Blackjack, I feel like it's like absolutely compulsory, right for
a six-year-old because this Edition combinations,
unfortunately, like discrete math.
That's very short shift in the math, curriculum, right?
You just gently, you forget about it for a long time.
It's Counting. Hello, welcome to data, shatter
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There is an ongoing debate on when children should be taught
to code. One group of people say that we
should be starting at a very early age.
The other group says, leave them kids alone.
They learn when they have to the argument continues on social
media and newspapers opinion Pages.
What about data science and analytics?
Do is there a right age for children to get started?
My guest on today's show. Argues that means to be in Using
at least the Core Concepts to children, as early as the age of
six. His name is Rahul draggable.
He is a multi-city educator and founder of Beth school.
We to a Montessori School in Bangalore, before getting into
education. The other was in the corporate
world, working in Impact investing, and then, with Amazon
over the years traveler, and I have had many haiji
conversations on various subjects, and this one is no
different. Enjoy.
Rahul show you run a Montessori school for the benefit of our
listeners. Can you give a brief
introduction to Montessori and also into Elementary which which
I think very few people really know about.
Yeah, sure. So Montessori is a methodology
of Education, which was introduced by the Italian
educator and physician Maria Montessori.
Maybe I'll give a little bit of context about Montessori herself
so that we can take the conversation forward in space.
Connections to Montessori was Italy's first female doctor.
So she was one of those people who set her mind to Medicine
where we already on there weren't many Avenues folklore to
actually study but she fought hard against the establishment
of the time and went and got her medical degree after she did
that again, you know, there's a problem in finding work at the
right place and so on and so forth, but she finally ended up
as you know, A person who work with so called idiot said and
that was the formal term at the time children who are having
some disadvantages, mentally speaking, and she started
working with them. She didn't know much about such
children, but she kind of just figured out that she could
potentially teach them in slightly different ways.
And she rested upon the work of, you know, various scientists
that came before her and she introduced some Allergies that
she started testing out on these children.
And because, you know, these children were so-called NoHo
pause, these experiments were allowed that.
Nobody really cared about. What is this woman doing with
these children, you know, go ahead and try whatever you want.
So she tried a bunch of stuff and she realize that, hey, some
things about about 23 years later.
He knows people at her, about her work and they said, hey, you
know, we're starting the school for children that live in slums.
It's in an apartment it sir. A really decrepit apartment and
is still a randomly running around, can you come and just
run a school for because then they'll be occupied and these
were so-called normal children, right?
There is no deficiency of any kind.
So Montessori said fine, I'll do it.
She went to this apartment. She set up her school, and she
took the same methods that she had developed with these
so-called idiots, and started deploying them in the school.
Right? And this school in a year of, so
became a sensation broken. And why was that?
Because at that time, it was unheard of for any child to be
reading at the age. Of 52 is really unheard of, for
any child to be doing, you know, math operations, at the age of
five, but somehow Montessori using these techniques that she
involved with deficient children managed to pull this off and
pull this off in a way in a school that look totally
different from any other school, right?
The teacher seem to be just sitting around.
The children seem to be doing what they wanted.
They were no desks per se. There was no board children of
all ages were together. So, just look really weird of
looking at it from the outside. Put these amazing results
started to happen and then she went and demonstrated this in
different cities and people started understanding that
perhaps is a new way, which we can educate, right?
And that started the Montessori movement.
Globally. This was the early 1910s.
It's the movement process about 110 years old and is very
popular in India, in particular, because Montessori, during World
War Two was actually a captive on Indian soil show seen as an
enemy alien, because she happened to be here and she
wasn't allowed to go back. And when she was here, she set
up a whole number of training courses and so on to help build
the Montessori method in India, and from, that period onwards
Matsuri is been around in India. Tagore was a big fan.
Gandhi was a big fan and you have, you know, the whole
so-called anganwadi system, which is, you know, the Indian
government's initiative to educate preschool.
Children across the country is basically a mode signal.
All of that being said, though. Montessori is known primarily in
India as a preschool method, right?
And as you pointed out, it's not really known as something that
can help children beyond the age of six, right?
But again, interestingly, it was in India or well.
Montessori was here in kodaikanal in the late, 1930s
that she really developed the Montessori method for children
from the ages of 6 to write and the Montessori method.
Also now exists for children from 12 to 18.
So globally, there are tons and tons of schools that go up to 18
in India. Today.
There would be video about 70 to 100 schools, that offer the
monastery, Elementary approach in a place like Bangalore there
about 25, but there's a mini. Lotion happening in the last
couple of years and we kind of see this as the beginning of the
curve exponentially growing in terms of having more and more
modest three schools in India, right?
So that's why we are and if I have to kind of summarize, one
of the key aspects of the approaching, like a simple
manner as I can write. The first and most important
thing is that we want to build children who are self-directed
learners. Conventional School, builds
children, who are learning because somebody told them to
you or was studying to get marks for was studying to keep their
parents happy, who are studying things that others told them to
study, right? Montessori.
We try to do completely the opposite where we want children
to choose for themselves, what it is that they're interested in
and go deep on that topic, right?
So the philosophy of education is diametrically opposite and it
Leads to a couple of interesting things.
First, it leads to a certain sense of concentration that we
start building incident, very early on right?
And you know, you're a Montessori parent.
You may have seen this that children, when they're choosing,
what they want to do, can spend an extraordinary amount of time
doing it versus giving them a problem set of say, do this math
question. They must like less likely to
spend a lot of time on it. So the belief The choice based
on interest leads to concentration is a very deep
inside and that's something that you will see all the time in the
Montessori environment. The second thing is there is no
such thing as a period of time. And we're all used to in our
conventional schools, right there.
The bell rings, every 45 minutes and then we switch from math, we
go to language. We go to Hindi, you go to PT.
We have a break in Montessori schools.
We have what is called a three year cycle?
I'm Rid of my first first-ever internship in the middle of
undergrad. I was two years of engineering.
Then I go to this company and I start working at 8:30 and I'm
the wells, the belly because I was completely unused to working
on one thing for more than 45 minutes a day.
I think that's, that's true for most of us know that we're just
not used to spending time. And I think if we don't spend
time, it becomes quite hard to solve hard problems that take
time and we end up being For things to do that only take a
small amount of time. And so the real world comes as a
shock to us. And so one of the key things in
any good Montessori school is that they will be what is called
a three our work cycle. Right?
And this is a period of time with children are free to choose
what they want to work with and work on it for that duration of
time. Our experience has been that as
the children grow older, that three are sometimes becomes for
out. Sometimes becomes fibers and you
have had to even consider extending the school day.
Because these guys don't want to go home the still working, and I
think that builds in both the work ethic and the sense that
great work takes time, and it just doesn't happen like that.
And I think that's a very valuable thing for young
children to have that sense that, you know, great things
take time. Okay, that's that guy.
So that intro now coming to the more, to the closer to the topic
of this podcast. So, so how is, let's just take
the example of maths, right? So how is mad?
I sort of thought differently in Montessori compared to
traditional schools. Maybe you could talk about both
the I don't know what with the three to six years and the
elementary years. Yeah, I think so principally.
The Mantra City View is that we must first give work to the
hands and trust that work to the hands translates to concept
building in the mind. Right.
And what does that really mean? It means that if you want to
teach a child math, you've got to make them play with math.
Using some materials that are available versus giving them
pencil and paper and asking them to write the numbers from 1 to
100. Right?
And which is the way, most conventional schools.
Even preschool will operated you start learning one.
You write one. You learn to you right to and
you go on till whatever number you go to Montessori instead
says that. Let's have some Thing where the
child can touch and feel one, let them touch him.
Feel to get them really understand the difference
between one and two. Let them sort out numbers in
certain orders either ascending or descending.
Let them sequence it out in interesting ways that them truly
play with the math. Don't want to see?
We never say Play, we say, work, what's really happening is that
there is informal, exploration of math, sensorially, in other
words, they using their hands to actually engage engage with
mathematical Concepts before it's translated into the
abstract math that we know of, right?
And that turns out to be a really, really important step.
So for example, in Montessori, the early thing that we offer
children after we introduce them to, you know, 129 and so on is
the idea of the decimal system, right?
And that's a really important idea, because if you think of
our schooling after nine, we just sort of take it on faith,
that 10 comes and we write 10 in a certain way.
And then you write Levin in a And we keep writing.
You ask a child wise 21 written as 2 & 1.
Most likely don't have a very good answer but it because it's
never been offered to them. In that sense.
They do has been told that this is what happens after 1920 comes
and then 21 comes instead Montessori in words that to say.
Hey, let's actually show the child.
How do we construct a large number from these small symbols
that we have of 0 to 9. And that's a tremendous Insight.
That's the inside of the only humans, right?
Who kind of figured out a way in which you can represent large
numbers using small symbols. And so we introduced very early
on the decimal system again concretely, right?
So again, if you've gone to the Montessori School, you would
have seen what we call the rod of 10, we'd have seen the square
of hundred and the child is then sort of discovering that 10 rods
of 10, put together becomes the square of hundred and similarly
10 squares of Comes the cube of thousand which are actually
seen. You're lifting it and you kind
of sense. Totally feeling.
Hey man, this thousand cube is heavy.
This hundred square is quite light.
But if I put 10 hundredths squares in one hand and I
compare it with the Cuban, the other hand, they weigh the same.
So the getting this really sort of Hands-On and truly little
baby, a sense of what quantities are actually, right, and that is
really, really important. They're not just seeing it on
paper and writing. Different numbers, they're
actually holding them, you know, moving them, weighing them, and
all of these things under learning how large quantities,
get constructed as they grow older.
We follow the same process where there's actually a, you may not
have seen this yet. There's actually a huge queue
for 1 million. So we take the 1 million where
it takes for children to lift it, right, and we compare it
with that one bead, which is the unit and we ask them to reflect
on it. And that's a really powerful
moment for a child because they truly then understand, man.
What is 1 million? Always exist, you know, one
followed by so many zeros, right?
Who cares when you actually see it in front of you like that.
It makes a tremendous difference.
Right? So 326 is all about that.
It's all about having different materials.
That concretely, represent quantities, and allow the child
to start understanding basic numbers, large numbers of
operations, with these numbers, with no addition, subtraction
multiplication division, and that usually sets up fairly
strong Foundation. For what is to come next, which
is in the element Rios, right? Are things that are covered in
the Montessori. The three to six years different
from were discovered is the at the same age, another school.
Yeah, so they are different in the sense of I'll give an
example, right? So in the Montessori World, once
the child understands quantity. Well, we think that there's no
reason why they can't add to 4 digit quantities together.
In the conventional World, literally in, you know, in kg
to, You'll add two single-digit numbers in grade.
One. You'll add two two-digit numbers
in grade 2, you'll add three digit numbers.
And that's how you proceed. Right, which is Criminal
actually. Because the concept, relearning
is addition, whether it's a two digit number of four digit
matter, doesn't matter, right? It's absolutely out of question.
So, first thing is, we offer more difficult things early on
focusing, on the concept, not on the representation of the
Concept, right? And that's a key difference.
Right? Like in the cities.
For example, that I gave you. The other example is in
Geometry, right? So, I think a lot of arithmetic
when you think of math in schools, we don't really think
of geometry. And if you think about your own
geometry education, basically didn't exist till you were in
grade six or something, and fix. I remember Euclid's axioms
coming in late, 2007, and then that's where it started off.
So yeah. Yeah, exactly, right.
So suddenly Things Are Grade 6 of grade 7 again, which is a
tremendous waste because if you're dealing sense, so really
with the world, the first thing you see around you are shapes,
you see shapes and you see colors, that's literally the
babies experience of the world. Right?
So it's a tremendous success opportunity early on to offer a
lot of geometry, right? And in the 326, it's a lot of
names that you kind of see something here.
That's a triangle. You see something else.
That's a quadrilateral and the 326 child is also You know,
Montessori says they have what is called the absorbent mind,
which is that they just pick up things like they learn to walk
by looking at you and they learn to talk by looking at you.
They acquire language incredibly fast, right?
So it's an opportunity to offer language or various kinds.
So we offer a lot of geometrical language.
Wait, so they'll end up, you know, looking at really weird
shapes and they'll know the exact term for it and so on and
so forth. And we introduce all of that to
set the foundation for what comes next, right?
So, purely from a curriculum point of view.
Yeah. It's very concept heavy and it
goes quite far much. The compared to water
conventional school would go in the elementary years now.
Things are a little bit different, right?
Because the child is no different.
The child, in the elementary years is really a strong reason,
or in the younger years. They are absorbing things.
It's putting things in their mind.
They're not perhaps reasoning as well about them when they're six
and or even five five and a half six to start saying that they're
asking a lot more intelligent questions by putting together
information. They've already acquired in the
last few years. Use and that just multiplies as
they go into the reasoning phase.
At this time. It becomes really important or
now go deeper into different concepts, and it becomes
important to start contextualizing, everything that
the child is learning, right? So, for example, I don't know if
you saw the around few months ago.
There was a stick. Talk video of, you know, of
thing, American High School student, who is learning math
and she complained for 10, for the 22nd, saying, by Inner
learning all this, it seems useless.
I became viral and everybody made fun of her and things like
that, but I'll send it to you. But the point was that she was
absolutely right that and even if you reflect on our
experience, why did we learn trigonometry?
Nobody told us why why we are in jaii.
So we like to do is there in the that's the answer right there.
Is that in jaii, so you better study at our table.
It becomes really, really important, especially in a
philosophy of education, bordering on centering on choice
and interest, but we start telling children why they're
doing certain things. Right?
And so we can't just give geometry.
We can't just give arithmetic. We need to contextualize it with
the Y, right. So, the most important thing
that we do in elementary is we start offering a lot of history.
So history is the super subject in elementary and every subject
comes out of History, which is a very different way of looking at
curriculums. Right?
So the first thing that we'll do then each child who enters the
Elementary classroom is will offer what is called the story
of the universe, right? Which is the big bang.
I drove attending this docket my daughter to school.
I think you were also there for that talk where I was like, what
is happening? What's for a dollar?
But I think now you're sort of putting into X.
Yeah, so the first thing that we do is we feel that it's really
important that children understand their place in the
universe, right? So we start with 0, Avi, and how
did we get here? And that really starts with the
big bang, it goes into how the stars were formed and how did
the planets formed and how did the Earth get formed into the
shape and form that it is today along with that we start going
into okay. The earth was formed.
What happened next? Oh, life emerged different
animals. Came different plants.
Came what? Next.
Oh, lot of things happened. And you know what?
The humans came at the very end, right?
We didn't come right in the beginning.
We are at literally the last few likes of this long journey that
Earth has had. But then we say now that humans
are here. We've done a bunch of great
things right there created this thing called fighting and we
created these things called numbers, right.
And we want children to understand and appreciate that.
We are all standing on the shoulders of giants, right?
And we want them to have that sense of Gratitude for what came
before and Inspire them to learn and do more.
And we feel that's really, really important.
Because otherwise, why am I doing all of?
This is an important question that we never answer for
children. So we do all of this
contextualizing through history first let and you know just
happens in the first couple of months as a child enters the
classroom and now they're ready to go deeper into specific
things. Right?
So if you take anything, right? And we can now come to data
science, for example, right? We can ask the question.
Holy probability a much and will turn out this wonderful human
story somewhere, right? So I don't know if you know, but
the first formalization of probability comes in the 17th
century because there was a gambler, you know, he was losing
a lot of money. You want to figure out how to
make money. So he went to Pascal and former
and he said, you know, I'm playing, you know, it's
something that dice or whatever. And the question was, if I throw
24 times, how many times for a certain pattern emerge not able
to track this? Problem.
What do I do? Right?
And he doesn't just ask anybody goes to Pascal and former,
right? And these two guys get together
have a solution and then put forward the first formal
Treatise on probability. Well, I didn't do to 7/2.
Yeah, exactly, exactly. Right.
So if you look at basic numbers and all its long back, but a
first formal formulation percent probability, 16th century, 17th
century. It's very, very late.
And once children sort of have taken time to digest, it,
they'll make Same observation as you know, that's not so long
ago. It's just one radius back,
right? And suddenly, it seems more
accessible to them. And then they relate to way.
This is guy called Pascal order. 3, Pascal Loop.
Let me go, look them up and we'll find Pascal's triangle or
will find other interesting stuff.
They look at four miles, of course, very interesting figure.
They look at Kye. What is gambling, right?
Is again a very interesting point and we'll talk a little
bit about it because and we can talk about it now because really
important thing is if you're playing with With math, which is
the true Insight of how we learn.
If you learning probability, you have to play card games.
You have to play, Blackjack Blackjack.
I feel like it's like absolutely compulsory, right for a
six-year-old because this Edition combinations and
understanding our Edition combinations.
Ladder Jack. You said, is that capacity for a
six-year-old? Yeah.
Okay. It's official kids edition
combinations at the end of the day, right?
I mean values are also some representation that a Jack is
also a 10. Then those exactly exactly.
Yeah, which is fairly straightforward.
We have six year olds, who played it, and who kind of
played well and it's quite straightforward.
It's not that complex. But the sort of path from
Blackjack, to Poker. And in parallel to bridge is
quite self-evident as a tool for teaching probability and well,
of course, not prescribed by Montessori per se Montessori
pedagogical principles demand, that it happens, right?
And it will happen inside. Good classroom.
Oops, I mean that's an aside but if we come back the idea is we
have to first contextualize and contextualize through stories
that and you can think of so many stories on probability that
you can just sit there for 5 minutes.
We'll come up with 20 stories that we have, you know, the
story of the Reverend Thomas Bayes.
We'll have the story of, you know, that H Petersburg Paradox.
Absolutely. And you'll have passed this one,
the, you know, the game show, one with the three.
What is that? That investment Monty Hall
problem? Yeah, the ones the Monty Hall
problem. Yeah, we sting operation
Investment Banking problem, but there's nothing that stops a
six-year-old, a seven-year-old from reasoning.
It out. Right?
Right, but there's the birthday Paradox, right?
The so many interesting questions and stories that
probability statistics. I don't know if, you know, the
great story of Florence Nightingale, you know, the, you
know, the story of Florence night.
I know that she came up with these sort of these.
Charts, I forget what those spirals kind of charts to
absorb. What was the mortality?
Kind of a think it, I think in Crimea itself.
It was absolutely. So Nightingale basically, you
know, we think of Arizona, but actually shows a really strong
administrator and she started looking at why people were dying
under her watch, right? And then, she realized that
people were dying. Not because of medical reasons,
like that was due to war, but because of things like
sanitation is bad, so they caught an infection and then
Struggling to communicate this to her Superior.
So she decided after represented visually and she came up with a
new chart which he then showed to her superiors and know the
chart made it very obvious that you know, what was happening was
that sanitation and then action happened?
So it's called the Nightingale chart and that's an amazing
story. It's, I mean, the chart is
something that's very easy for children to understand, right?
So much for visual story. Similar to the undivided of is
that London calls? Are that the don'ts?
No, those pile. He very did a scatter plot of
Where the Callback is escape. And if you go to is due to these
two water pumps, absolutely right?
I mean, to me that's data analysis of the highest order
and not difficult for a 78 year old to understand that you have,
basically, all of Edward tufte is like this, right?
I mean, any of his envisioning, you know, the envisioning
information books, you've seen, any of the books.
I have only read the main one, the visual display.
Visual display of quantitative about vision for me.
See, yeah. Yeah.
So I think so, all of that again, first will offer the
story. The story of Napoleon going to
Russia, after a very famous start on it.
This beautiful sort of a link to it.
It's a beautiful job. Yeah.
So Nightingale story, the story of Pascal and former write all
of this. It's very important that you do
that first. What age do you tell them at?
What age do you I know at around 60?
Start with the history of the universe and things like that.
So, when do you start of introduce them to the the guy
The Gambler going to Pascal, enter mind the interviews
probability? And yeah.
Yeah, so I think there's no reason why it can't be done at
six, right? And because you know, it's if
you're not in the pandemic and we all in school together, it
would happen at six. Now, of course, it'll happen a
little bit later because of various constraints that we
operate under. But when you think about
conceptually, there's nothing great here, right?
It's It's just a nice story that children can understand and
connect to put that must then be followed up with actual work.
Right, which is what can we then introduced to the child that
will allow them to take this forward on their own right?
And that comes, you know, that's a very critical point now and it
links to how we offer all the Sciences in Montessori, right?
If you look at Matsuri Elementary, The Sciences are
again. Offered since sorry.
And what's the sensorial? Version of science.
It's the experiment. So every classroom has an as a
lab inside it. And that's basically mandatory
for a Montessori Elementary classroom.
Right? That you need a lab inside which
children can perform different experiments.
Right? So, for example, when we give
the first story, the story of the universe one important
Insight is that when the earth forms, you know, the there are
some things that go to the Center of the Earth.
There are some things that come out and it turns out that is
related to temperature, right? That hot things behave in a
certain way, cold things behave. Certain different way, but hey,
don't take my word for it. Here's an experiment, you can
do. And then the children actually
go ahead and try the experiment dr.
Right? So the sciences and want to see
our heavy experimental, right? That you do an experiment, You
observe you hypothesize and you come to some conclusions, right?
And then Concepts get built upon in scaffolded way.
Now, let's take the same idea and bring it to statistics.
Right? What a simple experiments we can
do in probability and statistics.
The most obvious one is the coin toss.
Right? Right.
So and it turns out that the wrong way of doing probability
and statistics to Define probability upfront, which is
the textbook way that probability is a number of
positive outcomes by total outcomes or sample space.
What are we going to the terminology?
We get into all of that but we don't get a feel of what's
actually happened when you toss the coin.
And that's the reason why playing the card game and
actually tossing. The coin is so important.
So, this is the way we would do it.
Right? We say, hey, um, you know, ten
of us, whatever 10 kids are here.
Let's toss coins. Each of us, take a coin toss it.
10 times before we toss though. It's important to have the
conversation to say. Hey, what do you expect?
Karthik? You think will be foreheads,
two, things is going to be six. Things will be 7, so they
provide a hypothesis, then they do.
Actually, they do the trial. They get an outcome.
May be the same may be different.
They recorded, right? And the element region are very
social children. So it's a lot of fun reading.
Manga will say I got three younger they will say, I got
seven. I got six whatever, whatever.
Right. So they start talking right?
But this is still just one trial and you haven't yet got to the
realm of Statistics, but you see the path that Now lies in front
of It's a haircut and do it again.
And you do it again. I'll get something else.
We record that also, right and suddenly we see now how we kind
of move away from the science experiment.
The science experiment gives us largely the same outcome, right?
If I drop something in water, it will sink.
It's always going to sink. Right?
So will behave differently? Perfect toss a coin different
things are happening. Right?
And this is a fantastic way to introduce uncertainty because of
use of certainty so far, right? Right from three to six things
happen, or they don't happen, right?
But now in a 220, you can get used to little bit of
uncertainty. So we offer this so they do this
trial. Let's say they do 20 times,
right? And now they've recorded things
on their paper, right? And then the sharing, but now,
we have a problem at this stage, right?
Because you've done the trial 20 times, you've written something,
but now you have no tools however to compile result,
right? And that now sets the stage for
hey now, let me tell you. Okay.
What is mean? What is median?
What is mold? What is rain?
Change, right? And that's great now because
Kathy can go compared with, you know, whoever sonal and say,
hey, my main is 5.6 heads and she'll say my mean is 0.5 x,
right? And so suddenly some
conversation starts happening, right?
Which is great. And it's a very, very natural
way of a running, an experiment be generating your own data and
see actually analyzing the data but tools that we are offering
Eight. And then a lot of interesting
things can happen when we can ask different questions in the
experiment. We may have asked how many heads
do you expect? We can now, ask how many
sequences of two, heads to you expected.
When do you expect the first at, you know, all of those classic
probability questions that we end up doing on paper, which we
do at the age of 16. Not X6.
Exactly. Right?
But when you actually perform the experiment, you can do it.
Now, what's the big deal? There is no big deal.
Right, but it's an experimental view.
It's not the theoretical View. And that's important to keep in
mind, they be doing experimental probability here.
But now, more interesting things can happen.
You can say, hey Karthik personally run it 20 times,
right? You have some outcomes.
Now, let's try to do it a hundred times salute hundred
times in the start seeing the convergence, right?
And they won't know. This is the law of large
numbers. Like this is, it doesn't matter
but very intuitively. They'll start understanding
that. I do it more number of times.
I'll start reaching a common answer.
This is very deep result rate and the Same time, it can start
plotting the histogram of your results and this starts the bell
curve come, right? They will note.
It doesn't mean they don't need to know the formula of the bell
curve. Right?
Sudden, used here is something called a bell.
Curve that's coming in. Many different experiments that
I do it. What the hell is this?
Why is this coming? That's a great time to do story
of the bell curve, you know, find out more about, you know,
GAO. So, whoever and house has all of
these famous stories about him, right in his past what you think
about the konigsberg problem? Now, the OnePlus 2 Sleepless for
dinner at one one plus zero understood that 1099 to me.
That's a great Elementary question for a 67 year old,
which is it, which it was, by the way.
That so how goes solid solid when he was seven or eight in
the class. It is no reason why a child
can't crack it. But yeah, so all of these
stories for the children and now we have the bell curve as well,
you know, the law of large numbers and suddenly you have a
rich experience of probability. You don't know it.
The theoretical sense and not even thinking about any
theoretically would have the experience of it and that's
really really valuable. And from now, you can start
doing a lot of interesting things ready to get into the
base, theorem, right? You can get into, you know, all
of these laws of probability and so on, and then you can get a
critical definitions, right? This is the right way of doing
it. Start with the experience,
contextualize of the story. Once enough experience has
happened then go to the theorem, right?
Just by the way, is exactly the To do something like let's say
divisibility, right? I don't know if you remember how
we did with me, the school's, right and say okay divisibility
by 4 and we'll give you a rule. You must the rule, more guy
disability or three by was add up the digits and it was 20
years after that. I figured out why the
divisibility by three words lucky exactly.
But now imagine that you have these, you know bead materials
and you're actually making numbers and by manipulating
these numbers that kind of figure out when are some
numbers. Visible by three or not.
And you rent this copper rule for divisibility by 3.
You never? I mean, there's no experience
quite like it. No, you never forget that fool.
You found it yourself? Okay, and that goes to key
principle of want to see, right? And she said this of the
Pythagoras Theorem, which is that, if we could recreate the
conditions that Pythagoras had that with all the prerequisites
that he had. And if you offered all of those
two children, why can't they go and discover Pythagoras
themselves and that same inside applies to all streams?
Of course, datas and wasn't there and wants these days.
So it's been left to us to kind of take the work forward and
apply the same principles, but was, that's the key thing.
How can children discover rules instead of rules being offered
to them, as, you know, given from God, right?
So, yeah, so now we have all of these terms.
You are given to children. They've discovered various
things. Now we go into, okay, come now
mathematically. Let's Define probability, right
and then go and check back with all your previous experiments
and then they'll start seeing that.
He experiment in probability and Theory doesn't always match.
And so, which should I trust? Sort of broadly start developing
a sense of T value and some that whenever using those words,
right? But you kind of figure out
what's happening. They getting the inclusion of
it, which What we like for them to have the Adolescent is a
school is always there to build the algebraic formulations if at
all, but the time for intuition is 6 to 12 beyond that, it's
just time wasted right? And I feel like so we can take
any concept. Now.
They literally you can pick a concept in math or statistics or
data analysis and we can figure out.
Okay, how do we offer this store ten-year-old for a nine-year-old
or an eight-year-old and it's not that hard.
Okay, so you introduce the story of probability using the
gambling, its own at around 6 or algae and then like you is soon
after you start start start making them.
Do these experiments like the coin toss and then like sort of
which gives you the mean median which gives you that the sort of
the bell curve and things like that.
And then maybe I guess by our own 9 and 10.
You would be telling them about like about the bringing in some
of the more. Some mentions of the formal
terminology and things like that, I guess, right.
Let's look at the prerequisites. Now, again, if you think of a
truly pedagogically, if I have to offer formally not
definitions of probability and so on.
What should the child? No child should know, fractions
really? Well, they should.
It should be quite strong and fractions mathematically.
Right? Not just send, so really, but
they should basically be able to do the math on fractions pretty
well, and they should move percentages reasonably well for
them to sort of have the language It is not a big leap
from fraction, but they need to know it.
Well, it's also very helpful for them to know decimals somewhat.
Well it because it just helps in some of the manipulation work
that will come out. Finding a mean of 5.5 to get 5
.5, L know how to kind of work with decimals.
Right? So all of this typically, you
know, in the Montessori World children will know by 99 and a
half that maybe, right. So at that point, the ready?
Because I have the prerequisites in place now, they can
formalize. Leti, right.
And then we get into some of these, you know, rules and what
is the limits of probability? What are all the samples?
All the events, you add up, what you get.
Now things like that. We can start deriving, and by
this time children can derive these rules.
They don't need us to spell out that, you know, the common
probability is equal to 1 then what intuitively right, right.
So that's one way of doing it. But, if you not take it Forward,
right, I think you can think of any area of discrete math, where
discrete math is, let's say we working with integers, broadly.
And if you're working with integers broadly, you can count
them. So if you look at, think back to
your permutations and combinations of work and school
with again grade, eight grade nine, right?
Completely theoretical. Right?
You given a condition, you kind of apply.
OK. And CR is so much.
You put it down on paper, get an answer.
We move on. Now, you can actually count.
You put those skinny things there and see how many ways you
can get four things, do it. Derive a formula.
Right. That's the way we do it, right?
As opposed to here is the formula plate.
Right? And I think and I mean we
haven't done this yet, but I was thinking the other day that you
can do graph Theory. No, the same way, it is just a
bunch of nodes. You know, we have a lot of
geometry material by convey, do some basic graph Theory results
that children can discover sensorially, you actually build
the graph in front of you. You can, you can build the
bridges of königsberg. Actually, you can have a scale
of scale model of that and against nuclear energy.
It's a Lutely, and then you cancel them about how you can
say, okay. Now you can see who's friends
with through. Why don't you draw a graph with
that? Now, we are going to plan a
party, is this going to be a good party which these people
together in textedit? Exactly.
And I think so, unfortunately, like discrete math gets very
short shrift in the math, curriculum, right?
You just gently, you forget about it for a long time.
It's counting. Let me forget about counting for
so long, and then we bring it back when you're great.
And suddenly Chow dumb. Comes and suddenly like wow,
like why am I learning about it only now, right?
And there's no reason and think about other things read, think
about number Theory basic modulo arithmetic for some reason only
Junta who kind of do Olympia and prepare for some you know other
stuff they get to see it. Yeah.
I did come across it in my school curriculum at all.
I only saw it in the Olympia. Curriculum and stuff.
It is simple. No reason for you to not be done
in school. Yeah.
It's very intuitive again.
Work with your hands can figure out these rules.
Right? What should the remainder be I
can imagine using decimal beads to kind of like do modular
arithmetic, right? So solutely, absolutely,
absolutely screaming enough phase to do it.
You know, we will do it. And I think that so hence, the,
the learning has been that large swades of math are offered very
poorly or at least offered, without a sense of experience.
Oh and the experience makes a big difference to Children.
It actually makes a big difference to adults as well
because when adults go through their training, they suddenly
discover things that they never knew.
Like once I don't know. I remember through some of the
geometry work that we do in Montessori and if you work and
sometimes as adults, we also just kind of play around with
the materials to see what's happening.
It's only struck me once. What was that?
That if you take, I don't know if you've seen this.
What is root 2? 1.41 something.
Something something it is part of what is Ruby. 7, 3 root 2 is
point 70. 72 to I know that fair enough.
So it is root 3. 1.71 something something.
I'm ugly Tucker. 1.7 1.73 out a 73k.
What is what is root 3 plus root 2.
What root 3 plus 3 over root 2. I am going to add it up and say
it is like, it's something close to pipe.
Correct? Why is it closed 2 pi?
It's actually 3.14 on. By the way. 1.7, 3, + 1 .4 one.
Yeah, this department is 3.14. Which is just shocking, right?
I never realized it all through his schooling.
I realized it was about 35. I realized it right now in
second spot. Yeah.
Yeah, exactly, right. The hell of a thing.
In fact, it goes back to Plato. Plato predicted the root 2 plus
root is exactly by that. He did some geometry stuff and
he said, okay man. This has to be equal to Pi and
of course. Now, we know it's not exactly
equal to Pi R. It's damn close.
Yeah. I mean if it were exactly equal
to Pi then of course like you would be able to square the
circle against square, a circle. Yeah, exactly.
Right, but the question Still Remains, why the hell is it so
close to pie? And what is the geometric
intuition behind this, right? It's you will get if you work
with the geometry materials because we have those circles
will have the, you know, the squares or the triangles with
the requisite sides, you put that together and you see what's
happening. And it turns out that you can
sort of provide an intuitive proof with the material just
aging track a little bit, having a few minutes back.
You mentioned about click actions and things like that.
So, I mean I had this joke, I might have put it on Twitter
that the With the Montessori education is that the first kind
of visualization that children learn is the pie chart because
that's how they are introduced to fractions.
Even now if my daughter, if let's say, I'm reading the
newspaper. My daughter comes in.
She sees a pie chart. She'll be like fractions.
So so study from Delhi, how do you do sort of introduce some
kind of some kind of visualizations?
Graphs, Etc, are two children either.
So, how do you how do you do that?
What is the, what are the things that children easily take to and
do there? Learn to sort of communicate
visually and so on. Yeah, I think it's like what we
discussed earlier, right? It's helpful to again, offer
greatness, right? So we'll offer Edward tufte or
will offer Florence Nightingale and will say first, let's
Analyze, This, it becomes quite hard to do the opposite there.
We create artificial data and say come, let's make a bar
graph, right? It doesn't have quite the same
impact. So we will.
Again, take a can Nickel example will be was story around it.
We invite the children to analyze it with us and then
we'll say, hey, would you like to try something like this with
some data of your own and that of your own is really important
because they don't have data of their own, they can go and
interview somebody and get data like they can go find a sample,
are some questions, get that data.
And that's a really important step.
We don't want to give them data for them to analyze posture.
We want them to create their own data.
Right. So first, we're showing them
interesting representations next to inviting them to go collect
some data and then we are inviting them to create
representations of data in any way they choose, right?
And often they'll try to mimic what they saw, which is fine.
Right? But that presents an opportunity
for us to say, Hey, you know, I have another way in which you
can represent this data. Can I show it to you?
And that could be the bar graph, for example, right?
Or some scatter plot or whatever.
Right? And then, we'll show that Them
and suddenly, you know, the other day someday end up with an
exponential corporate, really fantastic.
And then they realize that hates relative to.
This is Multiplied to, right? So suddenly there is to power 5
and they're like, oh my hands already, 32 is going out of my
page, what's gonna happen? Right.
So interesting problems and thus tempting at that moment to start
introducing, you know, logs our lives and also.
Yes. Yes, very kind of held off
rating, fell. Okay, that's a bit much right
now. Like some seven and a half year
old, but, but yeah, I think it Comes out of the data.
And this particular logarithmic graph came out of the story that
the child had, right? It's famous story.
Know that in the somebody comes and says, you know, put two
grains of rice. Then double it, the chessboard
story and then they said, okay, I'm cutting it another plotted.
It is built of very quickly. It went off.
Right? And that's fantastic, because
you kind of arriving it laughing.
So seven and a half year old person.
Read the story and decided to draw graph to see what it's
like. Yeah, but of conversation, What
you think will happen, right? And you know, I think one of the
questions that somebody posed it was actually very interesting.
I'm by the way said, okay, I don't want to know what I got on
the 10th day. I want to know the total of
everything I got till the tenth day.
Right? Which is the binomial sum,
right? The people are cracking it,
right? And the cracking it because the
putting the numbers out there that actually putting the rice
grains. Somebody actually, put rice
grains, rice is easy. No at home.
They put the rice gonna put it together and said, hey, it's the
same as the next number, right? Chisholm a Raising and nobody
told them what the binomial sound right or the binomial
expansion of think it is intuitively.
Derived it. Actually, we did that.
We did something like that recently actually.
So, of course, my daughter's sort of recently, learnt
addition, and things like that. So as try to get her to add
things using her stamps and the decimal beats and so on.
So I was teaching her the Fibonacci series.
So I quickly take daughter and she went up to like some the 200
something. I forget the numbers.
Okay, then she's like, she's written them all in a column and
then she tells me now. Can you add them up?
He asked me, I don't know what her intuition was.
So I was like, okay fine. Let me add it up.
I'm going to do it. The only way I know let me make
one more column with the right cumulative sum running.
Some. Yeah, then I'm like, okay these
two within bit of a lag there. Lucas a nice.
Now, at the age of 38. I'm discovering this.
Nice that nice. It's about prayer.
Yeah, and now I see where you come from, in terms of the
Montessori children coming up with your own things.
And then, like discovering things by themselves and making
others, discover things as well. Like.
Yeah. Yeah, and I think that's, I
mean, that's the inspiring thing for children, because you'll
never forget the joy of finding that thing out on your own.
It's that, like sometimes, you know, when we're doing puzzles.
As adults will have that aha moment.
Now, imagine a school day full of aha moments.
That's what they can possibly be like and then imagine the level
of understanding conceptually that they have what they want
have is they won't go by your timetable that you will want em
in. If as a parent or whoever you
want your child to know this by this day, they miss him are
interested in data analysis. Yeah, I don't do it now.
I'll come back to two years later, right?
And that's, that's fine. That's fine.
From school point of view, and from a parent point of view.
They have to kind of internalized slowly that.
Hey, it's actually fine. They are doing other productive
things now and they don't want to do this cool thing right now.
They'll do it a bit later and that works.
Because if you look at school curriculums, and if you go see a
grade 1 to grade 6 textbook, literally nothing changes from
grade. 1 to grade for, right? Like I said, no, you had one
digit. Then you had two digits and you
had three digits, that takes three years, right?
So and many people are now discovering this in the context
of homeschooling. You spend one hour per day and
it's more than enough to kind of finish the years curriculum
across subjects, right? So there's a lot of slack in the
system, which is actually very good, right?
From grade one to basically know how much slack.
So, if you just chill for two years and don't do something
that you're supposed to do. You can peacefully catch up
right? Because the system allows you to
do that, but furthermore, you can actually do other
interesting stuff that you like in those two years and go very
deep in that, right, so we'll have Have junk, the who are
like, super deep and I don't know you like European history
and they want to talk about the Napoleonic Wars.
The amount that math yet, right, they'll come back next year,
right? And suddenly at the end of grade
for, they know enough math, and they also know the Napoleonic
history really well, right, and to us, that's worthwhile, right?
That's worth having. And it takes some time for
families to kind of get used to that because we're all
conditioned by our own schooling, right?
We like to see things happen in a strad.
I see that is If all the time, as a modest, every parent.
I see that all the time. Okay, like a changing track
again. So so I think we will be talking
about the Montessori method and how you end up teaching data
analysis and statistics at a fairly young age, by starting
with story, starting with gambling, probability, hit
someone. Now, I think I'm sure there are
plenty of our listeners who, who, who are interested in this,
but like, whose children don't go to Montessori schools.
So what do you do? If you are going to a convention
school, is there any Way in which like, as a parent, you can
sort of introduce this. Is there a nice way to do it.
What would you is there something that you could
recommend on this one? Yeah, I think that, I think to
start with, I think that, I mean, we discuss this but I
think card games are just absolutely essential in every
household, right? In the sense that in it, needn't
be card games, right? It could be something like board
games dies. Yeah, I mean, even load.
Oh, there are some cool things happening.
Any kind of board game with any element of Randomness or to
start becoming good at that game and to understand the Dynamics
of the game and children want to become good at games, right?
They want to win very clear and children.
So the motivation to figure out how to do better is already high
and that's an opportunity to kind of really focus on the
mechanics of what's Happening below the hood and in to
introduce it in some kind of a gentle way.
The great thing about famous card games is that this is
already built in, right? Like Blackjack is Blackjack.
All right, you kind of display it and you will get better as
you start playing enough times without seeing what's happening.
And then I think that your playwrights you start counting,
which is great. Yeah, exactly, right.
Because you want to win you, you kind of figure out what more you
need to do. And then Complicated by adding
two decks. There are three decks there.
It's even better because I'm going to more complex math in
your mind. Just great poker.
I feel is I think, I mean it's unfortunately a lot of the you
know the good game. That sort of Tainted by their
close relationship with money and things like that, which I
think is very unfortunate because I mean, to me we haven't
done it yet. But to me, I'm like, you know,
10 year old needs to learn to play poker.
And there's no reason why they can't move the rules are fairly
straightforward. Right?
So we play for the fun of it. We play just to enjoy ourselves,
but then obviously everybody wants to win, and when they want
to win, they start really thinking about what's happening
here. And that's the first step to any
kind of learning right bridge. I mean, I'm not a bridge player.
I know you are, but I'm sure there's some, you are sure.
There's some, I don't know enough about the game, but I'm
sure there's enough there. You don't let me see him in
which film? Yeah, what more do we need?
So, I feel the mistake that a lot of parents met met is that
they want to do, you know, the conventional stuff.
They want to introduce probability is p equal to 1 by 2
or whatever. I would strongly say don't do
that. I would say, tell the stories of
probably tell the stories of this famous story about, you
know, how a lot of astronomical predictions made in the olden
days for I made using probability because you couldn't
observe forever. You don't have strong enough
telescopes. So you would have only small
samples and using small samples have to make these large
predictions. So Gauss makes a Supple couple
of these predictions back in the day.
Huygens, the Christian Huygens, the astronomers another.
Fantastic guy to tell stories on the very rich life.
A lot of interesting things so stories, I would say do that and
I would say play a lot of games, right?
And I think that applies for all fields of math.
Need to play with math. No, I feel.
We don't play with math enough. We want to learn math all the
time. You do it.
It becomes work too early on in life.
I guess. Does it work as a not like, in
the conventional sense rate? So so you stop sort of playing
with it and stuff. So yeah, I would also say magic
tricks by the way. Okay, magic tricks of super
interesting for all kinds of math.
Give me an example. I haven't tried it now.
I'll wait. Let's see, take a three digit
number. Okay, first and third is it
should be different? Okay.
Yeah.
Okay. You have the three digit number
reverse, the number, okay. Subtract the smaller from the
larger. Just give me a just give me a
minute. I've got my subtraction is
tested but I have have done it. Yeah, okay.
So you have a difference in your mind.
Yes reverse the difference, add the difference with the rivers
to difference 1089 1089. Yeah, it's always 1080 always
fun. So yeah.
The children. I'll do some fancy stuff.
Elsa. Tell me your date of birth.
Tell me that both of you die. Like a magician.
Normal kind of take them into four areas and then we'll just
shocked them by showing that, you know, I really thought hard
thinking about your dad's birthday.
And this is the answer I have and it's 1089 right?
And imagine the shock at that moment, right?
Saying what the hell just happened.
And then, once they realize that it's always coming out to be one
thousand, eight, nine, want to find out how this happened and
that's great. And it's not that trivial note
kind of reverse numbers need to go quite In the decimal system
to make this happen or you can get the materials and actually
figure out with patchy, replacing the materials and then
doing the difference and adding. So that's great.
Just a small thing is like a week of work that a child can,
you know, take forward and you know, figure out other such
examples, it goes into some other things of, you know,
interesting number Theory, stuff.
That is somebody's really interested.
We can get them going there. I mean, I learned of something
called the root of a number apparently, which is called the
digital root and of this hole. I don't know it well enough, but
apparently is related to this work that we just did, you know,
we can figure out and we can offer that to Children of their
interest to take it Forward. Right?
So there are lots of small tricks like this which are
interesting which can then Inspire them to do more.
So again this easy to do at home.
No doesn't need anything. Right and no Martin Gardner's
books are full of things like this, right?
Literally read a book for two days.
We'll have a hundred tricks to do the next day.
So, you know, I'd say do that. So yeah, it says yeah magic
tricks, games stories right. Forget about showing this guy,
you know, what is p equal to and so on that's not going to end.
Well. Forget telling this is the
formula for Bayes theorem and things like that is never going
to work. Exactly.
Exactly, right? Yeah, I think so.
That's the way to do. It is to always play and we
would always ask yourself. How can I play with this
concept? It's not, how do I formally
offer it? That's always the wrong answer.
Okay, that's fascinating. Okay.
So one last question for you, which is like, so I mean, you're
told us about why we need to introduce maths early why, why
we can introduce things like probabilities early, how we can
introduce it and so on. So apart from the fact that the
mind is sort of receptive to these things at that age.
Are there any other sort of any other sort of benefits that you
see by off? Things like things are.
I would saw broadly call it data science at the elementary level.
Sure. I think the way we think about
it is that at every age of the child, we are not offering them
curriculum. We're trying to offer them
various aids to their development.
The curriculum is only a tool that offers an 82 development
and we must never mistake it for development itself, right?
To do that. We need to understand a little
bit. If a child is seven or eight
years old broadly. What are things?
That they need or what are those characteristics that we must
promote? Right?
And what we know today is the child.
Let's say, between 6, to 12 is very, very seasoning.
Oriented is very, very imaginative and is very, very
taken by working with friends, in comparison, the child, whose
3 to 6 years old is usually a lone worker while they like the
friends, the like to work alone. They're very very sensitive.
Native to physical order. Let's will keep their, you know,
they've been sort of shown the process.
They'll want to keep things nicely.
They'll keep their shoes in the proper place.
They will follow instructions when shown really well.
So, that great note to show them sequencing basic quantities,
because can just order it. Easily.
It comes very naturally to them. Right?
So, by knowing the basic characteristics of children at
different ages, we can then choose to offer different
things. So, coming back to 6 to 12.
Reasoning imagination. Working with peers, right?
Three big things at that age and we can now think of various
aspects of the curriculum that we can now offer.
Given that we know these three, right?
So literally anything that involves any kind of reasoning
we can offer Right? And we should offer with the
knowledge that not everything will stick of many children will
not take to data science. And that's fine.
What is the other thing that I wanna offer to them to promote?
Their reasoning is a problem, as a teacher.
I have to solve right? For somebody could be historical
reasoning rate. We look at reasoning very
quantitative way, but there's also sort of anecdotal or
looking at, you know, the sequence of history and why one
thing happened after the other, and that's more through literary
analysis. That's another way of reasoning
and we will For that and that's a job for us to do, right?
So I'll sort of also quote something that you know, we that
the made a lot of sense when I was going through my training
few years ago, which is in the 326 as Educators get trying to
understand the child as part of our training.
When we are in 6 to 12 as Educators.
We are trying to understand the universe because the child wants
anything and Everything offered to them and it's our job to
offer anything and everything right today data science.
Is there 50 years back, there was no data sets 50 years later.
They may not be any data science again.
So things will keep changing but it's our responsibility to
figure out what is it today? That builds reasoning in the
child. Thank you for listening to data
shatter. If you like this show, please
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Once again, this is Karthik signing off.
Thank you.