things
that are not so familiar to us
-
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and some of us enjoy it
some of us don't, that's life.
-
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We cannot expect everyone to find
the same thing exciting.
-
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You cannot expect every child to find
milk bottles exciting.
-
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Okay, some of them do but...
-
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most of them don't.
-
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But they will still learn
to imagine it.
-
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And we, as adults can help them.
-
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We can Google, we can show them that
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"oh you know, in some countries,
they actually sell milk in bottles".
-
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"in some countries, they bring
milk bottles to the shop
-
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and then they get their milk".
-
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But for us we go NTUC
it comes in a box
-
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sometimes plastic.
-
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We are not very green in that way.
-
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So engage them
in that kind of conversation
-
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that's very important.
-
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Very often parents ask,
"how do I prepare my child for Mathematics"
-
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and they think the answer will be
-
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buy more workbooks,
by more assessment books
-
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It not.
-
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It's doing things that
parents do very well.
-
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Engaging children with things around them
-
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both familiar, but also unfamiliar.
-
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So these are some kind of images
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children need to encounter.
-
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So one more example on visuals,
-
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Farah, okay probably somebody
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a girl
-
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I see the word she, so it must be a girl.
-
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I don't have a friend called Farah
so I don't know whether it's a boy or girl.
-
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And I am not so familiar with this name
-
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but I saw the word she,
must be a girl.
-
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But shouldn't matter right?
whether it's a boy or a girl.
-
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Farah has some cards
-
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okay I understand that.
-
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Rectangular cards...
-
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oh so the cards are rectangle
-
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I know what rectangles are
we learned that in primary 1.
-
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Farah has some rectangular cards
-
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okay I understand that.
-
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Measuring 10 centimeter by 6 centimeter
oh I can see that.
-
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So this is what we mean by children
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using visual to support
their reading comprehension.
-
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So some children struggle with language
-
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for example, I have one question like this.
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How can I improve my sons language
or Mathematical language capability?
-
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He has delayed language processing.
-
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So that's the answer actually,
use visuals
-
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use visuals.
-
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And very often even in examinations,
-
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there are some items
where visual support is provided
-
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whether or not you have delayed processing
-
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it is just something
they support children with.
-
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So even if a child doesn't have
any issues with language
-
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often, a visual can help them
with comprehension.
-
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So I see, 10 centimeter by 6 centimeter
-
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now parents, try not to be...
-
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try not to be lazy
-
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don't say 10 cm
-
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it is actually called centimeters
-
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say in full
so children hear it
-
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if we use truncated language,
lazy language too early...
-
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Children doesn't get the full meaning
eventually
-
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don't say three times five,
-
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say three rows of five,
three groups of five
-
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especially in the beginning
-
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once they understanding it
you can be lazy
-
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but in the beginning,
try to say it completely.
-
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So that they know
that cm is a symbol for centimeters
-
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otherwise some of them may not know
-
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and they will be wondering what is this
-
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and then in exam, whether it is millimeter
or centimeter they don't really care.
-
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??? sometimes you see that
amongst your children also
-
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they don't really care what the unit is
and they do very strange things to it.
-
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So do read it in full.
-
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And the question is what is the smallest
number of cards she needs
-
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to form a square
-
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without overlapping the cards.
-
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So let your children try,
give them papers like that
-
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let them try.
-
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If you are hardworking you can
go and get the exact measurement
-
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but it's not necessary
but if you want to
-
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And let them try.
-
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That's how you make
Mathematics interesting.
-
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Mathematics is initially
a hands on experience
-
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in Singapore we call that (CPA)
Concrete, Pictorial, Abstract.
-
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You first learn it by experiencing
-
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you take a paper, you take a rectangle
and you try to make a square
-
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like a puzzle
like a jigsaw puzzle.
-
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Use the rectangular parts to form a square
-
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without overlapping.
-
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You do it,
-
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once you have done it
you can understand the visual.
-
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So how does your child learn
and process a visual like that
-
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in the exams?
-
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In P4
-
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it's because in P1, P2, P3
you let them use concrete materials.
-
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Even in P4 of course I will let them
use concrete materials still.
-
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But because they are exposed to doing
-
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when they see a picture
of what they have done
-
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obviously, they understand it better.
-
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And when they read and they have a
picture to support the reading
-
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That's where comprehension
of the word problem
-
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becomes possible.
-
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Let me take a couple more questions
before I move on.
-
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Quite a few have similar questions
-
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like my son has problems
with English language,
-
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part of problem sums,
word problems
-
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so we cannot understand the question
-
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and therefore cannot apply
the Mathematics principle.
-
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How can I help him?
-
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So a lot of questions along this line
I'll be demonstrating that further
-
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I have demonstrated some strategies
you can use
-
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Yeah, my child is still catching up
-
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on his language skills how can we best
translate Maths problems to visuals
-
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for his better understanding.
-
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And how do we slowly get him to be
less dependent on visual.
-
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A very important question.
-
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Whatever help we give children,
is with the goal of not helping eventually
-
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less dependent.
-
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Let me answer those
questions about language.
-
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Parents, up to this point
-
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I have shared with you that
Mathematics is a language
-
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comprising of:
-
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visuals, pictures, diagrams, even graphs
-
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but also symbols
-
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and of course words.
-
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In our case, English language.
-
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I will now focus
on the question just asked
-
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how do I help with the language part
-
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of word problems.
-
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How do I help them with language
that's embedded in Mathematics?
-
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Oh let's look at this story
-
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not a very long story right?
-
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Just two sentences
short story.
-
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Who is in the story?
-
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Hmm... how interesting
-
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Pierre, I don't know how to pronounce it
I cannot speak french
-
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Is it Pierre?
Yeah maybe it's Pierre
-
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doesn't matter.
-
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Oh he's a boy
okay doesn't matter either
-
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but well...
-
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Pierre had marbles
-
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you know marbles right?
-
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Yeah the one you see at aquariums
-
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actually marbles are for playing
-
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I don't know why it is put in
aquariums nowadays
-
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and plants.
-
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But anyway, Pierre had marbles
i hope he's not losing any.
-
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So children learn language
-
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right?
-
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So they learned that
-
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oh you know in English language,
very funny language,
-
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when people say you lose your marbles
it means something.
-
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It means like
-
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You are going a bit crazy
you are not getting it all together.
-
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Anyway,
-
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let's not get distracted
-
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let's come back to the story.
-
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So Parents, you've engaged your child
in what might happen to them
-
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don't be so straitjacket
I am quite sure you are quite fun parents
-
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but when it comes to Math suddenly you
become a different animal altogether.
-
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Don't be like that,
-
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make it fun.
-
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make it informal
-
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just engage your child
in what might happen to them.
-
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when children read stories
their brain go in all directions
-
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I'm sure you know that.
-
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Don't scold them
-
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because they are just being themselves
-
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nothing wrong with being themselves
-
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what they need is guidance.
-
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How to refocus
-
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so I was just demonstrating
that awhile ago.
-
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Pierre has some marbles,
okay that's easy to understand.
-
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We know how many right?
-
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There are 315.
-
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He divided them
-
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equally
-
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into 3 boxes.
-
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Oh, what does that mean?
-
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So you ask your child that
-
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and your child
will tell you in his own words.
-
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Parents, I have so far demonstrated
three strategies,
-
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if you missed them let me
articulate them one by one.
-
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What strategy did I use?
-
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Strategy number 1:
To help them with language
-
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I deleted the question
-
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the question is there
-
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but I deleted it.
-
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I deleted the question
-
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why?
-
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When you give a child a question
what will they do?
-
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They answer it.
-
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But I don't want them to
answer the question just yet
-
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I want them to learn to comprehend,
-
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I want them to learn to understand.
-
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So because my goal for them is to learn,
to understand things
-
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I removed the answering point first.
-
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So try to cultivate that habit.
-
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Many children have the bad habit
-
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of trying to answer the question
-
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before they understand it,
-
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that's how they make mistakes.
-
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if you don't understand the story
how can you answer the question.
-
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You cannot.
-
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So to cultivate the good mindset, a good ???
-
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Mathematics is not answering questions
-
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Mathematics is understanding stuff.
-
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Once you understand stuff
-
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you can answer whatever question
they ask you.
-
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That's the truth right?
-
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So focus on understanding,
-
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how do you help them
focus on understanding?
-
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Remove the distractions,
remove the question.
-
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Question is the distraction
-
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because they try to answer
they do strange things.
-
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Second strategy I demonstrated:
-
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I did not read the question
-
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sorry... I did not read the numbers
-
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Second strategy:
I did not read the numbers.
-
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I'm sure you saw me
doing that earlier already
-
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remember the more, less problem?
-
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In face all the questions so far.
-
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So you might notice I said
Pierre had marbles
-
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Pierre had some marbles.
-
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I replaced the number
with a qualitative word.
-
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Pierre had some marbles.
-
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There is ample research to say that
-
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numerical information breaks a sentence up
-
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and decreases comprehension
-
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so that is well documented.
-
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Especially for those children
with language issues
-
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try to help them
-
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try to help them by letting them
-
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not have that problem
-
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so avoid reading the numbers.
-
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Pierre had some marbles
-
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oh how many? 315.
-
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So you read the sentences to understand it
then you put in the numbers later on.
-
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Third strategy: ask your child to paraphrase
some lengthy cumbersome sentences:
-
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Oh he divided them equally
into three boxes
-
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so hard for me to understand
-
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can you explain to me?
-
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Or if the child is not very good
in explaining,
-
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can you draw for me?
-
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So let your child have a choice,
-
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to draw or to tell.
-
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So you might even have that as a routine
-
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"do you want to tell?
or do you want to draw?"
-
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draw or tell,
-
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then those who like to draw will say draw
-
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then those who like to tell or
lazy to draw will say yeah I want to tell.
-
Not Synced
But sometimes you don't give them a choice
-
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okay you've been drawing a lot
-
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next one I choose
-
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tell me
-
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then you force them a little bit
out of their comfort zone
-
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so they learn something more.
-
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So those are three strategies
quite well documented,
-
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letting children paraphrase sentences
by drawing or in their own words,
-
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leaving our numbers,
-
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and then the other one
that I mentioned earlier
-
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the three strategies.
-
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Anyway, once they have their ???
they will answer the question
-
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and they will say "ok".
-
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Pierre had three boxes
-
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and they are equal in size
-
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and he had 315 marbles
-
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and he put them equally
-
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I can replace divided with put right?
-
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He put them equally into three boxes
-
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so the 300 is quite easy to do
-
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100 each
-
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and the 15
-
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I think can
-
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5 each
-
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and together is 105.
-
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So 315 put equally into three boxes
result in... 105
-
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and then write a sentence if you want
-
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or if your teacher say you
write a sentence to answer the question.
-
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Let me demonstrate with another example.
-
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Oh who is in the question?
Who is in the story?
-
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Oh in this case it is nobody
-
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just now was a boy named Pierre
but here it is nobody.
-
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What is it about?
-
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Oh it's about COVID-19
-
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when else did we talk about masks
-
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and hand sanitisers.
-
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Oh it's about a factory
do you know what a factory is?
-
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Okay, let's see what the story is about.
-
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A factory produced some masks
and hand sanitisers.
-
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Quite a lot right?
-
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You can see the number
-
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the factory produced
-
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some masks and hand sanitisers.
-
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Can I calculate already?
-
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Probably not yet.
-
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Can I draw a diagram?
-
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Not sure
-
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never mind lets read the next sentence.
-
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It produced fewer
hand sanitisers than masks.
-
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Whats "it"?
-
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Oh the factory ,okay
-
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the factory produced fewer
hand sanitisers than masks
-
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so hand sanitisers
-
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so many
-
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masks
-
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oh mask more is it?
-
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So fewer hand sanitiser.
-
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Is my diagram showing
what the story shows?
-
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The factory produced fewer hand sanitisers
than masks.
-
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Okay I can draw
so I will draw.
-
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What information I have?
-
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Oh 2821...
where should I put that?
-
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It produced 2821 fewer hand sanitisers
than masks.
-
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When children first learn this
comparison thing,
-
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pieces of paper like that is quite useful
-
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let them use paper strips
-
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or you can go to
-
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shops and buy paper strips
the longish one
-
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or just cut your own,
make your own.
-
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Color is quite useful,
also quite interesting
-
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when you overlap
the colors will show up also
-
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then they can se
"oh that's where the 2821 is"
-
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oh we also know 5743
-
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do you know where that is?
-
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And if the child understands the story...
-
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they will know that this is the total
number of hand sanitisers and masks.
-
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Then ask your child...
what do we do next?
-
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And
-
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hopefully the child will say
-
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"I need to take
this number off that number"
-
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that's another strategy.
-
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Talk about what to do,
-
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don't always like...
-
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write down the working
write down the working
-
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get them to talk about it.
-
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So you know "oh my child knows,
-
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my child knows the first step
is subtraction".
-
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The idea that we subtract is more
important than the actual subtraction
-
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by the time they take PSLE, the
subtraction itself is done by calculator
-
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but they must know to subtract
otherwise it is pointless.
-
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If the children cannot identify
the right operation: that I subtract first
-
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then the result we divide by 2,
-
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the calculator is still useless.
-
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So from a young age
-
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engage them in telling you
what operation.
-
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Children are children,
they are not very good at multitasking.
-
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Sometimes when they
-
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identify the operation
-
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and do the operation,
-
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they don't realise that
these are two separate things.
-
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So it's not
clear in their mind.
-
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Meta-cognitively speaking,
-
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they are not learning somethings useful
for years to come.
-
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So do engage your child
in telling you the operation
-
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Don't bother them with the actual
calculation which is quite boring
-
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to be honest.
-
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The actual calculation 5000
you know like whatever we normally do
-
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that one is quite boring
-
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there's nothing exciting about doing this
-
Not Synced
nothing exciting about doing this
-
Not Synced
but they will do it
and they can do it.
-
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In this case they'll probably say
-
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"okay, this one is easy"
-
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yeah the 43 and 21 part is easy
-
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oh the 5728 part is slightly harder
-
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but that's okay
-
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I can rename it 4170.
-
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But anyways... that's another strategy.
-
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ask them to tell you that operation.
-
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And if they identify the operation,
-
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at least you are assured that
they know what they are doing.
-
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??? to the actual calculation.
-
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And then even in the event
they cannot get calculation
-
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or don't like to do the calculation
or cannot do the calculation,
-
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at least you know that they're okay.
-
Not Synced
Identification of the Mathematics
is more important than the computation.
-
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The computation, eventually they are
going to use some calculator
-
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to actually get the answer
-
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for example: in the PSLE
-
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for numbers that are tedious.
-
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Let me take some questions now.
-
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My son always dream away
in the middle of his work,
-
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how do I get him to concentrate?
-
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I think... we must first understand
why he is dreaming away.
-
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Some children dream away
because the work is meaningless to them.
-
Not Synced
So that's what I have been talking about
the whole of this evening,
-
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we must make Mathematics
meaningful to them.
-
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How?
-
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By being able to read the language.
-
Not Synced
Some children cannot read the language
-
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they cannot read the language
-
Not Synced
for example in P2, P3
-
Not Synced
they cannot read this
-
Not Synced
correctly.
-
Not Synced
They cannot read this as one half
-
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but that's what it is.
-
Not Synced
The denominator tells you
what the thing is... hal
-
Not Synced
the numerator tells you how many
-
Not Synced
or three-fifths.
-
Not Synced
They say three upon five
-
Not Synced
nobody talks like that,
-
Not Synced
maybe once upon a time
-
Not Synced
somebody tlaked like that.
-
Not Synced
In modern day language
we say one apple
-
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we say three slices.
-
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In modern English language
we don't say once upon a time,
-
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in modern day language
we use number plus the noun.
-
Not Synced
We say three slices
we say three children
-
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we say three apples.
-
Not Synced
In modern English,
we put number followed by a noun
-
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this is what they are familiar with
-
Not Synced
number plus noun
-
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which is what they are reading.
-
Not Synced
Three and the noun
-
Not Synced
fifth is a noun
it's a name of that slice
-
Not Synced
it's a name of that ???
that you get out of one.
-
Not Synced
When out cut one in to five equal slices,
that slice has a name... fifth
-
Not Synced
and then we write fifth using that symbol.
-
Not Synced
So, three fifths..
-
Not Synced
but for some reason
we prefer to put it just underneath
-
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so it's three fifths
-
Not Synced
It's like that right?
-
Not Synced
So many children cannot read it
-
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that's why they think
thing's are meaning to them
-
Not Synced
but actually it is quite meaningful.
-
Not Synced
So by P3, P4, P5
they learn things like this
-
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like half and one-fourth.
-
Not Synced
They know even as a child,
-
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one apple and one orange
what do you get?
-
Not Synced
you don't get two
-
Not Synced
you don't get two apples
of course not
-
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you don't get two oranges
any child can understand that right?
-
Not Synced
One apple and one orange
is not two apples it's not two oranges
-
Not Synced
They know from a very young age
-
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when the nouns are different,
you cannot add.
-
Not Synced
Like three boys and two girls
-
Not Synced
you should be horrified to get five boys
-
Not Synced
you don't, so no need to panic
you don't
-
Not Synced
And any child knows
-
Not Synced
that three boys and two girls
don't give me five boys nor five girls.
-
Not Synced
What? Different type what.
Different noun what.
-
Not Synced
And if I can change the noun
then I can add,
-
Not Synced
three children and two more children
ah business as usual, five children.
-
Not Synced
One apple and one orange,
-
Not Synced
one piece of fruit
and another piece of fruit
-
Not Synced
that gives me two pieces of fruit.
-
Not Synced
So one-half and one-fourth
-
Not Synced
different kind, cannot add
just yet.
-
Not Synced
Can I change the half into fourth?
-
Not Synced
Not so convenient or okay?
-
Not Synced
It's okay right?
-
Not Synced
Half is two fourths
they learned that in P3 right?
-
Not Synced
Oh so now two fourths and fourth
-
Not Synced
business as usual
same kind.
-
Not Synced
Children dream off because they
cannot make sense of the gibberish
-
Not Synced
that is in front of them.
-
Not Synced
But when they can
-
Not Synced
when they can
-
Not Synced
they can do the work.
-
Not Synced
Like most of us are
-
Not Synced
probably not able to function
if I give you something in Russian
-
Not Synced
if you don't understand Russian.
-
Not Synced
It'll be that exciting
I ask you to read a page in Russian.
-
Not Synced
No matter now exciting
or engaging the story is
-
Not Synced
you surely dream off
and definitely give up
-
Not Synced
because you don't even
understand the first thing about it.
-
Not Synced
This is the main reason why children
cannot focus and they dream off.
-
Not Synced
So the big answer is
make things meaningful to them
-
Not Synced
and earlier today I've also said
"make things interesting for them".
-
Not Synced
A third answer to that is
-
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remember these are children
-
Not Synced
and some of the children we have Pathlight
-
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they do have attention issues
you know that
-
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your own children you know that.
-
Not Synced
Break things down for them
-
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frame them up slowly
-
Not Synced
start with 10 minutes,
go on to 15, go on to 30 minutes
-
Not Synced
don't expect them to be able to sit
there for an entire hour
-
Not Synced
it's not possible.
-
Not Synced
Even for adults we do struggle with it
let alone children.
-
Not Synced
So if your children dream off,
-
Not Synced
Two strategies.
-
Not Synced
The practical one:
Just write things down for them.
-
Not Synced
Llet them do things in small
bits and pieces
-
Not Synced
and that will train up
their ability to focus.
-
Not Synced
But the bigger answer
is make things meaningful for them.
-
Not Synced
I am sure you know your children can
be engaged for a very long time
-
Not Synced
if it is something
they are very interested in.
-
Not Synced
Like some of the children
who loves dinosaurs
-
Not Synced
they will spend hours
-
Not Synced
watching YouTube
or reading about dinosaurs.
-
Not Synced
Some of them like transports
-
Not Synced
and they will spend enormous
amounts of resources, cognitive resources
-
Not Synced
learning what bus goes where,
this bus goes through which route
-
Not Synced
I am sure you know that.
-
Not Synced
It's not that they cannot engage,
it's not that they cannot focus,
-
Not Synced
it's just that the material
is not meaningful for them.
-
Not Synced
So that's a bigger answer actually
make things meaningful for them.
-
Not Synced
Let me illustrate a little bit more.
-
Not Synced
Bby now I think you know
some strategies already
-
Not Synced
to tell how children process information
-
Not Synced
I use them all the time
in every single example.
-
Not Synced
Here is the story
never mind the question.
-
Not Synced
Important is to understand the story
-
Not Synced
once we understand the stories
we can answer any question.
-
Not Synced
My strategy of removing questions.
-
Not Synced
Who is in the story?
-
Not Synced
This story has nobody.
-
Not Synced
What is it about?
-
Not Synced
Beads, what are beads?
Do you know beads?
-
Not Synced
If you know them great
if not we Google.
-
Not Synced
There are some beads in a box
can you imagine that?
-
Not Synced
There are five times
-
Not Synced
five times
-
Not Synced
if I use this to be one time
can you show me twice?
-
Not Synced
If this is one time,
can you show me three times?
-
Not Synced
Or what Singaporeans call thrice.
-
Not Synced
Can you show me four times?
Can you show me five times?
-
Not Synced
Engage your child using pieces of paper.
-
Not Synced
Tf they don't want to draw the model
don't force them
-
Not Synced
let them use paper.
-
Not Synced
The purpose of drawing
is to create the ability to visualise
-
Not Synced
so that they know the operation to use.
-
Not Synced
Pieces of paper for building the model
serve the same purpose.
-
Not Synced
If they don't want to draw,
this is your option
-
Not Synced
let them use paper like that
to build the model.
-
Not Synced
The goal is to get the right operation
-
Not Synced
that's the goal.
-
Not Synced
And to get to the right operation,
either you know it
-
Not Synced
for easy cases
-
Not Synced
or you use a diagram, a model
to get to it.
-
Not Synced
So model drawing is to
tell you the right operation
-
Not Synced
that's the purpose of model drawing.
-
Not Synced
It's not because they lose marks in PSLE.
-
Not Synced
Examiners don't care about your model
-
Not Synced
they don't even give marks to your model
-
Not Synced
they give marks to your equation.
-
Not Synced
So when they are young
let them do those things as well.
-
Not Synced
Anyway, there are five times
-
Not Synced
what a long sentence
-
Not Synced
let's read it carefully.
-
Not Synced
There are five times
-
Not Synced
five times? I use five pieces
compared to the other one.
-
Not Synced
There are five times
-
Not Synced
five times as many green as red beads
in the box that is very long.
-
Not Synced
Okay, don't want the box
ignore the box thing.
-
Not Synced
There are five times
-
Not Synced
as many green
-
Not Synced
don't want the beads
-
Not Synced
there are five times as many green as red
-
Not Synced
ah I understand already!
-
Not Synced
There are five times
as many green as there are red
-
Not Synced
oh so this is green
five units
-
Not Synced
and this is red
one unit.
-
Not Synced
There are five times as many green as red
-
Not Synced
oh I understand already
-
Not Synced
there are five times as many
green beads as red beads
-
Not Synced
understand already.
-
Not Synced
There are five times as many
green beads as red beads in the box
-
Not Synced
understand already.
-
Not Synced
If I want to drawn,
I can draw
-
Not Synced
if not I can use the paper just now
-
Not Synced
to say that green I use five pieces
-
Not Synced
and red I use one piece of paper
to represent it.
-
Not Synced
Okay I understand that already
I can draw.
-
Not Synced
Can I calculate?
-
Not Synced
Oh I can, but I got information like 78,
where does the 78 go?
-
Not Synced
There are 78 beads in a box, okay
-
Not Synced
it must be all the beads
the red and the green ones.
-
Not Synced
So the 78 must put into 1, 2, 3, 4, 5, 6
-
Not Synced
78 put equally into 6 boxes.
-
Not Synced
Parents, I hope you are seeing me applying
-
Not Synced
the various things I suggested earlier.
-
Not Synced
Always read as you write,
-
Not Synced
putting 78 equally into 6 boxes
-
Not Synced
I didn't say 78 divided by 6
-
Not Synced
that doesn't give them the meaning
of whatever they are doing.
-
Not Synced
Many children eventually
-
Not Synced
does not became good enough
in Mathematics when they get to PSLE
-
Not Synced
because they kind of
wasted their six years
-
Not Synced
trying to understand gibberish.
-
Not Synced
It is really gibberish to them
-
Not Synced
they have no clue
-
Not Synced
what all these squiggles actually mean
-
Not Synced
so sometimes by luck they get it right
-
Not Synced
and often they get it wrong
-
Not Synced
and they struggle
-
Not Synced
they struggle because
it's Martian to them.
-
Not Synced
But it doesn't have to be
-
Not Synced
and we adults, both parents and teachers
-
Not Synced
can really help them
-
Not Synced
especially for most of you
your kids are in Primary 1, 2,3
-
Not Synced
still plenty of time
to put all these into practice
-
Not Synced
in a more regular basis.
-
Not Synced
The teachers have spoken to them
over the years
-
Not Synced
we have constant professional development
-
Not Synced
and they try to do this.
-
Not Synced
The information we share
with you this evening
-
Not Synced
is for you to have the
same consistent practice
-
Not Synced
so that your child can learn Mathematics
-
Not Synced
in a rather easy way.
-
Not Synced
So from there they will do
whatever they...
-
Not Synced
This is a calculation for Primary 3
-
Not Synced
so 78 is too hard
for me anyway
-
Not Synced
but I think I can take out
-
Not Synced
I think I can take out 60
-
Not Synced
60 is quite easy, I get 10
-
Not Synced
and then left with 18
-
Not Synced
18 put into 6
that one is okay, I get 3.
-
Not Synced
So 10 and 3, I get 13 as
the value for 1 unit.
-
Not Synced
Can they do this mentally?
-
Not Synced
Yes.
-
Not Synced
For those of you with children
who can do Mathematics mentally
-
Not Synced
sorry
-
Not Synced
For those of you with children
who can do calculation mentally
-
Not Synced
encourage them to do so.
-
Not Synced
That is the end goal of
learning calculation anyway
-
Not Synced
you learn calculation by writing it down
-
Not Synced
so that one fine day
you no longer have to write it down.
-
Not Synced
Mental calculation.
-
Not Synced
Mental calculation is a pinnacle
to learning computation.
-
Not Synced
By the way computation is arithmetic
it's not Mathematics.
-
Not Synced
it's part of Mathematics.
-
Not Synced
Mathematics is a thinking part
-
Not Synced
the arithmetic is the computation part.
-
Not Synced
Some of your children like
to do mental calculation?
-
Not Synced
That's perfect, that's alright.
-
Not Synced
In fact, those who are over reliant on
paper all the time to do simple things
-
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example, things like
-
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things like 11 minus 9
-
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it break my heart to see P6's do this
-
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11 minus 9
what has happened?
-
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really what has happened?
-
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if you still do 11 minus 9 like that.
-
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Then the best part is then they will do
what the teacher taught them to do.
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Like why?!
You are still doing 11 minus 9 right?
-
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So can't you like
-
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oh what's the difference between
11 and 9.
-
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So if they only read it,
what's the difference between 11 and 9?
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Oh the difference, so the gap between them
9 to 11, only two steps
-
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So this will all translate into better
things when they deal with bigger numbers.
-
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When they have to do 401
-
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then they will say
-
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"oh what's the difference between
the two numbers?
-
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oh the two numbers are quite close
399 is only one step to 400
-
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400 to 401 only one step
-
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the difference is two.
-
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Like that.
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When you can read,
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difficult things
-
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become quite easy you know.
-
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Let me just show you
when your kids get older
-
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when they get to P5
-
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they do things like three-fifth
share among 3
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so when they can read this
as three slices,
-
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three whatever, three nouns,
three-fifths
-
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they will say
-
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"oh three share among three
is easy, it's one"
-
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and the item is fifth
so the answer is one-fifth.
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For this case,
it's so straight forward
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but then I see P5 who does this
because they do what adults tell them.
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Maybe some of us tell out older children
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"eh boy ah, remember ah
dividing fraction very easy one
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got formula. just remember ah
-
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you change divide to multiply
-
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and then this one you write
as three upon one
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and then this one you terbalik
the thing lah."
-
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Terbalik is Singlish for invert
invert the thing
-
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then you cancel your life away lah
-
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then you get the answer right?
-
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All that hassle for something
that quiet simple
-
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three whatever share by three
the answer is one.
-
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No need all that
nuts and bolts and
-
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all those nonsense
-
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to just get to the same answer.
-
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Just to illustrate that once you can read
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a lot of things are actually
quite straightforward.
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Now let me take a couple more question's
as we wrap things up.
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Some of you are quite lucky
-
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because your children seem to be
doing really alright
-
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better than alright.
-
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How can I bring out the best of the child
-
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which Is in primary 1
but he's able to do primary 4 Mathematics.
-
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Any advise besides volunteered training?
-
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Five things I would suggest
-
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for those of us
who have children
-
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who seems to be quite
capable in Mathematics.
-
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How do you push them further?
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I think part of the answer is this:
-
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let them choose what to learn.
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Since they already can learn
what they are supposed to learn
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let them decide.
-
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Like okay you know there is
this thing called prime numbers
-
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and let them find out
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if they are interested,
they will pursue it
-
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if they don't like it,
they will ignore it
-
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it's fine.
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So that's my global answer
-
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let them choose
to do whatever they want to do.
-
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No need to go to primary 2, primary 3,
primary 4, primary 5 but let them choose.
-
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Oh you know, your brother in P4
learned about factors and multiples
-
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do you want to find out more about it?
-
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Go to this website or watch this video
or whatever.
-
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So that's my answer actually
-
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expose them to some things
but let them choose
-
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let them choose.
-
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So that is more liberating
-
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than sending them to cookie-cutter
kind of enrichment activities.
-
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What else can you do
-
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if they are not ready
for higher level content.
-
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So some children are quite good
-
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and these strategies can be applicable
to all children actually.
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If they are quite good,
-
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and they can do their Mathematics
quite easily
-
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like they know their timetable
in primary 2, primary 3 quite readily
-
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what else can they do?
-
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You can ask them to write a story
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if they don't want to write
you can always ask them to draw it.
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Anyone can do this,
not just the advance children.
-
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But if they're advance, these are
some things that are quite helpful
-
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to further their understanding
of Mathematics.
-
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You can also ask them to explain
-
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can be oral, can be written form.
-
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So keeping a Math journal
is quite useful also
-
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a little diary where they record stuff.
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I believe most of your children
have a Math journal anyway in school
-
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you can also have a Math journal at home.
-
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I don't understand how come
9 groups of 7 the answer is whatever
-
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why is it like that
why is it like less than 70
-
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and see what your child say.
-
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And maybe they will say
-
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"oh you see, 10 groups of 7 is 70 already"
-
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oh course ah
-
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if 10 groups is 70 then 9 groups
must be less than 70.
-
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In fact it should be 7 less than 70.
-
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So if a child is fully advanced
they usually can do this
-
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they can explain orally
-
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or if they have enough writing skills they
can write it or draw it in their journal.
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Finally,
-
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they can challenge themselves
-
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children when advanced
will find avenues
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to challenge themselves
-
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and you can help them in that.
-
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Example, maybe they do
a lot of calculation
-
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they do a lot of calculation in P3
when they are asked to multiply
-
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a two digit number by a one digit number.
-
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Like in a worksheet,
quite boring actually.
-
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you can say
"eh, why don't we challenge ourselves".
-
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We notice that the answer is two digit
-
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but this one the answer is three digit.
-
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and this one the answer
is also three digit.
-
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I wonder if it is possible
-
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for two digit number
multiply by one digit
-
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and the answer is two digit
-
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we know it's possible already
we have one example.
-
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But this one
-
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this one the answer is 26
so the digit 2 is repeated.
-
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I wonder if it's possible
all the five digits
-
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all the five digits are different
-
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you know?
-
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Let's find if it is possible.
-
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So children who are quite advance
will challenge themselves
-
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but when they are younger
they don't know what to do
-
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so you can expose them to some examples
and over time you should see them
-
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you should see then challenging themselves
rather independently.
-
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Let me conclude now
-
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with one final example.
-
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Let's look at something that's more
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involved.
-
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In today's webinar,
-
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the topic is helping children
process information in Mathematics
-
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So we need to know
-
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the different types of information.
-
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What are they?
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Visuals, yes visuals
-
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pictures, diagrams, graphs
-
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some are from daily life,.
some are more formal
-
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What else?
-
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Language, words, English
-
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some are familiar
like stories about bakery
-
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some are quite strange
about milk bottles.
-
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What else?
-
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Symbols.
-
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So today we learned that
these are the kind of information
-
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children deal with in Mathematics
-
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language, symbols, and visuals
-
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and I have suggested some strategies
-
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on how we can help them become better
in processing those information.
-
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Those are mere suggestions,
-
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I am sure you can come up
with other ways
-
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which are equally effective
or engaging for your children.
-
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The webinar this afternoon
is just to give you a starting point
-
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to inspire you to try to make
Mathematics more palatable
-
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hopefully more exciting, more interesting
for your children.
-
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But if not at least meaningful
-
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because Mathematics is a language
-
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once we cannot read the symbols
-
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everything falls blank.
-
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Once we cannot read the English language
with comprehension
-
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everything cannot happen.
-
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Symbols sometimes they really cannot read
-
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like I said, children say three over five
three upon five
-
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that's really,
cannot speak proper Mathematical language.
-
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So it's like in English,
the child only knows Singlish
-
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sure fail PSLE English
confirm
-
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If all you know is Singlish
and no understanding of standard English.
-
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Likewise in Mathematics
some children cannot read symbols
-
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do help them
-
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do help them by reading,
don't by lazy and say three times five
-
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say three rows of five
three groups of five
-
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fifty-one share among three
twelve put into groups of four.
-
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There are many ways to read
-
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important thing is read, don't spell.
-
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Let me demonstrate this final example
-
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and you'll be able to see the various
strategies addressing language difficulty.
-
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Many of you raise questions
-
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so many I cannot answer
every single one of them live.
-
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There are some important questions
that I would still want to answer
-
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so we are going to put this
as a eCampus course
-
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so some of your questions that are not
addressed will be featured on the course
-
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so do visit eCampus
to revisit today's topic
-
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and you might get other insights
from the answers to
-
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some important questions that were
also raised
-
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just that you know we only have
less than two hours
-
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there is only so much we can cover anway
-
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but do go to eCampus to
continue to get more ideas,
-
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more information about this topic.
-
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Oh never mind the question
let's look at the story
-
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notice the question is not there yet.
-
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Who is in the story?
-
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Oh finally we have someone in the story
-
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Mrs Baey and Mrs Chia
-
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I don't really know them
but that's alright.
-
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What are they doing?
-
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They went shopping.
-
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Quite a long story
-
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one sentence...
-
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two sentences...
-
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three sentences
alright it's a long story
-
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but never mind
one by one ,one at a time.
-
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They went shopping
-
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alright I can understand that
-
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with the same amount of money
-
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okay not too hard.
-
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Can I calculate.
-
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Can I calculate?
-
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Probably not yet
-
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no numbers.
-
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Can I draw?
-
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In this case I can,
same amount.
-
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So I can draw model
that will make my teacher happy.
-
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I can draw this
-
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but sometimes I don't want to draw
-
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it's okay, I said wait
I want to read more.
-
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So it's up to you
-
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sometimes you want to do it straight away
-
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sometimes you decide to wait
maybe another sentence
-
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it's better to draw
or better to calculate
-
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so you decide.
-
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Parents, the final thing
I want to share with you is
-
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do teach children to make decisions
-
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don't decide everything for them.
-
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When you help them with Mathematics,
don't always tell them what to do
-
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that's not helpful.
-
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Children that become successful
in Mathematics eventually
-
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are independent
-
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it is a characteristic.
-
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You cannot be not independent
and be highly successful.
-
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You may be artificially successful
that means you get AL1 for PSLE
-
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A-Star for PSLE
-
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but my O-Level not so good anymore.
-
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Some of them still quite okay
for O-Level
-
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but by A-Level, Polytechnic
not very good anymore.
-
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So at some point,
they will become not very good.
-
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They'll be found out.
-
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So independence is a
very important characteristic
-
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do let children learn to make decisions.
-
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"Do you want to draw now?
-
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okay go on
-
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don't want is okay
-
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you decided".
-
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If it's a bad decision it's fine
-
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later we just correct ourselves.
-
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"Do you want to calculate?
Do you want to draw?"
-
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it's a simple question
you can ask all the time.
-
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Alright, that is done.
-
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They went shopping with th.e
same amount of money
-
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One of them spend so much
-
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the other one spend so much.
-
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Mrs Baey spent $480
-
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so Mrs Baey...
-
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spent $480
-
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can I draw?
-
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Yeah I can, I put in $480 somewhere
but I want to wait.
-
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I don't know how to calculate
so cannot calculate anyway.
-
Not Synced
Mrs Chia spent $620
-
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Can I draw?
-
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Yeah, just draw
Put $620 in.
-
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that's what she had
-
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she spent so much
so that's what she had left.
-
Not Synced
I can do that, but I don't want
to do it yet.
-
Not Synced
Sometimes I don't it straight away,
sometimes I want to wait
-
Not Synced
I can decide.
-
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Anyway,
-
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Mrs Baey spent $480 and
Mrs Chia spent $620.
-
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In the end
-
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Mrs Baey had 3 times
-
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oh I can draw
-
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I can draw how much they spent
-
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and how much is left.
-
Not Synced
Do I want to draw how much they spent?
-
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Or do I want to draw how much is left?
-
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I can decide.
-
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Whichever that is easier to do.
-
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For me,
-
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I think it is easier for me to draw
-
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how much is left
-
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because 3 times is easy to draw
-
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3 times is like use the paper right?
-
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It gives 1 time
-
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this is 3 times
-
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so 3 times is easy to draw.
-
Not Synced
In the end, Mrs Baey has 3 times
-
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so I can draw that one
-
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Mrs Baey has 3 times
-
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So if Mrs Chia has this left,
-
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Mrs Baey will be 3 times
-
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one, two three.
-
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So this is what...
-
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what is left.
-
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If I am afraid people don't understand me
I can write, this is what is left.
-
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So that means,
-
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this is what they spent.
-
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For Mrs Baey, it was $480
-
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and for Mrs Chia it is $620.
-
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Parents,
-
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if they can understand all that
-
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whatever question that is asked of them,
they can answer
-
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because from here,
they will notice that well...
-
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they do know the values
-
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they do know the values of
-
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of these two units
isn't it?
-
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I leave the Mathematics to you
-
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but you can find the value
of these two units
-
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because you know the whole thing
is $620
-
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the whole thing as in
the whole thing I have just drawn.
-
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And this little bit here is $480
-
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so I think we can find out
the value of these two units
-
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and the rest is pedestrian
just a bit more of calculation.
-
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And then when they are done...
for those children who are more advance...
-
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you can ask them to critique the diagram.
-
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like "do you think this diagram is good?"
-
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so they may say
"oh it's not good"
-
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or whatever reason they will say.
-
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Say "oh look, the proportion is not right"
-
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then they may want to draw
a better one.
-
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Right?
-
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So that's my concluding example
-
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for me to make two additional points
about individual independence
-
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but also inviting them
to critique solution.
-
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Parents, this webinar is about
helping children process information
-
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and we want to help them.
-
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We can only help them if...
-
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we ourselves portray
Mathematics as a language
-
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comprising of information
given as visuals,
-
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given in words,
sometimes given in symbols.
-
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Throughout today, in answering
some of your questions
-
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I have demonstrated some strategies
that we parents, adults, teachers
-
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we can use with children
-
Not Synced
to help them become better
-
Not Synced
in reading comprehension,
making use of diagrams, pictures
-
Not Synced
words, phrases, sentences,
symbols, expressions.
-
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Right?
-
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I want to thank all of you
for spending your precious evening with me
-
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and hope to see you again
-
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hopefully in person
-
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in the next seminar that we have.