Hi, good afternoon parents.
Welcome to our 2021 Parent Empowerment Workshop Series.
My name is [Name]
I am a senior manager for student and corporate affairs.
Now before we start,
I know a lot of parents are still coming in
so let me just go through some of the housekeeping rules.
I think for many of you who have already used zoom
you will know that upon entry
participants will be muted and their video function will been disabled.
Please ensure that your devices speakers are enabled
and for best audio experience you may wish to use your earphones.
If you have technical issues, please use the chat function to alert us
and to encourage interaction for this workshop series
you can ask questions throughout the session.
Please use the QNA function below
and please do not use the chat function because we will not be monitoring that.
We will be monitoring the QNA function for the questions asked
And doctor Yip, our workshop facilitator
will be answering the questions as they come along.
And just a reminder
strictly no recording by participants is allowed
This workshop series will be put up on Learn for Life eCampus
to enable parents who have missed this session
or if you wish to revisit some of the highlights of the workshop.
Many of you with children in mainstream schools
you'll be very familiar with Parents Support Group (PSG).
In Pathlight we don't have PSG
we have what we call
Parent-School Collaboration Teams
and we have five of them.
So basically we have one PSCT for short on safety
and this safety is when parent volunteers can come in and
accompany our students when they go for external learning journeys.
We also have a PSCT for work opportunities
so some of you who are highly placed in your organisation
and are able to open doors for us for
FAM tours or even internships
please volunteer in this PSCT.
We also have a PSCT for family bonding
to organise activities for the families to enjoy family time together.
And there's also a PSCT for greening
so we have a group of enthusiastic parents who usually come
and help to contribute to make the school beautiful.
And then of course I head the PSCT for parent empowerment.
So it has been more than a year since we
suspended all PSCT activities due to COVID.
So this year, I think we are very pleased to bring back this
Math workshop series
conducted by Doctor Dr Yeap Ban Har.
It's a very very popular series
we always get more than 95% approval rates
from parents who attended our workshops.
Let me give you a short introduction of Dr Yeap.
Dr Yeap is our director of curriculum and
teacher development at Pathlight School.
He usually conducts paid math education courses around the world
and he told me he has covered close to 40 countries to date.
He is an author of math textbooks and consultant
and his books have been translated to seven languages.
So don't play play ah!
he's a very accomplished and
learn-et??? educator.
He holds a Master of Education and Ph.D. in math education.
So without much further ado
let me pass the floor to Dr Yeap.
Lets welcome Dr Yeap please.
Good evening parents
thank you for joining me this evening
My name is Ban Har
and I'll be conducting this webinar.
The focus of today’s webinar
is on helping children
process information in Mathematics.
In this webinar
I will help all of us understand
the kind of information that students...
need to process...
whenever they do mathematics.
And I will suggest some ways of helping them
ways that adults including parents
will be able to use quite easily
whenever we engage them with their mathematics at home.
So that's our plan this evening.
Through examples,
we are going to be looking at
the kind of information
that students need to handle in Mathematics
and I will suggest some ways
to help students become more proficient in this.
But before we get into the content
let me give a brief introduction.
Whenever we help students with anything
we are always helping them with not only the skills
but also the mindset.
Without the corresponding lens
without the corresponding mindset
students sometimes cannot use the skill that they have acquired.
In other words,
skills...
without the right mindset...
sometimes are still not useful.
Do you sometimes see your children able to do something
but then...
on their own...
they don't seem to be able to do it?
That will be symptomatic of having skills
without the corresponding mindset.
What do I mean by that?
Some students...
think that Mathematics is a subject where they remember stuff.
That mindset...
is counterproductive.
Research has shown us that
children who think of Mathematics
as a subject where they remember things,
they do less well...
than children...
who understand the exact nature of mathematics.
So what is the exact nature of mathematics?
Mathematics is a language.
Children who understand mathematics as a language
and learn mathematics as a language
they do far better...
than children who think that
mathematics is a subject where you remember things
where you memories things.
Secondly,
children sometimes accidentally think that
mathematics is a subject where you answer questions.
They perceive mathematics as
a subject where people ask you question
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.
So sometimes as adults, parents, and teachers alike
we have made children perceive mathematics
with a incorrect mindset.
In summary,
children who are successful...
highly successful in mathematics
they see mathematics as
1. A language
2. A subject where they think
a subject where they figure things out.
Mathematics as a language.
Do you know that mathematics is a language?
Yes it is
it is a language to describe things around us.
When you see things around you,
you try to describe it.
Example:
you might try to say
"4 groups of children"
and in mathematics we have multiplication
to describe that.
Or sometimes you try to put
a tray of 60 cookies
you try to pack them into
maybe...
containers of 24's
and I wonder whether there is enough cookies
to give you full containers or not
or there might be some leftover... some remainder.
So putting 60 cookies into containers of 24
can be described quite precisely
in this case using the concept of division.
Mathematics as a language is a productive way
for children to think about the subject.
And like in any language there are different alphabet systems
so to speak.
There are different grammars
there are different rules.
In mathematics,
there are three alphabet systems
so when we say that "oh I understand mathematics"
as in I understand Spanish or I understand Japanese
or I understand whatever language
what does it mean?
It means 3 things:
Firstly,
it means we can read and comprehend visuals
we might see,
1 row of 3
2 rows of 3
3 rows of 3
4 rows of 3
5 rows of 3
and so on...
6 rows of 3
7 rows of 3.
Of course it's written like so
7 rows of 3
I know as adults sometimes you get lazy
and we don't read
we spell.
Spelling is making sounds of the symbols
so we say 7 times 3
that means you are spelling out that expression.
In what language do we spell out every single word?
Can you imagine reading a book
and spelling every single word in the book?
How much of it will you actually understand?
and how much of it will you actually enjoy?
quite little right?
Do children know how to read mathematics?
Or are they spelling out every single expression?
When we say that children understand mathematics,
it means that they look at the visual
and they can read it,
they can comprehend it,
they can make use of it.
This is one kind of information that children need to process
meaning: Read, Comprehend, Make use of it.
I can make use of this. For example,
let's say I forget my times table
and I need to know 7 groups of 3
7 rows of 3.
I can say "well I know 7 rows of 3 is actually...
5 rows of 3...
that's 15
and also 2 rows of 3 that's 6.
so 7 rows of 3 is simply 15 and 6
15 and 6,
6 is really 5 and 1
15 and 5 is simply 20
20 and 1 is 21.
Do children read when they do mathematics?
The way I just demonstrated it.
So that is what I mean parents
by mathematics is a language.
And this is the first type of information
that out children need to be good at
Visual information:
how to read,
how to comprehend,
how to make use of it.
Other than visuals,
they also need to be able to comprehend...
symbols
they must be able to read symbols.
So when they see things like
this...
they know what that means
they know it's five 10's and one 1
so they know that it actually represents
5 of the blues
and 1 of the yellow
so when they see the symbol 51
they know the 5 refer to one item, the blues
which is actually 10
and the 1 refers to the yellows which refer to 1.
So this is a highly efficient way of saying
5 of this and 1 of that
which if you say in plain language is quite lengthy
you have just heard that
five of 10 and one of 1
but in mathematics we have a short and
a highly precise way, highly encoded way
of symbols to describe the same thing.
So when children look at symbols,
they understand what it means.
51
share equally among 3.
So just like what I said earlier
do children read mathematics?
They must.
If they say 51 divided by 3
they may not get the full meaning of it.
in this case as sharing among 3.
So parents,
Mathematics is a language
and it's a language that comprises of
not just visual,
but also symbols.
What else?
Words
a verbal language.
In our case English.
English or Spanish or Japanese or Chinese
whatever language the children are learning mathematics in
in that society.
For ours it is English language.
A verbal language like English language is part of mathematical language.
In summary, mathematical language
comprises of
visuals, diagrams, pictures, graphs,
tables,
it also includes symbols,
notations,
finally it also includes a verbal language
example, English.
So children need to be able to understand
when I write a sentence
Spiky... has
more... coins
than Curly,
they must be able to read this
and make sense of it,
they must know who has more
and who has fewer coins.
Spiky has more coins than Curly.
3 more.
Spiky...
has ten coins.
So if Spiky has ten coins
and he has more coins than Curly
then obviously Curly's number of coins will be less than ten.
Because Spiky has more and Spiky has ten
so obviously, Curly whatever number she has
that number is less than ten.
So Curly has fewer than ten coins
isn't it?
So in this case, we can obtain the answer by doing a subtraction.
Isn't it?
So...
if you do this
please stop doing it from now on.
Please don't tell your children
"eh ah boy ah
you see the word more you add okay?"
parents please don't do that.
Why?
It's wrong
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,
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
to describe whatever we want to describe.
Alright so parents
those are the three kinds of information
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
learning a language includes oral skills
speaking but also listening.
It also includes reading and writing.
When children do not have the full experience
in learning mathematics as a language
not talking,
rarely listening to another person other than the teacher,
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...
"my son always write answers without working
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
writing answers without working.
Example,
In primary one
they say nine, ten, eleven
write it down.
Did the child do working?
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
"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
for questions like this
they can just give the answer.
Example, at PSLE this kind of question answers are given
the marks are given
for the answers.
If they show working it's fine.
If they don't show it's also fine because all the marks are given for the answer.
Okay?
So they said "Okay so try to buy three"
Yeah? Try to buy three.
So $5, and I know that
oh now I need to write because I cannot remember so many things.
I know that I got a lot of $5 in $30
in face I got six of them.
Because six times $5 dollars gets $30
and then I got $2 more.
So this $30 there are six $5
and every $5 gets me three
so I can get six of three cupcakes that's eighteen cupcakes.
But then the $2 I can get more
so I get whatever I can get and give a final answer.
Parents,
I have illustrated what I mean by
Mathematical language include visuals.
In this first example
I demonstrated visuals that are common place
in our everyday life.
Let me move on.
Sometimes, at a higher grade level
the visual dissapears
like this problem.
If you read it
you'll realise that it's the same kind of Mathematics involved.
It's what we call division with remainder
like just now the division remainder.
The visual disappeared.
So what is the learning progression?
First is you let them see the visual
in the actual context.
In the bakery in Whampoa market
for example
then they come to school
they will see this.
The same visual or similar visuals
but printed on paper.
Finally, the visual disappears.
So parents, we can help the teachers
by alerting our children to visuals around them.
That one is harder for teachers to do
because the teachers only see them at school
and not taking them out to the market
or just engaging them with everyday experiences
that one I think parents can do and can do quite well.
So do alert your children to visuals around them
and engage them with a bit of Mathematics
don't have to use worksheets.
So that's a strategy
a strategy to help them process information better.
In this case visual information.
That is commonplace.
Oh we have a question here!
Lets look at what the question is all about.
Crate...
oh what is a crate?
Ask your child that.
Give me other words that's similar to crate.
If they don't know,
just Google
and then they can see a picture of a crate
as simple as that actually.
Use technology
that we already have.
Don't complain
"oh is this Maths or is this English ah
how come they use words like that"
there is no question whether this is Maths or English
English is part of Maths.
So remember, Mathematical language include:
symbols, visual, and English
English is part of Maths.
If the don't know the word,
just do what we normally do, Google it.
And then "oh that's a crate!"
then your child will give you other words like box or whatever they want to say.
A crate can hold milk bottles,
okay a crate can hold milk bottles.
Actually I haven't seen milk bottles in a very long time.
Once upon a time when I was a child
wow that's a long time ago 50 years ago.
You know the milkman who goes round
and they give you the milk in a bottle
F & N bottle with a little...
banana leaf stopper.
Okay, most of you are too young to even know this.
So sometimes, children are asked to read stories
that are so alien to them.
But that's... that's life
we also read stories that's alien to us.
Harry Potter, you mean you grew up like Harry potter?
No right? but you still enjoy it.
Right?
So, that's normal in a language
we sometimes read things familiar to us like the bakery, selling the cupcakes.
But sometimes we also read things that are not so familiar to us
and some of us enjoy it some of us don't, that's life.
We cannot expect everyone to find the same thing exciting.
You cannot expect every child to find milk bottles exciting.
Okay, some of them do but...
most of them don't.
But they will still learn to imagine it.
And we, as adults can help them.
We can Google, we can show them that
"oh you know, in some countries, they actually sell milk in bottles".
"in some countries, they bring milk bottles to the shop
and then they get their milk".
But for us we go NTUC it comes in a box
sometimes plastic.
We are not very green in that way.
So engage them in that kind of conversation
that's very important.
Very often parents ask, "how do I prepare my child for Mathematics"
and they think the answer will be
buy more workbooks, by more assessment books
It not.
It's doing things that parents do very well.
Engaging children with things around them
both familiar, but also unfamiliar.
So these are some kind of images
children need to encounter.
So one more example on visuals,
Farah, okay probably somebody
a girl
I see the word she, so it must be a girl.
I don't have a friend called Farah so I don't know whether it's a boy or girl.
And I am not so familiar with this name
but I saw the word she, must be a girl.
But shouldn't matter right? whether it's a boy or a girl.
Farah has some cards
okay I understand that.
Rectangular cards...
oh so the cards are rectangle
I know what rectangles are we learned that in primary 1.
Farah has some rectangular cards
okay I understand that.
Measuring 10 centimeter by 6 centimeter oh I can see that.
So this is what we mean by children
using visual to support their reading comprehension.
So some children struggle with language
for example, I have one question like this.
How can I improve my sons language or Mathematical language capability?
He has delayed language processing.
So that's the answer actually, use visuals
use visuals.
And very often even in examinations,
there are some items where visual support is provided
whether or not you have delayed processing
it is just something they support children with.
So even if a child doesn't have any issues with language
often, a visual can help them with comprehension.
So I see, 10 centimeter by 6 centimeter
now parents, try not to be...
try not to be lazy
don't say 10 cm
it is actually called centimeters
say in full so children hear it
if we use truncated language, lazy language too early...
Children doesn't get the full meaning eventually
don't say three times five,
say three rows of five, three groups of five
especially in the beginning
once they understanding it you can be lazy
but in the beginning, try to say it completely.
So that they know that cm is a symbol for centimeters
otherwise some of them may not know
and they will be wondering what is this
and then in exam, whether it is millimeter or centimeter they don't really care.
??? sometimes you see that amongst your children also
they don't really care what the unit is and they do very strange things to it.
So do read it in full.
And the question is what is the smallest number of cards she needs
to form a square
without overlapping the cards.
So let your children try, give them papers like that
let them try.
If you are hardworking you can go and get the exact measurement
but it's not necessary but if you want to
And let them try.
That's how you make Mathematics interesting.
Mathematics is initially a hands on experience
in Singapore we call that (CPA) Concrete, Pictorial, Abstract.
You first learn it by experiencing
you take a paper, you take a rectangle and you try to make a square
like a puzzle like a jigsaw puzzle.
Use the rectangular parts to form a square
without overlapping.
You do it,
once you have done it you can understand the visual.
So how does your child learn and process a visual like that
in the exams?
In P4
it's because in P1, P2, P3 you let them use concrete materials.
Even in P4 of course I will let them use concrete materials still.
But because they are exposed to doing
when they see a picture of what they have done
obviously, they understand it better.
And when they read and they have a picture to support the reading
That's where comprehension of the word problem
becomes possible.
Let me take a couple more questions before I move on.
Quite a few have similar questions
like my son has problems with English language,
part of problem sums, word problems
so we cannot understand the question
and therefore cannot apply the Mathematics principle.
How can I help him?
So a lot of questions along this line I'll be demonstrating that further
I have demonstrated some strategies you can use
Yeah, my child is still catching up
on his language skills how can we best translate Maths problems to visuals
for his better understanding.
And how do we slowly get him to be less dependent on visual.
A very important question.
Whatever help we give children, is with the goal of not helping eventually
less dependent.
Let me answer those questions about language.
Parents, up to this point
I have shared with you that Mathematics is a language
comprising of:
visuals, pictures, diagrams, even graphs
but also symbols
and of course words.
In our case, English language.
I will now focus on the question just asked
how do I help with the language part
of word problems.
How do I help them with language that's embedded in Mathematics?
Oh let's look at this story
not a very long story right?
Just two sentences short story.
Who is in the story?
Hmm... how interesting
Pierre, I don't know how to pronounce it I cannot speak french
Is it Pierre? Yeah maybe it's Pierre
doesn't matter.
Oh he's a boy okay doesn't matter either
but well...
Pierre had marbles
you know marbles right?
Yeah the one you see at aquariums
actually marbles are for playing
I don't know why it is put in aquariums nowadays
and plants.
But anyway, Pierre had marbles i hope he's not losing any.
So children learn language
right?
So they learned that
oh you know in English language, very funny language,
when people say you lose your marbles it means something.
It means like
You are going a bit crazy you are not getting it all together.
Anyway,
let's not get distracted
let's come back to the story.
So Parents, you've engaged your child in what might happen to them
don't be so straitjacket I am quite sure you are quite fun parents
but when it comes to Math suddenly you become a different animal altogether.
Don't be like that,
make it fun.
make it informal
just engage your child in what might happen to them.
when children read stories their brain go in all directions
I'm sure you know that.
Don't scold them
because they are just being themselves
nothing wrong with being themselves
what they need is guidance.
How to refocus
so I was just demonstrating that awhile ago.
Pierre has some marbles, okay that's easy to understand.
We know how many right?
There are 315.
He divided them
equally
into 3 boxes.
Oh, what does that mean?
So you ask your child that
and your child will tell you in his own words.
Parents, I have so far demonstrated three strategies,
if you missed them let me articulate them one by one.
What strategy did I use?
Strategy number 1: To help them with language
I deleted the question
the question is there
but I deleted it.
I deleted the question
why?
When you give a child a question what will they do?
They answer it.
But I don't want them to answer the question just yet
I want them to learn to comprehend,
I want them to learn to understand.
So because my goal for them is to learn, to understand things
I removed the answering point first.
So try to cultivate that habit.
Many children have the bad habit
of trying to answer the question
before they understand it,
that's how they make mistakes.
if you don't understand the story how can you answer the question.
You cannot.
So to cultivate the good mindset, a good ???
Mathematics is not answering questions
Mathematics is understanding stuff.
Once you understand stuff
you can answer whatever question they ask you.
That's the truth right?
So focus on understanding,
how do you help them focus on understanding?
Remove the distractions, remove the question.
Question is the distraction
because they try to answer they do strange things.
Second strategy I demonstrated:
I did not read the question
sorry... I did not read the numbers
Second strategy: I did not read the numbers.
I'm sure you saw me doing that earlier already
remember the more, less problem?
In face all the questions so far.
So you might notice I said Pierre had marbles
Pierre had some marbles.
I replaced the number with a qualitative word.
Pierre had some marbles.
There is ample research to say that
numerical information breaks a sentence up
and decreases comprehension
so that is well documented.
Especially for those children with language issues
try to help them
try to help them by letting them
not have that problem
so avoid reading the numbers.
Pierre had some marbles
oh how many? 315.
So you read the sentences to understand it then you put in the numbers later on.
Third strategy: ask your child to paraphrase some lengthy cumbersome sentences:
Oh he divided them equally into three boxes
so hard for me to understand
can you explain to me?
Or if the child is not very good in explaining,
can you draw for me?
So let your child have a choice,
to draw or to tell.
So you might even have that as a routine
"do you want to tell? or do you want to draw?"
draw or tell,
then those who like to draw will say draw
then those who like to tell or lazy to draw will say yeah I want to tell.
But sometimes you don't give them a choice
okay you've been drawing a lot
next one I choose
tell me
then you force them a little bit out of their comfort zone
so they learn something more.
So those are three strategies quite well documented,
letting children paraphrase sentences by drawing or in their own words,
leaving our numbers,
and then the other one that I mentioned earlier
the three strategies.
Anyway, once they have their ??? they will answer the question
and they will say "ok".
Pierre had three boxes
and they are equal in size
and he had 315 marbles
and he put them equally
I can replace divided with put right?
He put them equally into three boxes
so the 300 is quite easy to do
100 each
and the 15
I think can
5 each
and together is 105.
So 315 put equally into three boxes result in... 105
and then write a sentence if you want
or if your teacher say you write a sentence to answer the question.
Let me demonstrate with another example.
Oh who is in the question? Who is in the story?
Oh in this case it is nobody
just now was a boy named Pierre but here it is nobody.
What is it about?
Oh it's about COVID-19
when else did we talk about masks
and hand sanitisers.
Oh it's about a factory do you know what a factory is?
Okay, let's see what the story is about.
A factory produced some masks and hand sanitisers.
Quite a lot right?
You can see the number
the factory produced
some masks and hand sanitisers.
Can I calculate already?
Probably not yet.
Can I draw a diagram?
Not sure
never mind lets read the next sentence.
It produced fewer hand sanitisers than masks.
Whats "it"?
Oh the factory ,okay
the factory produced fewer hand sanitisers than masks
so hand sanitisers
so many
masks
oh mask more is it?
So fewer hand sanitiser.
Is my diagram showing what the story shows?
The factory produced fewer hand sanitisers than masks.
Okay I can draw so I will draw.
What information I have?
Oh 2821... where should I put that?
It produced 2821 fewer hand sanitisers than masks.
When children first learn this comparison thing,
pieces of paper like that is quite useful
let them use paper strips
or you can go to
shops and buy paper strips the longish one
or just cut your own, make your own.
Color is quite useful, also quite interesting
when you overlap the colors will show up also
then they can se "oh that's where the 2821 is"
oh we also know 5743
do you know where that is?
And if the child understands the story...
they will know that this is the total number of hand sanitisers and masks.
Then ask your child... what do we do next?
And
hopefully the child will say
"I need to take this number off that number"
that's another strategy.
Talk about what to do,
don't always like...
write down the working write down the working
get them to talk about it.
So you know "oh my child knows,
my child knows the first step is subtraction".
The idea that we subtract is more important than the actual subtraction
by the time they take PSLE, the subtraction itself is done by calculator
but they must know to subtract otherwise it is pointless.
If the children cannot identify the right operation: that I subtract first
then the result we divide by 2,
the calculator is still useless.
So from a young age
engage them in telling you what operation.
Children are children, they are not very good at multitasking.
Sometimes when they
identify the operation
and do the operation,
they don't realise that these are two separate things.
So it's not clear in their mind.
Meta-cognitively speaking,
they are not learning somethings useful for years to come.
So do engage your child in telling you the operation
Don't bother them with the actual calculation which is quite boring
to be honest.
The actual calculation 5000 you know like whatever we normally do
that one is quite boring
there's nothing exciting about doing this
nothing exciting about doing this
but they will do it and they can do it.
In this case they'll probably say
"okay, this one is easy"
yeah the 43 and 21 part is easy
oh the 5728 part is slightly harder
but that's okay
I can rename it 4170.
But anyways... that's another strategy.
ask them to tell you that operation.
And if they identify the operation,
at least you are assured that they know what they are doing.
??? to the actual calculation.
And then even in the event they cannot get calculation
or don't like to do the calculation or cannot do the calculation,
at least you know that they're okay.
Identification of the Mathematics is more important than the computation.
The computation, eventually they are going to use some calculator
to actually get the answer
for example: in the PSLE
for numbers that are tedious.
Let me take some questions now.
My son always dream away in the middle of his work,
how do I get him to concentrate?
I think... we must first understand why he is dreaming away.
Some children dream away because the work is meaningless to them.
So that's what I have been talking about the whole of this evening,
we must make Mathematics meaningful to them.
How?
By being able to read the language.
Some children cannot read the language
they cannot read the language
for example in P2, P3
they cannot read this
correctly.
They cannot read this as one half
but that's what it is.
The denominator tells you what the thing is... hal
the numerator tells you how many
or three-fifths.
They say three upon five
nobody talks like that,
maybe once upon a time
somebody tlaked like that.
In modern day language we say one apple
we say three slices.
In modern English language we don't say once upon a time,
in modern day language we use number plus the noun.
We say three slices we say three children
we say three apples.
In modern English, we put number followed by a noun
this is what they are familiar with
number plus noun
which is what they are reading.
Three and the noun
fifth is a noun it's a name of that slice
it's a name of that ??? that you get out of one.
When out cut one in to five equal slices, that slice has a name... fifth
and then we write fifth using that symbol.
So, three fifths..
but for some reason we prefer to put it just underneath
so it's three fifths
It's like that right?
So many children cannot read it
that's why they think thing's are meaning to them
but actually it is quite meaningful.
So by P3, P4, P5 they learn things like this
like half and one-fourth.
They know even as a child,
one apple and one orange what do you get?
you don't get two
you don't get two apples of course not
you don't get two oranges any child can understand that right?
One apple and one orange is not two apples it's not two oranges
They know from a very young age
when the nouns are different, you cannot add.
Like three boys and two girls
you should be horrified to get five boys
you don't, so no need to panic you don't
And any child knows
that three boys and two girls don't give me five boys nor five girls.
What? Different type what. Different noun what.
And if I can change the noun then I can add,
three children and two more children ah business as usual, five children.
One apple and one orange,
one piece of fruit and another piece of fruit
that gives me two pieces of fruit.
So one-half and one-fourth
different kind, cannot add just yet.
Can I change the half into fourth?
Not so convenient or okay?
It's okay right?
Half is two fourths they learned that in P3 right?
Oh so now two fourths and fourth
business as usual same kind.
Children dream off because they cannot make sense of the gibberish
that is in front of them.
But when they can
when they can
they can do the work.
Like most of us are
probably not able to function if I give you something in Russian
if you don't understand Russian.
It'll be that exciting I ask you to read a page in Russian.
No matter now exciting or engaging the story is
you surely dream off and definitely give up
because you don't even understand the first thing about it.
This is the main reason why children cannot focus and they dream off.
So the big answer is make things meaningful to them
and earlier today I've also said "make things interesting for them".
A third answer to that is
remember these are children
and some of the children we have Pathlight
they do have attention issues you know that
your own children you know that.
Break things down for them
frame them up slowly
start with 10 minutes, go on to 15, go on to 30 minutes
don't expect them to be able to sit there for an entire hour
it's not possible.
Even for adults we do struggle with it let alone children.
So if your children dream off,
Two strategies.
The practical one: Just write things down for them.
Llet them do things in small bits and pieces
and that will train up their ability to focus.
But the bigger answer is make things meaningful for them.
I am sure you know your children can be engaged for a very long time
if it is something they are very interested in.
Like some of the children who loves dinosaurs
they will spend hours
watching YouTube or reading about dinosaurs.
Some of them like transports
and they will spend enormous amounts of resources, cognitive resources
learning what bus goes where, this bus goes through which route
I am sure you know that.
It's not that they cannot engage, it's not that they cannot focus,
it's just that the material is not meaningful for them.
So that's a bigger answer actually make things meaningful for them.
Let me illustrate a little bit more.
Bby now I think you know some strategies already
to tell how children process information
I use them all the time in every single example.
Here is the story never mind the question.
Important is to understand the story
once we understand the stories we can answer any question.
My strategy of removing questions.
Who is in the story?
This story has nobody.
What is it about?
Beads, what are beads? Do you know beads?
If you know them great if not we Google.
There are some beads in a box can you imagine that?
There are five times
five times
if I use this to be one time can you show me twice?
If this is one time, can you show me three times?
Or what Singaporeans call thrice.
Can you show me four times? Can you show me five times?
Engage your child using pieces of paper.
Tf they don't want to draw the model don't force them
let them use paper.
The purpose of drawing is to create the ability to visualise
so that they know the operation to use.
Pieces of paper for building the model serve the same purpose.
If they don't want to draw, this is your option
let them use paper like that to build the model.
The goal is to get the right operation
that's the goal.
And to get to the right operation, either you know it
for easy cases
or you use a diagram, a model to get to it.
So model drawing is to tell you the right operation
that's the purpose of model drawing.
It's not because they lose marks in PSLE.
Examiners don't care about your model
they don't even give marks to your model
they give marks to your equation.
So when they are young let them do those things as well.
Anyway, there are five times
what a long sentence
let's read it carefully.
There are five times
five times? I use five pieces compared to the other one.
There are five times
five times as many green as red beads in the box that is very long.
Okay, don't want the box ignore the box thing.
There are five times
as many green
don't want the beads
there are five times as many green as red
ah I understand already!
There are five times as many green as there are red
oh so this is green five units
and this is red one unit.
There are five times as many green as red
oh I understand already
there are five times as many green beads as red beads
understand already.
There are five times as many green beads as red beads in the box
understand already.
If I want to drawn, I can draw
if not I can use the paper just now
to say that green I use five pieces
and red I use one piece of paper to represent it.
Okay I understand that already I can draw.
Can I calculate?
Oh I can, but I got information like 78, where does the 78 go?
There are 78 beads in a box, okay
it must be all the beads the red and the green ones.
So the 78 must put into 1, 2, 3, 4, 5, 6
78 put equally into 6 boxes.
Parents, I hope you are seeing me applying
the various things I suggested earlier.
Always read as you write,
putting 78 equally into 6 boxes
I didn't say 78 divided by 6
that doesn't give them the meaning of whatever they are doing.
Many children eventually
does not became good enough in Mathematics when they get to PSLE
because they kind of wasted their six years
trying to understand gibberish.
It is really gibberish to them
they have no clue
what all these squiggles actually mean
so sometimes by luck they get it right
and often they get it wrong
and they struggle
they struggle because it's Martian to them.
But it doesn't have to be
and we adults, both parents and teachers
can really help them
especially for most of you your kids are in Primary 1, 2,3
still plenty of time to put all these into practice
in a more regular basis.
The teachers have spoken to them over the years
we have constant professional development
and they try to do this.
The information we share with you this evening
is for you to have the same consistent practice
so that your child can learn Mathematics
in a rather easy way.
So from there they will do whatever they...
This is a calculation for Primary 3
so 78 is too hard for me anyway
but I think I can take out
I think I can take out 60
60 is quite easy, I get 10
and then left with 18
18 put into 6 that one is okay, I get 3.
So 10 and 3, I get 13 as the value for 1 unit.
Can they do this mentally?
Yes.
For those of you with children who can do Mathematics mentally
sorry
For those of you with children who can do calculation mentally
encourage them to do so.
That is the end goal of learning calculation anyway
you learn calculation by writing it down
so that one fine day you no longer have to write it down.
Mental calculation.
Mental calculation is a pinnacle to learning computation.
By the way computation is arithmetic it's not Mathematics.
it's part of Mathematics.
Mathematics is a thinking part
the arithmetic is the computation part.
Some of your children like to do mental calculation?
That's perfect, that's alright.
In fact, those who are over reliant on paper all the time to do simple things
example, things like
things like 11 minus 9
it break my heart to see P6's do this
11 minus 9 what has happened?
really what has happened?
if you still do 11 minus 9 like that.
Then the best part is then they will do what the teacher taught them to do.
Like why?! You are still doing 11 minus 9 right?
So can't you like
oh what's the difference between 11 and 9.
So if they only read it, what's the difference between 11 and 9?
Oh the difference, so the gap between them 9 to 11, only two steps
So this will all translate into better things when they deal with bigger numbers.
When they have to do 401
then they will say
"oh what's the difference between the two numbers?
oh the two numbers are quite close 399 is only one step to 400
400 to 401 only one step
the difference is two.
Like that.
When you can read,
difficult things
become quite easy you know.
Let me just show you when your kids get older
when they get to P5
they do things like three-fifth share among 3
so when they can read this as three slices,
three whatever, three nouns, three-fifths
they will say
"oh three share among three is easy, it's one"
and the item is fifth so the answer is one-fifth.
For this case, it's so straight forward
but then I see P5 who does this because they do what adults tell them.
Maybe some of us tell out older children
"eh boy ah, remember ah dividing fraction very easy one
got formula. just remember ah
you change divide to multiply
and then this one you write as three upon one
and then this one you terbalik the thing lah."
Terbalik is Singlish for invert invert the thing
then you cancel your life away lah
then you get the answer right?
All that hassle for something that quiet simple
three whatever share by three the answer is one.
No need all that nuts and bolts and
all those nonsense
to just get to the same answer.
Just to illustrate that once you can read
a lot of things are actually quite straightforward.
Now let me take a couple more question's as we wrap things up.
Some of you are quite lucky
because your children seem to be doing really alright
better than alright.
How can I bring out the best of the child
which Is in primary 1 but he's able to do primary 4 Mathematics.
Any advise besides volunteered training?
Five things I would suggest
for those of us who have children
who seems to be quite capable in Mathematics.
How do you push them further?
I think part of the answer is this:
let them choose what to learn.
Since they already can learn what they are supposed to learn
let them decide.
Like okay you know there is this thing called prime numbers
and let them find out
if they are interested, they will pursue it
if they don't like it, they will ignore it
it's fine.
So that's my global answer
let them choose to do whatever they want to do.
No need to go to primary 2, primary 3, primary 4, primary 5 but let them choose.
Oh you know, your brother in P4 learned about factors and multiples
do you want to find out more about it?
Go to this website or watch this video or whatever.
So that's my answer actually
expose them to some things but let them choose
let them choose.
So that is more liberating
than sending them to cookie-cutter kind of enrichment activities.
What else can you do
if they are not ready for higher level content.
So some children are quite good
and these strategies can be applicable to all children actually.
If they are quite good,
and they can do their Mathematics quite easily
like they know their timetable in primary 2, primary 3 quite readily
what else can they do?
You can ask them to write a story
if they don't want to write you can always ask them to draw it.
Anyone can do this, not just the advance children.
But if they're advance, these are some things that are quite helpful
to further their understanding of Mathematics.
You can also ask them to explain
can be oral, can be written form.
So keeping a Math journal is quite useful also
a little diary where they record stuff.
I believe most of your children have a Math journal anyway in school
you can also have a Math journal at home.
I don't understand how come 9 groups of 7 the answer is whatever
why is it like that why is it like less than 70
and see what your child say.
And maybe they will say
"oh you see, 10 groups of 7 is 70 already"
oh course ah
if 10 groups is 70 then 9 groups must be less than 70.
In fact it should be 7 less than 70.
So if a child is fully advanced they usually can do this
they can explain orally
or if they have enough writing skills they can write it or draw it in their journal.
Finally,
they can challenge themselves
children when advanced will find avenues
to challenge themselves
and you can help them in that.
Example, maybe they do a lot of calculation
they do a lot of calculation in P3 when they are asked to multiply
a two digit number by a one digit number.
Like in a worksheet, quite boring actually.
you can say "eh, why don't we challenge ourselves".
We notice that the answer is two digit
but this one the answer is three digit.
and this one the answer is also three digit.
I wonder if it is possible
for two digit number multiply by one digit
and the answer is two digit
we know it's possible already we have one example.
But this one
this one the answer is 26 so the digit 2 is repeated.
I wonder if it's possible all the five digits
all the five digits are different
you know?
Let's find if it is possible.
So children who are quite advance will challenge themselves
but when they are younger they don't know what to do
so you can expose them to some examples and over time you should see them
you should see then challenging themselves rather independently.
Let me conclude now
with one final example.
Let's look at something that's more
involved.
In today's webinar,
the topic is helping children process information in Mathematics
So we need to know
the different types of information.
What are they?
Visuals, yes visuals
pictures, diagrams, graphs
some are from daily life,. some are more formal
What else?
Language, words, English
some are familiar like stories about bakery
some are quite strange about milk bottles.
What else?
Symbols.
So today we learned that these are the kind of information
children deal with in Mathematics
language, symbols, and visuals
and I have suggested some strategies
on how we can help them become better in processing those information.
Those are mere suggestions,
I am sure you can come up with other ways
which are equally effective or engaging for your children.
The webinar this afternoon is just to give you a starting point
to inspire you to try to make Mathematics more palatable
hopefully more exciting, more interesting for your children.
But if not at least meaningful
because Mathematics is a language
once we cannot read the symbols
everything falls blank.
Once we cannot read the English language with comprehension
everything cannot happen.
Symbols sometimes they really cannot read
like I said, children say three over five three upon five
that's really, cannot speak proper Mathematical language.
So it's like in English, the child only knows Singlish
sure fail PSLE English confirm
If all you know is Singlish and no understanding of standard English.
Likewise in Mathematics some children cannot read symbols
do help them
do help them by reading, don't by lazy and say three times five
say three rows of five three groups of five
fifty-one share among three twelve put into groups of four.
There are many ways to read
important thing is read, don't spell.
Let me demonstrate this final example
and you'll be able to see the various strategies addressing language difficulty.
Many of you raise questions
so many I cannot answer every single one of them live.
There are some important questions that I would still want to answer
so we are going to put this as a eCampus course
so some of your questions that are not addressed will be featured on the course
so do visit eCampus to revisit today's topic
and you might get other insights from the answers to
some important questions that were also raised
just that you know we only have less than two hours
there is only so much we can cover anway
but do go to eCampus to continue to get more ideas,
more information about this topic.
Oh never mind the question let's look at the story
notice the question is not there yet.
Who is in the story?
Oh finally we have someone in the story
Mrs Baey and Mrs Chia
I don't really know them but that's alright.
What are they doing?
They went shopping.
Quite a long story
one sentence...
two sentences...
three sentences alright it's a long story
but never mind one by one ,one at a time.
They went shopping
alright I can understand that
with the same amount of money
okay not too hard.
Can I calculate.
Can I calculate?
Probably not yet
no numbers.
Can I draw?
In this case I can, same amount.
So I can draw model that will make my teacher happy.
I can draw this
but sometimes I don't want to draw
it's okay, I said wait I want to read more.
So it's up to you
sometimes you want to do it straight away
sometimes you decide to wait maybe another sentence
it's better to draw or better to calculate
so you decide.
Parents, the final thing I want to share with you is
do teach children to make decisions
don't decide everything for them.
When you help them with Mathematics, don't always tell them what to do
that's not helpful.
Children that become successful in Mathematics eventually
are independent
it is a characteristic.
You cannot be not independent and be highly successful.
You may be artificially successful that means you get AL1 for PSLE
A-Star for PSLE
but my O-Level not so good anymore.
Some of them still quite okay for O-Level
but by A-Level, Polytechnic not very good anymore.
So at some point, they will become not very good.
They'll be found out.
So independence is a very important characteristic
do let children learn to make decisions.
"Do you want to draw now?
okay go on
don't want is okay
you decided".
If it's a bad decision it's fine
later we just correct ourselves.
"Do you want to calculate? Do you want to draw?"
it's a simple question you can ask all the time.
Alright, that is done.
They went shopping with th.e same amount of money
One of them spend so much
the other one spend so much.
Mrs Baey spent $480
so Mrs Baey...
spent $480
can I draw?
Yeah I can, I put in $480 somewhere but I want to wait.
I don't know how to calculate so cannot calculate anyway.
Mrs Chia spent $620
Can I draw?
Yeah, just draw Put $620 in.
that's what she had
she spent so much so that's what she had left.
I can do that, but I don't want to do it yet.
Sometimes I don't it straight away, sometimes I want to wait
I can decide.
Anyway,
Mrs Baey spent $480 and Mrs Chia spent $620.
In the end
Mrs Baey had 3 times
oh I can draw
I can draw how much they spent
and how much is left.
Do I want to draw how much they spent?
Or do I want to draw how much is left?
I can decide.
Whichever that is easier to do.
For me,
I think it is easier for me to draw
how much is left
because 3 times is easy to draw
3 times is like use the paper right?
It gives 1 time
this is 3 times
so 3 times is easy to draw.
In the end, Mrs Baey has 3 times
so I can draw that one
Mrs Baey has 3 times
So if Mrs Chia has this left,
Mrs Baey will be 3 times
one, two three.
So this is what...
what is left.
If I am afraid people don't understand me I can write, this is what is left.
So that means,
this is what they spent.
For Mrs Baey, it was $480
and for Mrs Chia it is $620.
Parents,
if they can understand all that
whatever question that is asked of them, they can answer
because from here, they will notice that well...
they do know the values
they do know the values of
of these two units isn't it?
I leave the Mathematics to you
but you can find the value of these two units
because you know the whole thing is $620
the whole thing as in the whole thing I have just drawn.
And this little bit here is $480
so I think we can find out the value of these two units
and the rest is pedestrian just a bit more of calculation.
And then when they are done... for those children who are more advance...
you can ask them to critique the diagram.
like "do you think this diagram is good?"
so they may say "oh it's not good"
or whatever reason they will say.
Say "oh look, the proportion is not right"
then they may want to draw a better one.
Right?
So that's my concluding example
for me to make two additional points about individual independence
but also inviting them to critique solution.
Parents, this webinar is about helping children process information
and we want to help them.
We can only help them if...
we ourselves portray Mathematics as a language
comprising of information given as visuals,
given in words, sometimes given in symbols.
Throughout today, in answering some of your questions
I have demonstrated some strategies that we parents, adults, teachers
we can use with children
to help them become better
in reading comprehension, making use of diagrams, pictures
words, phrases, sentences, symbols, expressions.
Right?
I want to thank all of you for spending your precious evening with me
and hope to see you again
hopefully in person
in the next seminar that we have.