Good morning.
Thanks to the organizers for a great opportunity
to talk in front of such huge crowd.
And I actually learned only a couple of minutes ago,
how famous I am going to be thanks to this.
They will watch me even in Šaľa.
What I came to talk about is,
how Mr. Lacko said, mathematics as a source of joy.
Sure, it sounds like "dark blond" or something like that.
How could math be a source of joy?
Indeed, there are people, and you know them,
here in Slovakia, we call them "cube heads",
these are people for whom mathematics is a source of joy.
Is it fate? Are they only exceptions?
We are convinced quite the opposite,
that the number of those "cube heads" could be far greater.
The current state in Slovakia and Czech Republic, where I have been working now, is that
the attitude towards math is really bad and getting worse.
If we look at TIMSS and PISA results,
it is a reliably declining function.
But why?
Because mathematics is a "scarecrow",
some kids are frustrated,
and others are bored.
I'll use Czech now: "And again those columns",
A pupil that can already count to a hundred
and we force him to do 7 minus 4 equals 11 minus 2 equals, etc.
Why is that?
We do not respect the laws of cognitive process.
We do not respect the natural learning setup of every child.
Not only for math, for anything. But we are mostly interested in math here.
We explain, instruct, we force pupils to reproduce.
I said it this way, you have to do the same.
To Imitate!
I know of a tragic case of one very talented pupil, Vicky,
that went through our 1-5 program,
very excited about math, but in the first year of secondary school,
(we have 5 years of primary school in Czech Rebublic, right?)
in the first year of secondary school, she had all A's at the end of a school year,
with a single B from math.
When I asked the teacher,
why is that, she said: "She is stubborn,
if she does not learn it the way she's supposed to,
I can't give her an A."
The greatest land's treasure is the talent of these kids,
and it is considered a sin,
something to be punished.
Well that is education for a totalitarian regime!
The best education for a totalitarian regime!
To forbid creativity!
What is this TEDx? It's creativity!
It's not top-down.
We heard at the beginning how hard it is to get those,
who sit on stamps, money, in office,
to understand it makes sense.
And, unfortunately, the same thing happen in the classroom,
like in case of Vicky, I talked about.
My father passed away in '77.
He was the architect of all I'm talking about, he created it.
And I was his first pupil.
It's been 70 years since the method was born
and he gave me problems that were really interesting
and I really liked solving them, but I have bad grades at school.
But father told me: "You're good."
Well, father sees it one way, the teacher another.
Well, I got by.
Well, then came the sixth grade, fractions, and negative numbers,
and suddenly I was really good, even for the teacher.
I remember when Headmaster Lepieš in Martin told me:
"You see, Hejný, when start to learn, you get it."
He didn't understand that I really got it,
I wasn't taught in rules
I was taught in schemas.
I'll get to that later.
I won the regional Mathematical Olympiad,
and I chose math to be my proffession.
When my son got to the fourth grade
I suffered seeing how he's been taught mathematics,
I started teaching him and I continued through grades 5 to 8.
After that I did another round of 3 through 8 grade
and I fell in love with this job.
And the lesson I've learned in those nine years of teaching,
the main lesson is:
"Students are able to figure out all the math by themselves."
I thought it only worked under the supervision of highly math skilled person, such as me,
but not under average teacher.
It turns it is wrong.
Even average teachers can do it.
And the kids and the results are brilliant.
How do we do that?
We give kids problems, they solve them and discuss them among themselves.
We teach mathematics of schemes: it's not rules, but schemas
that kids create in their heads. Like this stepping schema.
I'll show you 2 + 3 = 5.
How do you usually teach that?
Two fingers and three fingers is five fingers.
Two apples and three apples is five ap...
These are states.
We will do it differently.
I will ask for two volunteers here,
please, ladies, if you will...
come and volunteer.
And you imagine... come here...
I have to learn your first names...
Because we are in first grade. We are in first grade, the end of september.
So here it is: Languages, travel, hiking. Simone.
Susan. Ok, we put Susan here.
Shoulder to shoulder and in front of them there is a stepping belt.
There are marks, not too far from each other.
About 30 centimeters, ok?
And you get the command for stepping forward.
Simone will get command for two steps and then three steps,
start now.
She will take the steps and you'll see what follows.
You are the class, you are the audience.
And the audience role is to keep the rhythm,
as Simone walks, one, two,
we clap, one, two.
She stops, one, two, three, okay?
So I'm Mrs. Teacher,
it's a tragedy that I can't be Mr. Teacher,
cause it's and empty set, right?
So Simone, two steps, then three steps, start now.
One, two, one, two, three.
Once again, Simone.
She went one, two, three, four, five, right?
It's not how it's supposed to go.
One, two, pause, legs together, one, two, three.
So here we go again.
Simone, two steps forward, then three, start now.
One, two, one, two, three.
Great, now you see... here, here...
Actually, I don't need this, I have microphone here.
You're the class: "Kids, what command we give to Susan,
with only one number, so that she is next to Simone again?"
And we are at the end of September in fist grade,
so most of the kids are saying five but there are some fours.
Me, as Mrs. Teacher, I choose the wrong one.
Why? Because we learn from mistakes.
Ok, Mary, so you're saying four.
Well, let's try that. Mary, give Susan the command. And Mary commands: "Susan,
four steps forward, start now."
One, two, three, four.
Did we get it right, kids?
"I told you, it's five!"
Well, let's try five then...
Thank you, ladies,
you did a great job.
What we've seen here is different from two fingers and three fingers.
The steps are not permanent, we see them only when the child is walking
but then they're gone.
What do we prepare the kids for?
We prepare the kids for the future, when they have to
solve the problems like: "Cyclist left at this and that hour and
is travelling by this speed, and after him leaves the motorcyclist,
at this and that hour and is travelling by that speed,
when do they meet?"
These kind of problems are scary.
Or problem such as: "Eve is three, when she's as old as Paul now,
Paul will be 11. How old is Paul?"
These problems are scary even to teachers.
I've got another schema here. Cube schema.
That's cube, right? If someone asks you,
how many vertices does a cube have,
if you learned it, you say eight right away.
If you didn't learn it, you imagine the cube,
or draw it, and then say eight.
The second knowledge that it has eight vertices
is better, because it's a knowledge of cube,
the knowledge of a schema, not a rule.
Here you can see the addition and subtraction.
With the stepping, you can go backward.
You can do negative numbers. You can't do 2 minus 3 on fingers.
I want to end with saying what a teacher should and shouldn't do.
He should not explain, correct, interrupt, be impatient.
He respects pupil's intellectual autonomy.
There are interactive rules... he must never mock the pupil.
He should have respect for the child, respect for his thinking.
He choses primary problems, organizes discussion,
admires great ideas and encourages those
that are somewhat tired.
The results are great, not only in mathematics.
And I would like to end my talk by this appeal,
and why is it meaningful.
This is not about mathematics only.
No institution, no laws, are greater guarantee of democracy
and social prosperity than thinking citizens.
Thank you for your attention.