Hello and welcome to another episode of Blooming Curious.
So, hey, listen, last week was a really important episode I feel for
many of us, and it was about how we help children with math anxiety.
So last week I interviewed Dr. Aditya Nagrath on the podcast,
and he is a mathematical expert and has written a book on math
anxiety and how to help children.
And we learned from him that he was saying that the majority of
children entering kindergarten today are already behind in mathematics.
And so of course, that really perked my interest.
So the reason that children are behind coming into kindergarten is
because they don't have mathematical language and understanding of numbers.
And you know, if I tell you a little story, when I was teaching pre-primary,
we used to do these tests really early on so that we could identify
children that potentially would be struggling with mathematics.
And then we can obviously tailor our programs to help them.
And I so distinctly remember there being some children where you would
show them it was very hands on test, by the way, it wasn't a paper test,
it was an interview test with actual physical objects where we would ask
children to count objects, and a variety of other methods of testing their
understanding of numbers and counting.
And you know, I remember there being one child where there was a group
of objects, maybe you know, five or six, and you'd ask them to count
them and they'd go, 1, 3, 25, 36.
This child had no idea about numbers or what numbers actually meant.
And to me, when you have a four or a 5-year-old starting their first year of
formal schooling, and they don't even know how to count from one to five,
they don't understand what the thinking is behind those words.
In other words, the names of those symbols.
That is pretty concerning because we don't have to be teachers or
have degrees in mathematics or be professors in mathematics at university
to be able to help children and prepare them to start school with
a really good basic foundation,
an understanding of mathematical language and mathematical knowledge.
So this episode today, I wanna talk about how we as parents and educators can give
children that basic understanding and set them up for success in mathematics and
not have that math anxiety that if you listened to the episode last week, Dr.
Nagrath said that 50% of Americans, which I'm absolutely sure we can equate to
probably the rest of the world, uh, 50% of Americans have mathematical anxiety.
In other words, they struggle with maths, they're worried about
maths, they dunno how to do maths.
That means that 50% of teachers, 50% of students, 50% of parents
also have mathematical anxiety.
And I really believe that it starts with the basics.
We need to be able to understand the basics of math so that we
can set kids up for a future.
And as you listen to today's episode, you will hear that everyone needs maths, not
just engineers and accountants, everyone, every single one of us, especially in a
unknown future where we don't know what kind of jobs or what we are going to need.
So even if you are not so great at maths, I was great at math in elementary and
primary school, but then I lost the plot in high school for various reasons, and
I think that that has really held me back in many, many instances because what it
did do was it destroyed my confidence.
It's not that I'm, ridiculously bad at maths or that I'm don't understand maths.
I actually do, I do have quite a logical brain, but I don't have confidence.
My confidence was destroyed somewhere along the line.
So today's episode is for each and every one of you listening to help to
establish that basic understanding of mathematical language and mathematical
concepts in children, to set them up with success so that they have confidence
and not be part of the statistic of half the world having maths anxiety.
So today we are gonna look at some practical advice, how you can do that.
So let's start with that right now.
Number one is that we have to build the language of mathematics in and around
everything we do and everything we say.
And we can start with things like positional language.
So for example.
You've got your kids and you're talking about, you're sitting on a chair,
the dog is lying under the table.
Or if you go to the park and you're talking about them coming down the
slide, or they're running around a tree, or they're running between the poles.
So start getting that positional language established, and all it means is that you
just need to be aware of your situation, aware of what you're doing and how you
can bring just normal, everyday language,
I mean, we don't even think of it as positional language, right?
But it is, and so we just bring that positional language into our everyday
language when we're talking to children so they can start associating those
words of under, over, in between, on top of, below, beside, through, when
they start to understand those kind of concepts, we are actually building
their mathematical language vocabulary.
The second way we can build that mathematical language
is when we're in the kitchen.
When we're in the kitchen, we're doing things with our children, especially
when you're cooking or you're baking, start showing them those scales and
the measuring cups and talk about, you know, the one cup or one tea spin, and
we need three eggs for this recipe.
Start using that language.
This recipe calls for 500 grams and this is the scale and this
is how we check for 500 grams.
So it's getting them involved, hands-on in a normal everyday experience,
which we don't even think of as being mathematical, but it absolutely is.
The next thing is comparative language.
Again, it's not something we think about, but it's absolutely imperative
so that children can start to use this language and understand it as
part of their everyday experience.
And that's things like, when you're sorting and classifying and reasoning.
So you can talk about one thing being heavier than the other, or something
being lighter than something else, or something being longer than something
else, or shorter than another thing.
So we're using that longer, shorter, bigger, smaller, wider, narrower,
something being broad and something being narrow or thin, we are using
this kind of comparative language so that children can start understanding.
And you know, there's that really great
activity or word that children don't know, and that is hefting.
That's when you're holding something in your hand or you're holding one thing
in one hand and another thing in another hand, and you're weighing them up and
you're trying to figure out your hefting.
Which one is heavier or which one is lighter.
Which one weighs more?
Which one weighs less?
That simple little task, that simple little thing that you can
do in your everyday experience of just, well, which one weighs more.
We don't always need a scale.
You can just heft and have a guess.
Those are the kinds of things that really are important for teaching
children this basic mathematical language and understanding, and with
this comparative language, of course, comes classifying and reasoning.
So you might be saying, okay, you're setting a table, which
kind of things go together?
Well, all the knives go together, all the forks go together.
All the spoons go together.
Well, why do they go together?
And you start reasoning through that?
Well, these objects are all things for cutting.
These objects are all things for scooping.
These objects are all things that you can poke things with.
So we have to start talking to kids and getting them to not just
arbitrarily group things, but actually try to get them to think about and
understand why they're classifying.
Why are they grouping them into those groups?
And of course, if you brought more items together, knives, forks and
spoons can also be grouped into one category because these are all
utensils or cutlery used for eating.
So there's a variety of different ways we can group and classify objects
according to criteria, which of course you try to get children to think
about for themselves and to explain.
So that's your building of language, mathematical language
for children, really important.
The next foundational skill we need to develop in children is probably
the first one, and that's counting.
Now counting has three major principles.
Firstly, it's the stable order principle, and that means that we name objects
according to their number order.
So that is when we are counting from one to 10, we're counting
them in a specific sequence.
1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
This is the stable order principle.
Before children enter formal schooling, like in their pre-kindergarten years,
they only need to do that up to 10.
It is once they get into their formal schooling years.
So in other words, kindergarten, if you're in the States or here in Australia, it'll
be pre-primary or foundation, then we need children to be able to count to 20.
But it is naming those numbers in a sequence and eventually
forwards and backwards.
So being able to name objects or count objects to 10 and 20, and then
to reverse it, counting backwards, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 as
they always love to put in as well.
And of course, the zero is a number.
It is a placeholder.
That stable order principle of naming numbers in order.
In other words, so children understand that each object, when you count
them, has a number, is a really important mathematical concept.
So a lot of children are able to recite numbers or just to
count, just to rattle them off.
Right?
And that's fantastic.
It's like when they're learning the A, B, C, that's only in the first part though.
They have to also know that when there are three objects, there are only three.
So it's not like that example I gave in the beginning when there were three
objects and a child may go 1, 7, 32.
That does not mean that you understand numbers.
It means that you can only count by rote to three.
It doesn't mean that you can understand them.
And then that brings me to my very next major principle, which
is one-to-one correspondence.
A one-to-one correspondence is that each object that you count has a value.
And then one-to-one correspondence is really important that children
actually physically touch the objects.
So they will take one object and count it as one, and then the next
object as two, and the next object as three, and the next object as four.
And this you can do in lots of different ways.
So, for example, in your everyday life, you are forever counting objects.
We don't even do it as adults anymore.
But remember, children don't have that skill yet.
So if you're setting the table very simply count the plates that you're putting down.
They actually physically putting down one plate, then two
plates, then three, then four.
The same with a cutlery, the same with the drinking glasses.
And even when you're doing things like folding up laundry,
let them count the socks.
They're taking one sock at a time and counting them, or they're taking one
t-shirt at a time and counting it, or they're putting away their toys at
the end of the day into a toy box, and they're counting each one of their toys.
That is the one-to-one principle.
They need to be able to understand that every single one of those objects
has a value associated with it.
The next principle is the principle of cardinality.
Now that means that we recognize that the last number that you speak in a set,
for example, is the total of that set.
So if you were counting those socks and the child was counting and picking up
each sock out of the basket or into a basket, or each toy or whatever it might
be, and they're counting, you know, 1, 2, 3, 4, 5, 6, and then there are no more.
The fact that there are six means that there were six toys or six socks in total.
The last number that they spoke was the total number of objects.
Very important.
Cardinality.
Once they have all these three principles, so now they've got the
stable order principle where they're actually able to name each number.
They've got the one-to-one correspondence and they've got cardinality.
You can now step it up and you can then start them from counting anywhere.
So children need to start understanding that they don't just
need to start counting from one, but in fact that you can start
counting from six or 10 or 25 or 35.
And this is also useful when, for example, children have to count a random amount
of objects or maybe even objects that are in a circle, or where do you start?
Well, you can start anywhere, right?
And that really also requires for them to have a strategy so that the
same object in that random organized, pattern, whatever you wanna call
it, is not counted more than once.
So they need to think about a strategy, you know, maybe they want to move that
object out or put an object, something next to it, or put a finger on the
object, whatever it might be, so that they don't count that object more than once.
So that's really important too.
The next skill they need is subitizing and subitizing is when you instinctively
recognize a quantity or group of objects as having a number without counting them.
So if you think about, uh, dominoes, for example, or even a die one, die many dice,
those dots should be recognized without having to count each one of them each
time you roll the die or each time you have a domino in your hand, the pattern
in which those objects are arranged, we should be able to instantly recognize.
So when you see those three dots, you don't have to start counting them
1, 2, 3, you know, it's three.
And this concept of subitizing comes in really handy when we are
learning addition and counting on.
So for example, you see three objects and you know automatically that's three.
You don't have to start counting them as 1, 2, 3, you know that's three.
So if you're counting on, three and then you're counting two more.
You start with 3, 4, 5, and you know, then that three and two make five.
So that whole subitizing, the concept of subitizing is a really important one that
helps children eventually with addition.
So playing card games and playing dominoes and games with a die
rolling their die are really important for learning those skills.
So now let's have a look at practical ways where we learn or help children
count in everyday experiences because we can count in lots of different ways.
And we can help young children count in lots of different ways.
One of the, probably most favorite ways in any pre-kindergarten or kindergarten
classroom is songs and rhymes.
So we're singing and we are singing songs like, 1, 2, 3, 4.
Five, Once I Caught a Fish Alive, or Five Little Ducks, or 10 in a Bed, or 10
Green Bottles, or One to Buckle my Shoe.
Those little rhymes are really important, not just for teaching phonological
awareness in terms of the sounds in words, but also for getting a mathematical
understanding really well established.
So there's rhymes and songs.
Really good for teaching children about numbers and understanding of numbers.
And then we can also combine numbers when we read picture books.
And there are so many fabulous picture books that all have to do with numbers.
There's one duck stuck.
And by the way, I'll put all these for you in, in a blog post, and I'll put links
in the show notes for you so that you can go and have a good browse about the kind
of books and songs I'm talking about.
If you think about those basic books, like The Very Hungry Caterpillar,
or How Many Legs, or One Thing by Lauren Child, for example, one Fish,
two Fish, red Fish, blue Fish by Dr.
Suess.
All these books really involve mathematics and very, very important to help children
understand mathematical language.
The next thing, of course we've already touched on is to
count absolutely everything.
You count the number of steps from your kitchen to your bathroom, count how many
steps to your front door, count how many
toys you have in your toy box.
Count how many books on the shelf, count how many knives and forks,
socks, , absolutely everything.
When you're cutting up a piece of fruit, ask children to count
how many pieces there are.
Count the numbers of houses on your street, wherever you can count.
Count.
The next thing is to go on number hunts, and this is a
really fun thing for children.
So you go on a number hunt and you find numbers in the environment.
So these can be numbers on signs, numbers on houses, numbers on on
doors, numbers on number plates, just everywhere where you can find numbers.
So a number.
Hunt is a really great activity for children to start
understanding that numbers are all around us in our environment.
The next thing is to pretend play, to set up a pretend play area in your homeschool
or in your home or in your classroom where you, for example, set up a shop.
This is really crucial for teaching children about money and numbers,
so you can actually get tin cans out of the cupboard, or
you can go and get pretend food.
There's no need to spend a fortune on buying these little kits of pretend food.
Just use real stuff that you have in your fridge and use real stuff that you have
in your grocery cupboard if you need to.
And what you can then do is then attach prices to those items, and you
can just write those prices, or the kids can write the prices on a sticky
note and attach it to the object.
Or if you wanna get fancy, create prices or cut them out of food catalogs or
whatever you have on hand, and children can then learn how to count money Now.
In today's world, getting children accustomed to counting money is a
really difficult thing to do because everything is now digitalized and we
now just tap our cards and off we go.
We are no longer dealing or handling cash, which makes things
really difficult for children.
So getting some pretend money, for example, or even creating
pretend money, doing it yourself on paper is a really handy idea.
Children then get to realize and recognize and see the patterns on money
and the different features on money, the different shapes of coins, for
example, and the features on coins.
And they can learn how to count money using those coins.
And then also the notes, the paper notes.
So those are really important features, especially nowadays when children
have such limited opportunities for counting money in our digital world.
But that is still an important feature of counting and learning
about money and quantities and giving change and all those things, but
that, you know, comes incrementally.
You can't expect a child for the very first time they're playing in a shop
to start giving you the correct change.
I think it's most important just for them to understand with when you go
to a shop, everything has a monetary value and we then have to pay for it.
How do we pay for it?, How much money do we need?
Those kind of concepts are very, very valuable for children and
something that you need to be talking about right from the start.
Great opportunity when you go shopping, children don't need to be
running around, throwing tantrums.
Have them in the trolley.
Get them involved.
Get them counting those apples that you're putting in the trolley.
Let them count the things that you've bought.
Have a look at the prices, and then obviously at the checkout, get them
to experience that whole checkout experience of how we pay for things.
You can also into your pretend play area, introduce scales so
that children can start learning about weight and how to use scales.
Again, unless you've got access to a fresh fruit and vegetable market or a
green grocer where they're still putting things on scales, children aren't going
to be having those experiences anymore.
So that's why it's so important for them to see you weighing things
in your kitchen when you're doing baking or whatever it might be.
And you can also introduce that into their pretend play so that
they can start experiencing how one weighs something using a scale.
And of course along with pretend play comes a playing of games, card games
and board games, and a whole host of other games where counting is involved.
Again, you're playing with a die or two dice even so there you're
practicing your subitizing of looking at those dots on the dice.
In the beginning, they may have to count them, but as they play more with them and
as they start recognizing the placement of those dots, they'll very easily be
able to then subitize and just know that that arrangement is three, that
arrangement is four, that arrangement is five or six or whatever it might be.
They also learn how to start taking turns.
Playing games is such an important part of our social fabric 'cause you really
start learning more than just the math, more than just the rules of the game.
It's also about fairness and taking turns and being polite and all
those kinds of things, and being a good loser and a good winner.
So when they're playing the games, of course they're learning how to roll die.
They're learning then that whatever the number is that they roll,
that is how many spaces they move.
And when they get to the end of the space, they leave their
counter there and they stop.
Really important, all parts of mathematical language and counting.
Another really important part of establishing this foundational
mathematical language and understanding is the playing with shapes.
So playing with shapes develops hand eye coordination and spatial
awareness and spatial recognition, and teaches children patience.
So if you've ever taught or if you've ever seen children playing with those
shape sorting toys or with a puzzle.
Being able to coax that child into continue playing through your own
enthusiasm and showing your own resilience and your own grit and
tenacity, that's what keeps kids going.
So when they get frustrated, you show them how they keep going because puzzles
are a really great way for teaching patience and grit and perseverance.
Not to mention all the spatial recognition that comes with that.
And of course, jigsaw puzzles, tangram puzzles, the shape sorting toys, as I've
said, all those kinds of things are really important for that geometry and spatial
awareness that children need in terms of their basic mathematical understanding.
And if you think about it, all of us, when you're designing, or figuring
out your furniture placement in your home, we're using those spatial
awareness and that geometry to do that.
If you sew and you've gotta cut out clothing patterns, you've gotta
know how you're gonna place those patterns on a piece of fabric.
If you're an architect, if you are an artist, if you are a builder,
all these people use spatial recognition and shapes in the process
of their jobs or their hobbies.
So geometry and blocks and spatial recognition is a really
important part of establishing that foundational mathematical
understanding in our children.
So what else can we do when we're playing with shapes and blocks and things, we
can also, for example, sort and classify.
This is another part that's really important.
So when we're sorting and classifying, you are asking children, okay, so
which shapes would you put together?
And they could do that in a variety of ways.
Perhaps they put all the ones with straight edges together, or the ones
with curved edges together, or perhaps they put triangles together and they put
squares together and they put rectangles together and they put circles together.
It's up to them as long as they then can describe their reasoning behind it.
Again, remember I've mentioned this before, the reasoning behind
the way they classify shapes or classify objects is really important.
Why did you put those things together?
Very important for their mathematical understanding and mathematical
reasoning and problem solving.
So make sure that you encourage them not only to sort and classify shapes, but
also to explain their reasoning behind it.
And then of course, we can also use, as we've said, describing
the features of the shapes.
So have a look at these, these have, straight edges, these
have corners, these have curves.
Making children aware of the different features of shapes so that they eventually
later on can classify shapes according to their characteristics, which is also,
by the way, part of the curriculum.
The other thing that you could do is when you're using blocks and you
can build towers, but then you can actually extend that child's reasoning
by saying, okay, here, we've built a tower with 10 blocks now still
using the same quantity of blocks, the same number of blocks, 10 blocks,
see if you can build a different tower or a different shape.
So again, you're getting that problem solving ability going in your children.
Very important.
Another thing we can do is make patterns, a very important pre-algebra concept.
And patterns can be made with absolutely anything with your normal household
objects that you find run, lying around the house or lying around a classroom.
Patterns are really important for exploring number, pattern,
of course, shape, and symmetry.
So the first thing we can do is we can look for patterns in our environment.
So you can go, for example, on a walk and look for manmade patterns
and look for patterns in nature.
Circles, rectangles, squares.
Uh, a pattern of course, is anything that repeats.
So all sorts of patterns.
You know, there's patterns on tree trunks and barks, they're natural patterns,
they're patterns in our paths and our, uh, our brick driveways and how bricks
are organized in a wall, for example.
There are patterns everywhere and it's just a matter of becoming aware of
them and making children aware of them.
So we first, we could look for patterns in our environment.
We can make patterns also without everyday objects.
So for example, you will start, maybe you've got, I don't know, your socks
while you're doing your laundry.
Maybe you've got some red socks and black socks and yellow socks.
And so you start the pattern, red sock, black sock, yellow sock,
red sock, black sock, yellow sock.
And then you ask them to continue.
Or maybe just start with two.
The ab B, AB B pattern.
So you'll just add red, yellow, red, yellow.
And then they continue.
Eventually we want children to initiate patterns on their own.
So in the beginning, you start the pattern and they continue.
And then further on down the line, they initiate the pattern
and continue the pattern.
Now patterns are not just be made with physical objects, but
patterns can also be rhythmic.
So patterns can also be your claps.
For example, we all know how to, how we are clapping those little beats, you know,
like one, two, that kind of pattern, and then they copy it and they repeat it.
So patterns are everywhere.
We can also make patterns with musical instruments, with your drum
or bells or triangles, for example.
Anything where a sound, or a shape or a color is repeated in
a rhythmic fashion in a pattern.
Those are patterns.
So we use numbers every single day, and children need to be immersed in
the language of mathematics so that it becomes a natural part of their every day
experience and to avoid that math anxiety that Dr. Nagrath was talking
about in last week's episode.
There is also, I want to make this very clear.
There is no need for a math textbook or a counting book.
You do not need to spend your money.
On such things, what you can do is just use your everyday objects in your home,
everyday objects in your classroom,
be it blocks, be it seed pods, be it pebbles, be it buttons, be it
macaroni, be it whatever you can find in your everyday natural environment.
Children can just count those.
Right.
They do not need fancy textbooks, in order to get a basic foundational
knowledge of mathematics and counting.
Children need to experience mathematics in a hands-on manner
in their everyday environment and in their immediate surroundings.
Things like going on a simple walk, as I've already mentioned, provide so many
opportunities for learning for children, not only to get them more curious,
where they can recognize their immediate surroundings, where you get them to,
recognize patterns and textures in nature, or hearing the bird calls and being
able to identify them or distinguishing between different plants and trees
and making them aware of their natural surroundings and the beauty around them.
Going on a simple walk is also the perfect opportunity to learn mathematical
concepts and the language of mathematics.
You can get children to recognize patterns in their surroundings.
If you've ever gone for a walk with a child.
You'll know that they love picking up objects, be it feathers, pieces of
sticks, rocks, whatever it might be.
And instead of telling them to throw it down and leave it because it's dirty
and yucky, take along a bag where they can actually collect those objects
and you can then bring them back to your home, bring them back to your
classroom, and they can then learn and use those objects to make patterns,
they can use them to classify objects, and sort them.
So many, many great learning experiences can come from a simple walk, and to help
you with that, I actually created two great little resources for you to use.
The first one is a little lesson plan.
It's free, totally free, and it goes along with a little picture book
called I Went Walking by Sue Williams.
And there I have a little lesson plan for you, which includes
literacy and math and science.
And you can then take that little lesson plan.
It's a whole week's activities for as long as you want to, actually,
it depends how deep you wanna go
and that little story I Went Walking, not only does it help you to nurture
children's curiosity, but also their literacy, their art and maths.
'cause you're gonna be doing problem solving, you're going to be doing
patterning, you're going to be doing sorting and classifying.
A whole bunch of things just to that one little story I Went Walking.
So I have that free for you, and I'll put a link in the show
notes so that you can get that.
The other thing is that I've also created a little e guide for you and
it's how to nurture natural curiosity in children, and that is just a great
explanation of how when you go on a walk, it opens up that whole world
of different learning experiences for children, including mathematics, and
that's a free little e guide for you.
And I will put links in the show notes for that so that you
can go there and download it.
There are endless opportunities all around us for ensuring that we give children
the confidence they need in mathematics.
Being confident in mathematics helps us in so many ways.
It's not just for engineers and for accountants.
We all use mathematics every single day, whether you're a homemaker,
a teacher, a designer, an artist,
or a plumber, maths is part of our everyday experience and all our lives.
I hope you found some value in this episode and that it's given you
somewhere to start when it comes to developing children's confidence in
mathematics and also to develop a love for numbers and problem solving
Because these are the tangible experiences that set children up for
success in a very uncertain future.
So thanks for listening today, and I really hope that
you have found some value.
And if you have appreciated the information that I've shared with you
today, could you do me a massive favor and click on that share button and then
send this episode to a friend or to a colleague so that we can spread the
word about the value of Blooming Curious to parents and educators everywhere.
So, until next week.
Remember that curiosity is your superpower, and so stay blooming,
curious, and remember to check the show notes for those free downloads to get
you and your students or your children well on your way to having confidence
and love for mathematics and numbers.
I'll see you all next week.
Take care.