Maths with a Specialist: Melissa Fanshawe’s Approach to Inclusive Maths Education

Hello, my name is
Melissa Fanshawe and I’m coming to you from Brisbane, Australia.
I work at the University of Southern Queensland.
I work in the school of Education and I teach at pre-service teachers
how to teach maths to students in that classroom.
But I’m also a trained teacher of students with visual impairments.
So I’ve been loving using the LEGO Braille Bricks to try and introduce
topics for our students and to help them make meaning of some maths concepts.
The first thing I’d like to show you today
is the concept of part part whole.
Now part part whole is one of the first understandings
that students have of number, and it helps them to understand
that number is not just a symbolical concept,
but it’s actually, broken up into different things.
So for example, the number 10 could actually be 2
and 8, or it could be 5 and 5.
And that’s really important for our basic understanding of number
and having flexibility of number
when we’re doing equations and those sorts of things.
So the first thing I’d like to show you, I’m just going to move
my screen down, to my LEGO Braille Bricks baseplate.
Now on my LEGO Braille Bricks baseplate, I actually have a double,
double number symbol.
And that is when I do that, it’s representing to the students
that I work with that
everything on this board is going to be number and I,
it’s it’s like having a capslock on, I guess on the computer
so that I’ve got capslock on everything on here.
It’s going to be number.
Now, I feel that it’s very important before we actually teach
the symbolic nature of number,
that students have an understanding of real life items and what it is.
So in this activity that I’m doing, it’s about partition in number.
And I have the number 20
at the top of my LEGO Braille Bricks baseplate.
And I want students to work out how many different ways can we break up 20.
What can we do to do that?
And so firstly, I’m actually going to use some real life manipulatives.
And that helps them understand that 20 isn’t just a symbolic figure, but it is
it is the representing real life.
So I have some little figurines and they’re of different,
people that could be in my classroom, and I’m going to work out
how I can put 20 into some groups.
So I get the students to play with it, with the,
the 20 little figurines, and we can break them up into some groups.
So I might have, for example, I might have 1 in 1 room
and 19 in the other.
And so then I get the students to represent that
by using the LEGO Braille Bricks.
So I have one and 19.
So one way we can partition 20 is to have one and 19.
So students get more familiar with this.
And they get they could do 2 in 18.
They could do 10 and 10.
And they could have the the different students in the in the different groups.
And they represent those same with the LEGO Braille Bricks.
I then start to go to, you know, could we actually have them in more rooms.
So in this one we had 3 in 1 room, 4
in another room, 4 in another room, and 9 in the other.
So then students can represent this with 3 and 4 and 4 and 9,
where partitioning is a really important concept
that we need students to understand so that they can understand numeracy.
It does help them a lot with with number
and number understanding, as well as that flexibility
when they go into operations, because then that they can work out
if they’re adding a number, they can go, oh 20 is actually 1 and 19.
I could add on 3.
So it really is a wonderful opportunity to help
students have the LEGO Braille Bricks because they can use them flexibly.
It’s like using, a notepad where they can write down
the different ways that they can make the number 20.

So the activity that I’d like
to show you next is an activity to do with place value.
And place value is incredibly important because it helps students to understand
why we can only go up to 9 in each house,
and to how our whole number system works, because we start with the pattern of ones
tens and hundreds in the units, and then ones tens and hundreds,
in our thousands and ones tens and hundreds in our millions.
And we actually go up and go up.
And, we also have that underneath our units
where we actually have, tens and hundreds and thousands etc.
So it’s really important.
Now, what I’ve done is I’ve made a baseplate
using units with ones tens and hundreds over here.
I’ve got thousands with ones
tens and hundreds and I’ve got millions with ones tens and hundreds.
And the importance of that is to show that patterning system for our students
and that they can actually, manipulate and use this place
board to put down
numbers, to pick up numbers to, to work out where they’re sitting,
which helps them to understand which has they’re in and how to say the nine.
Now underneath that I have the double numbers.
And again that’s representing that anything coming after that
is that in the number system.
And at the bottom of my base plate,
I actually have a pile of numbers that students can use.
And in this activity we’re not going to use those.
But I have them there just in case.
And I have seen on the LEGO Braille Bricks, on
the maths one, there was some wonderful 3D,
place value systems that somebody had made, which was great.
But you can also use LEGO Technic and Wiki sticks
and those sorts of things to break up your your house values.
So that’s really great.
Now I’m just going to move down to my baseplate,
and I’m going to show you that a game that I play.
Now the reason that I play,
I want to show you this is because it’s a game that I play
with grade sixes very commonly in a classroom.
And what the students have to do is that they have to actually,
roll the dice or take out some numbers, and they have to make the biggest number
that they can in, in the place value system.
So I’m actually just going to remove my, no spinning
because we don’t we don’t need that, for this activity.
And I’m going to the students have six numbers in a bowl.
And what they’re going to be doing is they’re going to
actually try and, put down
the biggest
number that they can make when these are random numbers.
So they’re not going to know what they are.
And what it means is that they have to have an understanding
that place, they need the biggest number at the front.
So, thousands is bigger than ones.
And so this would come after a lot of hands on
manipulatives and working out, you know, using,
you know, manipulatives to understand what ones are in tens and hundreds.
But this is a game, like I said, that I play, in upper to middle primary
so that grade six and the students would be about 12 or 13.
Yeah. So the first one I picked out is a three.
And I know three is a reasonably small number.
So I’m going to take a guess and put it around.
I’m going to make that 3/10 which is 30.
So that’s the first one that I’ve actually put there.
Okay.
So the next one I’ve picked out is a one.
So I’m going to say that that is a small number.
And I’m going to put it in my ones house.
Now I do risk of course.
Getting a zero and zero is an interesting discussion.
So zero is one that you can put in at the beginning,
or you can leave out until students are really confident.
But zero is a placeholder and it means that there’s nothing there.
So if I put it in the one house, it’s it’s small.
But if I put it in the, in the thousands, if I put it in 100,000,
it means my number is going to be significantly smaller.
So, it is
something that you can decide to put in or you can knock this one to number four.
So again, I’m going to put it in our, 100 tasks
and hope that I can get around this.
Keep getting some bigger numbers. Oh another four okay.
Well we’ll put that in our a thousands of units and see how we go.
And now I’ve got an eight and
oh I’m going to think that that’s a really big number.
So I’m going to put that in my hundreds, thousands.
And then lastly I have a five. So
I’ve now made the number
854,431.
Thank you.
Yes. A bit difficult really and upside down.
But anyway, so I, I’ve actually made the biggest number that I possibly can.
And now students can actually if they haven’t, they could rearrange it
and see what the biggest number is that they could have made.
You may have noticed that my board is on a stand, and,
this is just a little base board, that I use.
It’s it’s actually a tablet holder, an iPad holder
that you can, buy here in Ikea.
But I find it really easy to sort of it’s
a bit like a slope board for students and makes it a little bit easier for them.
I could then rearrange this number and make a smaller number
at the smallest number I possibly can, or I could get another six numbers,
and then I could work out which one was bigger
and which one is smaller and need some comparison.
So that’s just a little activity
with place value.

Okay, so I’ve
got my same base plate for this activity.
But we’re now moving to operations and I’ve got
I haven’t put back the millions because I’ve just got 100,000
and hundreds, tens and ones in my thousands
and I’ve got hundreds, tens and ones in my units or my ones,
which you can, call whichever one you want.
Now, I’ve kept my same number there
that we just keep from our previous activity in number.
And I, of course, have my double double numbers
so that we knowing that everything coming along here is now numbers.
And what we’re actually going to do is we’re going
to multiply this all by 3 now.
So for our students that we have some numbers down the bottom
so they can use those, I do have a big box
beside me with the numbers, already in the,
category.
So in this box I actually have a plastic box,
and all of the numbers and letters are divided by their number.
And let us so that it’s easy for students
to be able to get out if we require some more.
Now, the other little thing that I have down
the bottom is a little mini figure, and this one is police person.
And that was just, a little LEGO figure that I started using for my students
as they had done some sums or some operations.
If the, and just so that they could have a little reward when they had finished.
So I don’t mind him that he’s just sitting there ready.
All right.
So this first activity that I’m going to do is
I am going to multiply this number that I have,
which is 854,431.
And I’m going to multiply that by 3.
And so what I want to be able to do is
I need our students to know that we actually start at the ones house.
And so when we’re multiplying 1 by 3, it means that we’ve got 1 here.
And we are going to multiply them by 3.
So I have 3 manipulatives.
And I have just shown that I had one.
But now it’s three times that amount which is three.
So down the bottom here I would go one times
three and I would make a three.
And again like I said before, I’ve seen some really, really great, 3D
place value systems that people have made on some other videos.
So please do use something that works for yourself.
This really helps students to have an understanding of
of setting out I’ve found and how it’s setting the place value system.
It’s not going to work for all students,
but it’s just one idea that you might want to use.
So the next one is three times three, which is going to be nine.
And also students are
going to have to have a good understanding of the symbolic numbers.
So they that would be past, the manipulatives
and they would be starting to understand, you know, this place value system.
But the manipulatives could be there in case they couldn’t work it out.
So if they couldn’t work out three times three, they could get,
three into three groups and work out that the answer was nine.
All right.
So the next one is four by three.
Now this answer is 12.
So I’m going to grab 12.
And I’m going to put the two down there.
And I’ve got one left over.
But it’s not actually one.
It’s it’s one in the next house.
So you can when students carry that over,
you can actually put that there so that it’s sitting there and it’s ready to go.
And people use that in, in different houses.
They, they put it in different places in different countries.
So you could put it wherever you do you want to have it.
Okay.
So the next one is three, it’s oh again, 12.
But this time I’ve actually got my one here already.
So it’s now going to be 13.
So I actually need to get
the three
put down here and put my one back up here.
Okay.
Five three is a 15 but I’ve already got one again.
So it’s now going to be 16
okay.
Which is pretty handy having this little thing here actually
to tell you the truth.
And I’ve got three 8 to 24.
But again I’ve got another one.
So now it’s going to be 25.
So I need to get a 20, a two and a five.
So I put down a five and I’ve got a two left over which guess what I did.
Actually me my million’s house over here. So
that was required.
And we have hundreds tens and ones and I can put the millions back on there
and understand why we need to do that.
So our total number, if I multiply
854,431 multiplied by three
is 2,563,293.
So now I need to get another little LEGO figure.
for having completed the task!

Now after my students have been busy doing lots of work
and they have gained three little mini action figures,
I like to play a game with them and that is just to break up the working,
but also to be able to have fun, to be able to work together, to be
able to play and to have a lot of joy with what we’re doing with maths.
And I also want them to see
how maths is used in real life, to be able to interact with other people.
So the activity that I’m going to show you today
is very much based on dominoes,
and that is because you can have two players, you can have three players,
you can have four players, but it’s just a little twist to that.
And I guess, the reason that I love this activity
is it stemmed from one that Mark actually showed me where it was.
He plays this game called battleships, and the students
put forward a number H, and the biggest one gets to keep them all.
Well, this one is very similar, but it is based
on, as I say, dominoes now at the beginning
or at the front of the screen, I have actually randomly added the bowl.
You have selected seven numbers.
So you have a three, a one, an eight and nine, a five and eight and eight.
So you did pretty well.
There were some big numbers, but that may not help you in this game.
All right.
And I also have seven numbers selected.
Now the reason that I have not put these down on your numbers
down onto the board is because I’m going to spin the board in this game.
And if you have a lazy Susan that is fabulous
for this activity, but if not, you can just, spin the board.
So that is fun.
Now in this activity, the first person is going to start
and you’re lucky because you’ve got a big hand to start.
I don’t know how that’s
going to go all the way to the end, but anyway, let’s let’s have a go.
Now, you’ve probably noticed that I haven’t done one thing.
Okay?
I haven’t set up my game board with the double number system,
which means that everything now going to A is a number.
So let’s start with a and number nine okay.
Now in this activity to make the dominoes
go with the number nine on my side or my turn,
what I actually have to do is try and find something that makes up nine.
So I have six, six and three.
So I’m going to put six and three after the number nine okay.
So nine is six plus three.
And then it’s now your turn.
And you have to make up the number three.
Now I could have been a bit nicer and put three and then six because
making up six would be slightly easier than making up nine.
But I wasn’t, so it didn’t happen.
So you have to make a three.
But fortunately for you
you have eight minus five.
You have an eight and a five.
So you could do eight minus five, which then makes right
now you can, as I said, put your board on a lazy Susan.
Oh I’ve just put it back onto my board.
And then it’s easy to pass between people because they do want to up the right way.
If you’ve got two people
sitting across from each other, it makes a little bit hard
when one’s upside down trying to break their LEGO Braille Bricks.
But this can be played by four players.
Five players?
How many players you want to want to play?
So that person ranked three is eight minus five.
So I’ve got five.
Oh I’ve actually got five times one.
So you
can do any multiplication that you like.
It could be any operation.
It could be multiplication, division, anything you like
to make the previous number.
And that’s how we can play LEGO Braille Bricks
domino in our classroom.

Okay.
Now in this activity we’re going to do some algebra.
And when people hear the word algebra
they sometimes get a little bit stressed about maths.
But I’d like to show you how we can make it really fun for our students.
Now I have a box and in my box is a number,
but I cannot show you because it is my mystery box.
What is inside my mystery box?
I don’t know, but we do have a clue.
Now on my LEGO Braille Bricks baseplate, I have the double number system,
so I’m keeping everything up in capitals or in, number lock, as I like to say.
And I have this mystery box and what is going to be inside it?
We don’t know, but we have a clue.
The box plus two equals seven.
All right.
So the box plus two equals seven.
So this is the beginning of algebra.
Now we don’t know what’s in the box but it’s too hard to hold the box here.
So we can represent it either by using an x or y.
So we can choose one or the other of those.
Now I will tell the students we do have the double number lock.
But this is a variable.
So we’re just going to put that there for now.
Okay.
And sometimes we do need to tell them we need to explain what it is.
But it helps to make sense.
Now this activity
is actually very useful for all of our students in that classroom.
So we have seven okay.
And we have the mystery box and the mystery box
plus two equals seven.
How are we going to work this out.
Now algebra is like having a balanced scheme.
And if you have one on one side it must be on the other.
And I am demonstrating using a rod and it is going up and down.
But in algebra we need to have it balanced.
So if we do something to one side we’ve got to do it, for the other.
And what I’m trying to do is I’m trying to isolate the Y.
So I want to find out what it is.
And it’s here, it’s got one plus two.
So I’m trying to work out what it is plus two.
Well what we’re going to do is I’m going to take away two,
because if I’ve got plus two and I take away two, I have zero.
But if I do that, it’s not going to be equal.
So I have to do the same to the other side.
So I’m going to take away two from here.
So I’m going to take away two. Okay.
But that means I also have to take away two from the other side.
So seven take away two is five
okay.
So I’m going to take away two from both sides.
And I have five.
Let’s just check if this makes sense.
I had seven all together.
And y plus two equals seven.
So y plus five.
So that’s looking good so far. Let’s have a look.
And the number is five in my mystery box.
So what we’re trying to do is we’re trying to make algebra fun.
What I love about the LEGO Braille Bricks for algebra is that students
can manipulate, because when they’re using a Perkins brailler,
I’ve seen some students throw out this equation, and by the time they’re finished
brailling out the equation, they’ve kind of forgotten what was there
and they’ve had to do the next line, and it just becomes so complex.
There’s a lot of cognitive load, on the student when they’re doing algebra.
But by using the LEGO Braille Bricks, students are actually able to manipulate
and to feel the numbers and to be able to, explore what those numbers can be.
So that’s why I love using the LEGO Braille Bricks for algebra.