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So I'd like to introduce our presenter.
Today, we have Jo Boaler.
Dr. Jo Boaler is a professor of mathematical Mathematics education at
Stanford University, the cofounder of you cubed.
She's an analyst for PISA testing in the OECD, and
author of the first mook on mathematics, teaching, and learning.
Former roles have included being the Marie Curie professor of mathematics
education for Europe.
A mathematics teacher in London comprehensive schools and
a researcher at King's College in London.
Now, I'd like to turn it over to Jo.
>> Good morning, everybody,
it's really great to be talking with you all this morning.
I know we have people from across the education sector and
from many different countries.
So welcome, whether you're here in the United States or in a different country.
It's always great to have the international participation.
So I'm going to be sharing some research today, some of which may be new to you,
and some of which is probably less so.
And we're going to watch some videos together also.
And I'll just jump straight in by telling you that I was in Norway yesterday,
seems amazing, but it was a really interesting event.
I think you would like to hear a little bit about it,
in Norway they present a mathematics price called the Abel Prize for Mathematics.
And it was won by a mathematician called Yves Meyer.
And what's really nice is they also have a teacher prize that goes along with it.
And so I thought you'd like to see some of my photos from Norway.
The first one,
this is Yves Myer being presented with the prize by the King of Norway.
That was really exciting.
And this, I just thought you'd just like a picture, this is where the King lives.
And those banners are actually for the prize, the mathematics prize.
Which there was a whole series of events,
a week long in Norway, around this mathematics prize.
So it's pretty exciting way\g that they hired at Maxim\g that way.
This is the teacher Hanan Mohamed Abdelrahman who won the teacher prize.
And without any of us knowing this what was amazing was when she was presenting to
everybody she was showing all of the things from YouTube that she uses in her
teaching.
And very strongly talking about how she communicates with students that there's no
such things as a math person and that anybody can learn math.
So that was really great to see that and to see YouCubed getting out far and wide.
And this picture I thought you would like to see from the banquet.
We went to a very fancy banquet night before last.
And lots of mathematicians were there from an international
group of very important mathematicians.
That's a picture of me with the award winner.
And then, one of my favorite moments of the evening was a chat with
the minister of education from Norway.
Here he is with myself and Cathy Williams from YouTube wearing his national costume,
which I loved.
He said to me do you think your American colleagues will think I'm from Lord
of the Rings?
I don't know what your answer to that is.
So anyway, that was a great conversation about 21-century mathematics in Norway.
So starting some of the things I want to share with you today.
I am working more closely these days, really the intersection of mathematics and
learning about mathematics and neuroscience.
And we are doing that partly to dispel some really important myths about math.
And in dispelling those myths,
we find it changes people's relationships with math pretty profoundly.
So it be no surprise to anyone that I'm going to start with this idea that we know
now that nobody is born with a math brain and nobody is born without one.
And in fact, incredible research on brain Science brain plasticity showing
that everybody's brain can grow and change to learn any mathematics.
And we need to get rid of the idea that some students are born with a math
brain and some are not.
So the next slide was animated, but
it's not going to show up as an animation in WebEx, unfortunately, but not this one.
So the brain we know is our most complex organ.
It's made of over 100 billion neurons, and several thousand connections between them.
And how do we grow a map strain, how did it happen?
This is the slide and they're no longer animated, but what it would've
shown you is that when you learn something it's one of three things that happens.
One is a new brain pathway can form.
Another thing that can happen is a current brain pathway that you already have
becomes strengthened.
And then a third possibility is the brain pathways that you have connect with
each other.
So when we think about students having a mathematics brain,
this is how you get one from learning new ideas that form pathways in the brain.
And then stay with you for you to use, in your brain, from that point onwards.
And that seems pretty important for students to know that that's how brains
form and learn new mathematics and new mathematics pathways.
And that's really what's meant by growing your brain.
Some of you will know that we've been sending out messages that mistakes grow
your brain and mistakes are really good for your brain.
That's what really that sort of brain growth really means.
It's sometimes it's forming pathways.
Some times it's strengthening pathways and making connections between them.
So really interesting new research coming out I think on brian connections.
So people wonder what makes people more intelligent and know more things and
more accomplished and they really try to figure out what is it about their brains.
Some people think you have to have to have got a larger brain.
It's not that at all.
And in fact what makes people more accomplished,
more knowledegable is a stronger set of connections between half the brain.
As it says here, the dynamic interplay of neural networks
would operate in concert and draw from different parts of the brain at once.
So today, I'm going to talk to you about how to encourage those brain connections.
So it's a really interesting article that recently came out in
National Geographic And it was called, What Makes A Genius.
They were trying to figure out, if we call certain people in the world, a genius,
who have just done amazing things.
So they talked about Einstein and Michelangelo,
what makes them different in their brains.
And so they actually have Einstein's brain in a museum, chopped up, and
people stare at it all the time.
There's no difference in size of brain, but
what they're doing now is bringing in people who are super accomplished, and
having scans of their brains to look at what's going on inside their brains.
And they find, as it says here, that there's quite a notable
difference between those that they think of as a genius,
that there is more communication going on between the different hemispheres.
Those people are more flexible in their though processes.
And more contributions are coming from different parts of the brain.
So clearly this is what we want to develop in here,
more communication between parts of the brain, more connection, and
mathematics can play a really important role in that.
So lots and lots of evidence
that people may be born with differences in their brains, but those differences
are really affixed by the millions of opportunities to grow and change brains.
And all students have the potential to learn any level of mathematics with
the right teaching.
So I want to start to have us now look into something we
did at Stanford recently.
That is we brought 81 students onto campus and
we gave them these different messages about brain science.
We told them that mistakes are really important and
Struggle is really important.
We told them that speed is not important.
And then we taught mathematics differently, as an open,
creative subject that really backs up those messages we gave them.
And the new online class that I have coming out in the summer is
actually based around the videos that we took at camp.
Everything was filmed by a filmmaker, and we're going to watch some of that today.
This slide's a little mushed together.
We've lost some of it, so we'll send this out to you after the webinar.
But we ask, what would happen if we changed all of these things?
We stop kids thinking that you're a math person and you're not.
And we replace some emphasis on the speed and procedures,
and go more in depth in creativity.
And we got rid of the idea that there's one way, and instead celebrated
the multiple different ideas students have and different ways of visualizing.
And what's lost at the bottom is really moving away from work being individual to
being a collaborative process.
So this graph shows you the pre-scores of the 81 students we brought to campus.
It was a test they'd taken in their district on algebra.
And what you may be able to see there is 81 bars that represent the 81 students.
And you can probably tell there was a wide range of achievement amongst the students.
We have very high achieving students,
we have students who scored zero on the pre-test.
We put them into four classes.
They were all mixed.
We didn't have any tracking or grouping.
And then we taught them open, creative mathematics for 18 lessons.
They were with us in the mornings for the math lessons.
I was a teacher, Cathy and others, and regular classroom teachers also.
We had four classes.
And then in the afternoon they are able to sort of run around campus with my
undergrads.
So they had this day's experience in math.
And at the end of the 18 lessons,
we gave them the same district algebra test that they'd taken in their district.
And even though we didn't focus on that test at all,
the scores of the students, as you can see, had massively went up.
By an average of 50% per student, which is a huge amount for
an educational intervention.
Not all students, as you can see, increased.
But the increases that you'll probably notice come from across
the achievement spectrum.
High achievers, middle achievers, low achievers.
And that difference is equivalent to 1.6 years of school, so pretty huge.
These are our kids during one of their last days of camp,
wearing our YouCubed t-shirts, making our YouCubed logo.
Doing a pretty good job.
And I thought we could, well,
first hear from just one of the students reflecting on their camp experience.
They said this. They taught us how math is for everybody.
And I believe that I wasn't a math person before but
now I believe that anybody can do math.
And that helped me a lot.
And the way I thought the math was all about the right answers and wrong, but
it's really about ideas and it's very creative.
And that helped me like it a lot more.
So I chose this because it had two things in it.
One was we changed the student's belief about who they were.
All 81 of the students on the first day told the researchers,
I am not a math person.
It didn't matter if they were low or high achieving.
They could name the one person in their school or their class that they thought of
as a math person, the one who would put their hand up really quickly.
So we changed that idea for them.
We told them there's no such thing as a math person.
Everybody can do mathematics and grow brains.
And then we also, as this student said, we changed math for them.
So they didn't see it as a subject as right and wrong answers,
but one about ideas that's very creative.
So we're going to watch now a little film that this filmmaker made.
And what I like about this film is so she filmed teaching, but
she also filmed the students in school.
And she did a little of what happened before and
after the camp that we can watch now.
[MUSIC]
>> Some people think I'm not good at math.
I can never do anything, I'm not good at it, I'm just going to give up.
[MUSIC]
>> A lot of people think of it as like prison, like you don't have any freedom.
>> Okay, time to go to your notebook.
Okay, read chapter one.
Okay, here's your worksheet.
>> That math textbook is kind of like the Bible.
You have to kind of worship the textbook and I don't really like that.
[MUSIC]
>> Everybody is going so quickly.
And I thought if I didn't go quick, people will think I'm not smart.
[MUSIC]
>> I made a lot of mistakes and I got really sad about it.
>> You make a mistake, you're pretty much done, yeah.
>> I can't do it fast and they're so smart because they can.
And I'm not smart and I just kind of stopped.
[MUSIC]
>> You feel like you're serving a sentence for nothing.
[MUSIC]
>> I love it.
That does look like a cuboid.
[MUSIC]
>> We got it!
>> I've done better with math when I was talking with people, sharing ideas.
>> Four or five brains work better than one.
>> I'll see it one way, but then someone else will see it another way.
And I'll be like, my gosh, that makes so much sense.
[MUSIC]
>> I love that we're getting different answers out.
Because lots of problems in math,
there are different answers >> Have more than one way to solve
the question.
>> because in real life, you're not going to just do one thing.
You're going to do many things.
You're going to need to use different methods.
[MUSIC]
>> [SOUND] >> Hold on, hold on.
Take your time and just experiment with every way that could possibly work.
[MUSIC]
>> You definitely have to be patient, because certain problems,
they take forever.
>> Math isn't about speed.
And you can make mistakes and you learn from then.
Yeah, I did that too, yeah!
>> Yes, told you.
>> Math isn't the enemy and it can't hurt me.
>> You can run wild.
You can pass ideas by each other.
>> I thought that math was all about right answers and wrong.
Now I believe that math is really about ideas and creativity.
It's a lot more inspiring.
[MUSIC]
So I hoped you liked watching that film.
It's great to see the kids.
And that is on our website under videos,
if you'd like to show other people or share it with others, so.
Some of the different messages we gave the students in camp were these.
And we know these messages have a big impact on them.
We told them that mistakes, and struggle, and challenge are really important for
your brain.
They're the times when your brain is growing the most.
We told them that talking about math is really important.
And it special name in mathematics, which is called reasoning.
That's what makes somebody a mathematician, actually.
Scientists prove things by finding new cases or cancer examples.
But mathematicians prove things by reasoning,
by making logical steps between ideas and
We told our students it was really important to reason with each other.
We also told them that in mathematics,
people when they have sort of ideas that are half-formed ideas,
they call them conjectures, a bit like a theory in science.
But in mathematics, they're called conjectures.
And we learned to talk to each other about different conjectures we had.
And then we also told students, and this is really the topic of today,
that when we visualize and see mathematics visually and when we think about numbers,
those bring up, those involve different parts of the brain.
When we think about mathematics as if it's in words,
it's another different part of the brain.
And when we think about those things together, when we see something visually
and we think about it numerically, that causes a brain connection to happen.
That's really important.
So we wanted to start the count by really being very
clear that we want to see math visually.
And math is a really creative subject where we get to see it in different ways.
And that partly came from this research that I'm working now
with a neuroscientist.
And what they now know is that when people work on something mathematically,
there are five different areas of the brain involved.
And two of the areas are visual pathways.
And in fact, the dorsal visual pathway is the main brain region for
representing quantity.
So when you improve your mathematics understanding,
it's not about just building up knowledge in one area.
But it's about communication between different areas of the brain.
When mathematics for students is just always about numbers,
that's really strengthening one part of the brain and not encouraging those
connections that can come about when it's also visual, or about words.
So these are the two visual pathways that you see in this picture.
And what we want is
connections to happen between these different mathematical pathways.
And when we use numbers, but also visuals, and words, and algorithms,
and we communicate between these different ways of knowing math, that brings about
those really important brain connections that we see as part of the genius study.
This was one study at Stanford where they studied students between the ages of 8
and 12.
And they found that as they got older and learned more,
their brain becomes more interactive, and
that the connections develop between symbolic and visual representation.
Remember, those are particularly important connections.
So we've written more about this, if you'd like to read about it.
We have a paper on our website that's called Seeing is Understanding with
different ideas.
And I often say to teachers, it's really good to make all math visual.
But some teachers themselves haven't themselves had experience at
maths as a visual subject.
So that seems difficult.
How can I make this particular idea visual?
I think the best advice is, ask the students.
They're really good at coming up with different visual ways of expressing maths.
And that's always a great thing to do.
So I thought, I wanted to show you one of the first activities
I did with the students in camp.
This is a six minute video we're going to watch together.
It's called a Visual Dot Card, I know some of you know about dot cards.
And we did this really early on in camp, partly because
I wanted students to see that maths is a subject that people see in different ways.
There are many different ways of seeing it.
I also wanted them to know that maths is a creative subject, and
that we value the different creative ways that people see mathematics.
And you'll see in this video, I think, some of the connection between numbers and
visuals that help those brain connections.
So I am going to move to that video now for you to watch.
After the video, I'm going to ask you to think about,
why was this is an important exercise for students?
What was important about it, do you think, for them?
We now know that when you think about numbers as looking at
numbers like this, one pathway in your brain lights up.
And when you think about numbers visually, like if I were to draw
a picture of a number, a different brain pathway lights up.
So when you have different brain pathways light, up it's great.
You have double the impact.
So we are going to be doing some connections between visuals and
numbers now.
So this is what I'm going to do, this is kind of an unusual activity.
I am going to show you, up here, a collection of dots.
And I'm going to show you for just a few seconds.
And the reason I'm going to hold it up just for
a few seconds is, I don't want you to count the dots.
So I want you to look at the collection of dots and
work out how many dots there are without counting.
Is everybody ready?
Everybody looking this way?
All right, how many dots were there?
Let's just all say, everybody.
>> Seven.
>> Seven, excellent.
So now what I'd like to know is how you see the seven dots.
And why don't we start with Michael.
How did you see them Michael?
>> So I don't know why, but as soon as I saw them,
I just started thinking of Star Wars.
Because they look like a TIE Fighter.
And I know that TIE Fighters, the wings have three edges.
>> Great. >> And three points.
And then, the middle one is also a point.
>> So, I don't know this.
So are these the points?
>> Yeah. >> The three edges?
>> Yeah.
>> So it's this, and this, and this?
>> Yeah, that's it.
>> That's cool.
So Michael, I'm going to say you saw it kind of like that?
>> And if we connected numbers to that,
we would probably say this was 3 + 1 + 3.
Great, who saw it differently to Michael, Maya?
>> When I saw it, I thought of it more like in layers.
>> It's more like a circle, with a dot in the middle.
>> So like two, and then two farther apart, and then two.
>> Okay. >> And then a dot in the middle.
>> So, two?
>> Yeah.
>> Two?
>> Yeah.
>> And two? >> Yeah, and then a dot in the middle.
>> So is it M-A-Y-A, Maya?
>> Yeah.
>> So, Now I forgot which two it was.
Two?
>> Yeah.
>> Two?
>> Yes.
>> Two?
>> Yes.
>> Okay, so I'm going to say Maya's was two, two, a dot in the middle.
And let's make a dot, these two.
>> Yeah.
>> Great, so what would be the numbers we put with that?
>> 2 plus 2 plus 2 plus 1.
>> Great, who saw it differently to that?
Yeah, is it Carlos?
No, Matt.
Matt.
>> I saw it more as like a dice, like if you roll a five on a dice.
And then with two extra ones on each side.
>> Okay, so the dice you saw was like that, the five on a dice?
>> Yeah.
>> And then I saw two extra dots.
>> And then you saw two here?
>> Yeah.
>> Great, what numbers would we put with that?
>> Five plus two.
>> Great, who saw it differently to that?
Yeah, why don't we go, Cathleen?
>> I saw a pattern of two, three, and two.
>> Okay?
Say it again, was it two, three, and two?
>> Yeah.
>> So I'm going to say Kathleen saw it like that.
And the numbers to go with that would be?
2 + 3 + 2.
>> All right.
>> It's like a baseball diamond basically, a diamond.
>> Okay. >> And the bases are each pointing on the.
>> Would it be this diamond?
>> So. >> Do you want to come, show me,
probably everyone else knows what you're talking about, but.
>> So that's a baseball diamond.
>> Okay. >> Like that.
>> Yeah.
>> For example.
So from here to here to here to here, that was the first baseball diamond.
>> Uh-huh.
>> And then from here to here to here to here to here, this is the second.
>> Is another one, great.
So, two diamonds. So I realize I forgot to do numbers for
Sophia, we'll come back to that.
What numbers would you have Jack?
Using your.
>> Other in one kind of 4 plus 3.
>> Mm-hm.
Because you had used one all ready.
>> Yeah.
>> Well you guys did amazingly well.
How many, different ways of seeing it did we come up with?
>> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ,13.
Thirteen.
>> Wow, wow.
So, there's two over here.
So this is one of the reasons we do this, that I
wanted to show you this, is people think of math as a subject
where's there just one answer, one way of getting it, one way of seeing it.
And actually, you can solve any math problem in different ways.
And people see math differently.
So I just showed you a collection of seven dots, and
you saw it in 13 different ways.
So now I would like you to write down, now I'd like you to write down,
if you would, and we hopefully can look at some of your responses.
Why do you think is this an important activity for students to do?
I am just going to pause a little, to think about that and
write something down first, why do you think this is important?
So thank you for those of you who wrote down things, wonderful answers
been given and I think you can go back and see those after the webinar.
I wanted to add one that I didn't think would probably come up.
Which is, we know also from brain science,
that an important part of the brain is the ANS the approximate number system.
And it actually developed from students being able to
approximate numbers from collections of dots and other collections of numbers.
And it turns out that students with a well-developed approximate number system,
that predicts their maths achievement for a long time ahead.
Giving students the opportunity to develop that sort of area of the brain
where they are able to approximate is just inherently valuable.
As well as all the lovely things people are writing about
valuing the different ways of seeing and pathways and so on.
And to me, I often say to my students and we do math together at Stanford.
But one of the most beautiful aspects of mathematics for
me is the multiple different ideas people have, the way they see it differently.
And the different pathways that can be taken through every problem.
That is just a lovely thing to celebrate.
And whenever my students just come up with a different representation or a different
way of showing something mathematically, I always talk about that aspect.
You know, that's really such a nice thing about mathematics that
many students don't get to appreciate going through school unfortunately.
This is just a picture I thought you'd like to see of when we did that
dot card with a group of teachers in Canada.
And you can see their many different representations,
some different ones that the room came up with.
I don't remember, like 30 different ways of seeing it.
So, couple of other things I want to share with you before we finish for
questions and that is, I recently come to this scientist.
He's really interesting.
His name is Robert Bjork and he talks about how, when you learn something new,
your brain kind of relates it to what you already know.
It's very clever about the way it connects things together.
And he also talks about how when you retrieve something and when you talk about
something, when somebody's asking you a question, and you have to
think back in your mind and retrieve it, that itself is an act of learning.
And after you retrieve something,
that knowledge in your brain becomes more retrievable in the future.
So it's really an example of how important it is to
ask students questions, so they have that act of retrieval.
And he talks as well, again on this brain connection
piece on the importance of varying examples and situations.
So, how do you encourage these brain connections and growth?
We can probably all agree that a lecture, sitting and listening to a lecture.
Some people can be making some connections.
But the opportunities are to the pretty minimal to make those really important
brain connections.
Project-based learning has lots of opportunities for
that where students design and collaborate and connect.
But for many people it's a harder shift to go entirely to project-based learning,
and what I wanted to highlight is there are many things you can do in between.
So I'll just show you a couple of them.
That not lecturing over time, and maybe not completely project-based, but
it's more interactive, more opportunities for connections.
And I wanted to go back to what Bjork said,
that retrieving information is an act of learning.
So some people might think, well,
when we give students tests, then that is an act of retrieval.
But actually it doesn't help students as much when it's through a test
as when it's in a learning situation and
the act of performing can actually reduce that [INAUDIBLE].
John Hattie is an Australian researcher who looks at effect sizes, and
I thought this was really interesting, where they look at how,
if you did this, how much impact does it have on achievements.
And I thought these two were interesting differences.
Teachers who encourage students on tests,
the impact of that is so low and it's not even in the desirable range.
But engaging people in class in discussions has a very high impact on
achievement and that's a great way to get this retrieval going.
Asking questions, having people talk to each other.
Some cool things going on at Stanford around this.
Carl Wieman is a Nobel Prize-winning physicist and
he himself says he hardly learned anything from listening to someone.
So I wanted to look at how you can make people's learning more active,
even in a big lecture theater.
What they're doing now at Stanford, he taught the whole physics department here.
Which is instead of the lecture of talking about things, the lecture now asks
the question of the students and they talk about it together in groups.
Then they vote on an answer together, on a for
the voting system, then the lecture or professor,
they were to look at the students answer before giving a mini lecture on the ideas.
When they tried that in physics In the university,
the achievement was twice as high for people who were
asked those questions that they discussed, than when they were just listening.
So, we can all do this with maths.
We can all take ideas and open them up,
and think about how does those methods work how are they connected to others?
Can you represent an idea in a different way as a picture,
a cartoon, even a doodle.
However you are representing an idea differently will cause those brain
connections.
So I had a few examples and then I can stop for questions.
But maths facts are a perfect example.
The worst thing we can do with them is blindly memorize them,
where it's an act of memorization.
Instead, we can have students engage with the numbers visually and with numbers.
An activity on our website, how close to 100, is a perfect example of that.
Algebra if you haven't seen me,
I know many of you have probably showing algebra visually,
I have two TED Talks, one TEDx Talks, when I do that.
So you can look at that.
Any algebra example you can make visual in really cool ways.
Even things like this,
conversion of Celsius to Farenheit is usually given as laws to students.
Do this to the number to get this number and then they practice.
Even that we can completely transform by showing it as a visual pattern and
asking students different kinds of questions.
And all of these questions you see here engaging the square roots or
Pythagoras, can be engaged with visually when
we think of different ways to visually represent those ideas.
And it gives students different opportunities and
help with those brain connections.
I like this example from my friend Cathy Humphreys.
Instead of asking students calculate one divided by two-thirds,
which is a calculation in one part of the brain.
She totally opens up that question by saying to the students,
you may know a rule for working this out, but I don't care about the rule today.
What I wanted you to be able to make sense of this answer and
show your thinking visually.
And in a book I have with Cathy,
there's a video of the students coming up with these different visual solutions and
it really shifts the understanding of different students.
So any mathematics at all can be made visual.
I challenge anybody to show me an area of math that can't be visual.
And as I said, ask the students to think of visuals if you don't know ways.
My colleague Cathy Humphreys is often showing the really cool way of making this
diamond paper where you fold paper up.
We see teachers using this now where they ask a question but then the question,
like one divided by two-thirds for example, has different requests.
Like can you solve it numerically,
can you solve it visually, can you write a story about it?
I had an interaction actually with my own daughter's teacher when she was in fourth
grade that I really found interesting.
Where she was at a school where they had, I don't think homework's ever a good idea,
but they had much better homework where they.
But occasionally she'd come home with like a list of 40 questions, or 20 questions.
Parents know that those are kind of the times where kids' spirits sink.
When they're at home in the evening and they have lots of questions to go through.
And once I actually wrote a little note to the teacher.
I don't normally do this with my children's teachers.
You're probably thinking how terrible a school it would be if I was your child's
teacher, but she came home with a list of, I think, about 40 questions, and
I saw her just feel terrible about it.
And I wrote a note to the teacher where I said you know,
I asked my daughter to do the first few of these.
But then I asked her not to finish the work,
because I didn't want her to think this is what math is.
So it was good, we had a good conversation.
But what the teacher changed and I loved this, totally amazing,
is instead of giving 40 questions, now she gets 4 questions.
But she asks the students can you write the story about this,
can you draw a picture?
Can you do the calculation as well, but can you also do those things?
And you can see a little example in the diamond paper there, and that's amazing.
That is what we'll get, those different connections going and
doesn't make it feel terribly.
So they actually feel engaged with math.
So a lot of people think practice is very important, but it is important.
Practice is what changes that delicate brain pathway into a more permanent
brain pathway.
But what is productive practice is not repeating the same idea over and
over again.
It's seeing an idea in different ways, different forms,
different representations.
So, I will skip these and tell you if you want some lovely,
visual, creative math lessons every year, we give away a free week.
It's called our week of inspirational math.
There's already two weeks, so ten days on the website, a new set is coming out of
visual creative math lessons that really gives students these opportunities.
And those are all planned out for teachers to just take and use off our website.
And we're also working on a new set of books, and
fourth grade books are coming out this summer.
Where we've taken a whole grade level and
thought about how do we show this idea through big ideas and through visualizing.
So those, look out for those.
And youcubed is going great.
We now get 3 million on the site in our months where we
give things away, like our week's math.
So that's amazing.
Our newsletter is opened in over 120 countries so it's very cool.
So I think I'll stop now and answer some of the questions that have come in,
because I have quite a few in front of me.
And if you want to ask a question, now would be a good time to ask it.
So, I'm going to start off with the first question that actually popped up
during the webinar where somebody said, but
surely some people can perform calculations more quickly and more easily.
And I think this person was sort of challenging the idea that there's nobody
who's just a math person.
And it's true, some people can do calculations more quickly or more easily.
But what we know is that has come about because of the millions of opportunities
they've had for brain growth and the messages they've been given.
So, when you see students who find math more easily than other students.
I don`t think what you think of that is, this person is more of a math person.
But this person has had more opportunities for that to develop.
And we can make those opportunities more equitably available.
Somebody that said we're doing a summer camp in Chicago and
we've got students for ten days and three hours a day.
Is that enough to develop growth mindsets?
Yes, definitely, we had students for longer time than that, it's true.
But we recently did a one-day intervention with students where we
brought girls onto campus and did like a little mini camp for a day.
And even that day the students were really changed the way they
thought about math and themselves.
So definitely that's enough time, I think.
Somebody said, how often do you recommend a routine like dot cards for
grades 3 to 5?
I think that it's really good to use number talks of different types every day.
So a dot card is a particular type of number talk that's visual and I love them.
We have them inside of our week of inspirational math.
Then Sherry Parrish [INAUDIBLE] a book of many different dot cards.
But some of them could be numbers as well, and number talks are also wonderful.
And you can find lots of information on number talks.
So a dot card or a number number talk every day is a great routine for that.
Somebody said I'd love to access this video of a dot card for PD for
aspiring teachers.
Is it available?
So that video's inside the online class.
And that's the way that you can get that.
So I really recommend for those teachers that you'd like to learn from it,
getting them to register for the class for PD.
Best way to see that.
So somebody said once s sense of quantity is developed, is there a point to which
efficiency, calculation, processes, pathways, etc, should take over?
So, it is true that after you really understood something and
after you've engaged with it in different ways, visually and numerically.
You may get to a routine where you're able to very quickly come up with
different ideas or calculations or math facts for example.
Some people think that I'm saying math facts aren't important, that's not what
I'm saying but I'm saying we can learn math facts visually and deeply.
And after you've done that,
then they are more accessible to use in a more efficient way.
And yes, that's fine.
But what I try and get away from is a misconception that we do this in the early
years and with younger children so that later people don't need this.
And that isn't the case and people need to be
>> Engaging visually and
big numbers all the time whether they're 16 or 25.
Some people think well, some visual people and
they're visual learners and some people aren't visual learners.
That's also damaging an idea.
Because if you don't think visually or your students don't think visually,
you need visual learning more than anybody to develop those pathways.
And it's not okay to just think well,
we'll just work with numbers with those people.
We want everybody to be developing and
using those pathways through their lives not just in some years.
Someone said how calculators fit into student problem-solving for
our middle grade students.
I would think the calculator question is never a question of do you or don't you.
I mean, yes, we always want to use really good technology.
We may not have students use calculators all the time and
we don't want it as a replacement for number sense.
Number sense is really important for students.
but when they get past and into high level mathematics or in middle school,
for example, it may be better to have them use a calculator some times
that you can get onto other ideas that you're working with them on.
So they don't have to be calculating everything and that slows everything down,
and that's fine.
Yeah, you wanted to vote in a number sentence.
But yeah, at times having a calculator is a really good thing.
It allows you to move into other content, which is great.
As sixth to eight grade uses CMP3 curriculum,
does this curriculum still fit the bill?
In my mind, so yeah, I think the CM3 curriculum
is one of the good curricula that are out there.
I didn't think any public curriculum at the moment pays enough attention or
has taken it on, the brain, science and the eyes.
The knowledge we have that we need to think visually and creatively.
So, that's why we're actually working on our own set of materials now.
But definitely, that's
one of the [SOUND] one for you.
When are the new curriculum books released?
And how can we get them?
So, the Great Four book is on Amazon now.
The Great Five will be the one that follows fairly soon afterward.
And then I believe three and then the middle school grade and then two to three,
but it will take us a while with a little tiny team at Youcubed and
we're really trying to make really high quality materials for people.
So somebody said, how do you keep the spirit in practice [INAUDIBLE] frustrated
instead of talking about problems in multiple ways?
They talked of memorizing algorithms the same old way.
Not sure what that means, any of that means.
So I don`t think we have a need for kids just practice numerically without visuals,
without different ways of thinking about it and different ways of doing it.
With most successful students,
they are the ones who understand algorithms not just reproduce them.
I did a big analysis with the Pisa team, which was really interesting.
We had data from 13 million students from across the world,
15-year olds and we were able to analyse their approach to mathematics.
Some of the students have memorized their way and
thought memorization was the way to be successful as many people have in the US.
Other students are seeing big ideas and seeing connections.
What we found by analyzing the data set was that the memorizers were the lowest
achieving students in the world.
They were the lowest achieving students within each country and
every country that had a high number of memorizers is a low achieving country.
The US is one of those.
So, that we wrote about in an article to Scientific American and
you can find that on our website.
So, I think we're coming up to 11 o' clock.
Did you want to finish some things off?
>> Thank you all again for joining us today with the webinar.
Have a great day.
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