2017 Jack Cusack Memorial lecture
Connecting culture and mathematics
Our annual Jack Cusack Memorial Lecture reflects on and celebrates the contributions Aboriginal and Torres Strait Islander peoples have made and continue to make in addressing the national science agenda.
The 2017 Jack Cusack Memorial Lecture will be given by Dr Chris Matthews, chair of the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) and winner of the STEM Professional Award at the inaugural Indigenous STEM Awards in 2016.
The vision of ATSIMA is that all Indigenous learners will be successful in mathematics. Dr Chris Matthews will outline thinking around this vision which is centred on connecting culture and mathematics. Dr Matthews will explore general perceptions around mathematics and culture gathered from participants (mainly teachers) in numerous professional development workshops and published articles.
From these perceptions, Dr Matthews will explain the connection between culture and mathematics, and outline the development of the Goompi Model that uses this connection to create different ways of teaching mathematics to Indigenous students. He will also provide examples of this work i.e. new ways of teaching mathematics from Indigenous STEM (science, technology, engineering and mathematics) Camps in New South Wales, STEM Think Tank in South Australia and Yirrkala Community School in Arnhemland, Northern Territory.
Good afternoon, everybody.
– [Audience] Good afternoon.
– You there?
That’s good that you’re alive.
Good day to everyone that’s out in the Internet, too.
I believe that they’re all having a look, too.
So, thank you for tuning in if you’re out there.
Auntie, I just want to say thank you for the welcome.
And I really enjoyed our yarn before the start.
And, also, I was really happy to meet you, because the time I was seeing you is you going to open up Parliament.
And, for me, that was such a significant thing to do.
That Aboriginal people are actually opening up the start of that on your own land.
And that just…
I just want to say thank you for the honour of that yarn.
And thank you for the welcome that you inspired on me for coming to talk.
The topic of my talk is The Goompi Model: Connecting Mathematics and Culture.
And I will explain that.
As you know, my name is Chris.
I’m the chair of the Aboriginal and Torres Strait Islander Mathematics Alliance.
Which is a non profit organisation aiming to improve math education for all of our mob.
Well, actually, our vision is that all Aboriginal learners will be successful in mathematics.
So, we wanna have a positive vision along that sort of lines.
Our models are the inaugural recipients of the STEM professional awards
run by CSIRO and BHP Billiton.
And that’s a great honour for myself, as well.
Part of the reason I’m standing here giving the lecture today.
But, also, the honour, really, there, comes…
I didn’t put my name in a hat.
There was actually two other Aboriginal scientists who actually valued my contribution in life.
And they’ve put a case forward for me to get that award.
So, that was Mibu Fischer, one of my relations, actually.
And, also, Cass Hunter, who’s actually done one of these talks.
Or they actually both have done one of these talks, as well.
So, that was a great honour for them to nominate me for that award.
And for me to get that award.
So, thank you, BHP Billiton, CSIRO, and Mibu and Cassie.
It’s also an extreme honour to actually give this memorial lecture.
And, as I was reading Jack Cusack’s bio, I pulled up a few quotes that was really interesting to me.
You probably all heard this before, but Jack Cusack was an expert botanist, as they say.
And he actually gave a valuable contribution to CSIRO research effort.
So, he is actually recognised as being an expert person within the STEM fields.
They also say that Jack’s keen eye, extensive knowledge, and expert bushmanship helped train several generations of scientists.
So, he was a teacher, as well, that offered a lot of himself.
But, also, that statement also says that he actually walked into the scientific community as an Aboriginal man.
And actually was teaching from an Aboriginal point of view, as well.
Which is a thing that is very significant.
And the other part of that is that he was a technical officer from the early 1970s until he retired in 2002.
Now, I’m not having a go about HR people of CSIRO, but what seems to me is that he has actually worked far beyond what he is supposed to do as a role within the organisation.
So, he had a vision, I believe, from reading these things.
I’m just me just putting my thoughts across this.
So, his vision was to bridge that gap between him as an Aboriginal person, man from the Walpiri people, and this scientific community.
To the point where he was valued as a teacher and an expert.
And I think that’s quite a significant thing.
So, that’s why I’m extremely honoured to be giving this talk.
So, I might as well start with my story.
I always find this a bit self-indulgent, but I hope people get something from my story.
I suppose I don’t like talking about myself too much, but I’ll forge ahead.
My education journey is what I wanna talk about.
And, basically, my education journey was mired with racism from teachers, as well as students.
And there’s a certain dynamics of racism that occurs.
And this happened from when I was a very young age.
And from a very young age, you have to deal with these attitudes from people.
I’m from the Quandamooka people on Stradbroke Island.
But I actually grew up in a place called Toowoomba.
If anybody know Toowoomba…
It’s in Terry Heights.
I lived up the road in Ramsey Street.
So, Toowoomba is west of Brisbane, for people who don’t know.
Sitting on top of the range.
It’s actually very beautiful country up there.
But, at that time, I was generally the only Aboriginal kid within my peer group.
And there was only a very few of us in the school itself.
I went to school in 1975 through to ’87.
It was a time period where the referendum wasn’t too far off then.
It was not too far away.
Aboriginal people were coming in force to march about their own rights.
Their human rights.
Which manifested as being land rights.
And all this socio-political stuff was filtering in through the schools by the teachers themselves.
So, your typical class could be a teacher started talking about they saw the land rights march last night and what a waste of time.
And they’re only after money.
And all this sort of stuff was filtering within the school.
And I’ll be the only Aboriginal kid sitting in that class having to listen to that.
And the response of the teacher to students.
And them feeding off each other.
To be sitting there in this isolated position.
So, it’s a really strong sense of just being alone when you’re in that position.
And there is that explicit forms of racism that comes through from those discussions.
And there’s also the implicit stuff that comes through the education that you’re getting, as well.
That you don’t really belong within this system.
There’s a sense that you get as a child growing up through that.
And I often say that there’s a point where you’re feeling that you’re sitting on a knife’s edge.
The knife’s edge is where you can actually reject society.
Stick your middle finger up to the world and say stuff it all.
Or, luckily for me, I actually put all my energy into a part of life which I had an interest in.
So, my next point there is I thank Mister Spock.
I was, as a kid, I was a mad science fiction person.
Loved my Star Trek.
Loved my Star Wars.
As a kid, we saw Star Wars for the first time on the drive-in theatre.
There was this big impression on your mind.
But all that science fiction stuff sort of promised this other world.
This other, better world.
And Mister Spock was a bit my hero.
And I sort of look at that a bit retrospectively.
He was a person who sort of pushed away all his feelings.
And, at that point of time, I think I was doing that.
I just was burying myself in something to push away feelings.
So, I put all my energy into computers.
‘Cause they were the thing around that time.
Computers were still big chunky things that sat on a desk and only had about 8K of memory or something.
But, with those computers, I was teaching myself to programme.
And, from the school at that time, as well…
The computers were starting to be put into school.
We were actually taught a few new miracle techniques, as well.
So, this was the connection between maths and computing and programming.
So, I was madly, silently away learning how to programme integration techniques, which is, I think, a bit unusual.
But it’s something I could pour my energy into.
I put myself into sort of a cocoon away from society where I can just bury myself into this thing that I could do.
I avoided anything at school to do with social sciences, history, anything to do with people.
But, ironically, the dynamics I was talking about before with teachers bringing this stuff into the classroom, my maths teacher was one of the worst ones doing that.
But I still sat in that class and did the work, ’cause I can just focus on that maths work.
So, in those early days, I sort of used maths and science and computing to disconnect myself from people.
I must say, another aspect of my life was that I did come from a very strong community, Aboriginal community.
And my mother, who is from that community, made sure that we went there every year.
So, I did grow up with a very strong sense of who I was as an Aboriginal person.
And I did know, intuitively, that the stuff they were trying to feed us through the schooling system was not right.
But they weren’t supporting me who I was as an Aboriginal person. And, when they knew I was good at maths, they all sort of half supporting me.
Sort of a bit weird.
But I knew I was good.
That’s one thing I knew.
I knew I was good.
And I began to teach, even when I was in high school.
I had a group of high school kids who couldn’t understand the maths two at the time, which was the computing part of mathematics.
And they actually wanted me to run a class.
So, there was actually about 20 kids who sat in the classroom on a lunch break where I actually taught the class.
So, I taught this group of 20 high school kids who was having trouble understanding the connection between maths and computers and how to do miracle integration, I think was the actual lesson I did.
And, at the end of that period, one of them said to me, “You should become a teacher.”
‘Cause they thoroughly understood what was happening after that.
So, my interest and my passion got me to university.
That was my ticket out of Toowoomba, basically.
I needed to broaden my horizons.
The one place I did go to was Griffith University in Brisbane.
That was the first time in my educational history that I was actually supported by Aboriginal people within the education system itself.
So, I went to first year university in 1998.
Most universities at that time had an Aboriginal support unit within them.
And auntie just told me that she started the one here, at ANU.
So, all those support units was the only reason I got through my education in university.
And I actually felt at home.
I actually, also, where I lived was actually within an Aboriginal-Torres Island hostel.
So, that was the first time in my life, too, that I got to meet a lot of Aboriginal people from around Australia.
There was people from the Torres Straits.
There was people from Mount Isa.
There was people from just even Gold Coast and New South Wales and stuff like that.
So, I got to meet people from different communities
and hear their stories and how they struggled through their lives, as well.
And one thing at university I did is I always continued to teach in all of the ways that I could.
It was something I always did.
And that could be 101 tutoring through the Aboriginal-Torres Islander Unit, they called it at that time.
Through to when I actually started to do my post-graduate and I taught within workshops and stuff through university.
And continued this process of teaching maths through that process.
To cut a long story short, I did complete a PhD in applied mathematics.
The project I did work in was around soil physics.
But the whole idea of that was looking at a care for country type approach.
So, what I mean by that is that I was developing a model to look at different cover liner designs for waste dumps to prevent groundwater pollution.
So, the thing for me there is that, as a kid growing up in Stradbroke Island, we were always going out as a family group on the back beach, into the bush, swimming in salt water, swimming in fresh water, collecting food, making fires.
And, from that whole process of doing that, you actually are developing that connection for where you come from, the land you come from.
And also thinking about ways of protecting it.
Because on the island itself was sand mining.
And sand mining had two effects for our community.
One of those was this actually supplied employment.
But the other aspect of that is it did change waterways.
And it did change a lot of the island.
So, a lot of that was the talk that was around us, as well.
So, for me, actually doing a project where we look in that preventing groundwater pollution or something like that was that keyed me into that.
That was a real interest.
To actually do something like that.
However, as I was going through my PhD and towards the end of it, I was faced with two conundrums, really.
One, the ethical one, and there’s one about who I was, as an Aboriginal person, as well.
So, the ethical one was around…
There was one day where I was doing my mathematical modelling in my little world.
I had a thought that, if I did design the best cover liner in the world that prevented groundwater pollution, would this be an excuse to go mine Kakadu or go mine some other place?
So, I did approach my colleagues and supervisors around this idea at that time.
And the response I got from that was we’re the scientists.
We don’t worry about that.
That’s what social scientists do.
And, to me, that was sort of a big cop out.
You know, how can we just sit here and create something without even thinking about the implications for society and people around us for our own communities?
So that sort of thing didn’t ring true for me.
And I looked further within the science community and I did get a lot of good experiences from doing so.
So, don’t get me wrong.
I got to travel overseas to see what a lot of other people do.
One particular highlight was going to Oxford University and seeing how they do things.
But what still rang true for me was that the problems they’re working on was doing this advancement of industry.
And that didn’t sit well a lot with what I believed as an Aboriginal person.
So that feeds into the next one.
Which is why is an Aboriginal person doing this?
Why do we really need to do this?
And that’s the sort of thing that I’m sort of immersed myself in at this point in time.
For me to sort of start to look at that question, what I started to do is to look at the connection between maths and culture.
Now, when I say that’s where my thoughts were going, one other part of what
happened then in my life, just as I was having these sort of conundrums, Professor Tom Kuber from QUT rang me up out of the blue.
He’s a maths educator.
And he rang me up asking whether I wanted to be involved in maths education projects for Aboriginal kids, Aboriginal people.
And I jumped at the chance, ’cause it fitted much better with what I wanted to do anyway.
It’s sort of a bit of a funny story.
He said to me, when he first rang up, he said, “How can you exist?”
He said, “All the stats say that Aboriginal people can’t do mathematics and here you are doing a Phd.
So, how can you exist?”
And my response is, “Tom, I just do.
I don’t know what you’re talking about.”
And then, the other thing he was saying to me was that we had these projects in a lot of different Aboriginal communities, but they feel like they’re wading through wet cement.
They didn’t know why things weren’t working.
They were using the usual approaches to maths education, but they weren’t getting anywhere.
So, I thought this was a good challenge for myself to actually think about what does it mean to teach maths for our own people, for our own kids?
And this is where me looking at these connections really come into the fore.
So, what is culture?
So, what I did was basically, fortuitously, was starting to do a lot of professional development workshops to teachers at that time.
They’re mainly non-indigenous teachers.
And they were teaching Aboriginal kids.
We live in a point in time where most of our children get taught by…
Aren’t taught by a mob.
It’s taught by other people.
So, it was a good chance to talk through some of these ideas.
So, basically, I do a workshop where you use this iceberg model.
I’m not quite sure where it comes from.
But I did steal it from somebody else.
And, basically, the iceberg…
The wavy line’s the water.
The top of it is the stuff that you see.
But the stuff below is the stuff you don’t see.
So, it gives you that intrinsic sort of stuff.
So, culture, you have the expressions at the top, like art, food, stories.
And this is the stuff that would typically come up in a workshop.
So, I’m getting people to brainstorm what they understand about it.
And the underneath stuff is the stuff that sort of informs our expressions of it.
SO, you got who you are, your worldview, your philosophy, your spirituality, your beliefs, your practises.
All that stuff sort of informs how you express those things through art and food and stories, artefacts, and so forth.
And then the thing that I like about this model is that it’s actually very dynamic.
‘Cause, as you practise culture, you have an opportunity to think about what does that mean in terms of your knowledges.
And you can expand and grow that knowledges.
And, from the expanding and growing of your knowledge, your philosophy, your beliefs, and so forth, that then informs the way you start to express that culture.
That make sense?
So, when you think about stuff like that, culture is very all encompassing.
So, there’s no way that maths can’t be involved in that in some form.
So, when I actually talked to people about what is mathematics, generally we come up with this for the first thing.
And, particularly when you’re talking to teachers, they actually want to recite the curriculum to you.
So, most of the time, they’re talking about numbers, problem solving, geometry, and it goes on and on and on and on and on.
And that usually comes out first.
But, sometimes this one does comes out first.
Which is a fear and anxiety of mathematics.
I did one talk in a group of first year students with university and, when I put up the thing what is mathematics to you, what is maths, someone in the back just yelled out “Vomit.”
It was almost like a Tourette’s thing and they couldn’t help themselves.
They screamed it at me, really.
So, there is that image of mathematics where people have this strong fear and anxiety around it.
And there’s a lot of people with it in that thing.
But there are people who do love maths and think it’s fun.
I do find, when I do these workshops, that the love and fun are a smaller group than the fear and the anxious.
Correct me if I’m wrong, but I think that is true.
There’s actually fields in maths education actually looking at this maths anxiety idea.
I did sort of push the discussion along a bit, ’cause they usually get stuck there on those two things.
So, I do push it along a bit and say who does mathematics?
And, every group, they’ve always said everyone.
So, you have this thing that everyone does mathematics, but a lot of people fear it and are anxious about it and don’t have a good experience with it.
And I sort of ask the question what does the maths that everyone does…
And people like to talk about money, time tables, measurement, all that sort of stuff.
But the thing that I sort of reduce it down to, and I get them to agree with me, is that, basically, the maths that we do, that everyone does, usually can fall within number operation and, perhaps, some algebra.
I then ask them what is the other maths?
And most people struggle to articulate what that other mathematics is.
You know, some people will say calculus, maybe.
But they struggle to actually get some other form of maths in their mind.
Once I’ve sort of articulated some of those maths, I’ll ask them who does that type of maths?
And the people generally talk about the realm of the expert.
The engineers, the scientists, architects, whoever it is.
They actually can articulate those people.
And I ask them to think about the stereotype around that.
And sometimes people don’t really wanna say the word, but I get them to say the n-word.
The nerd word.
And actually talk about what that nerd word mostly means.
‘Cause it usually doesn’t mean a woman.
It’s sort of changing a bit with The Big Bang Theory, I think.
But most people don’t usually see nerds as women.
They usually see it as white males with beards and lab coats is what they usually see.
But also someone who has this innate ability.
Something that they’re born with to comprehend some stuff that no one else can comprehend.
They’re usually someone who is socially recluse.
They don’t relate to people at all.
So, we build this stereotype.
So, what I’m getting at when I’m doing this workshop is I say to a lot of teachers that the reason we get these two first is ’cause that’s our main experience with maths education.
Maths education, we do just sit in this world of numbers.
In maths education, we just do exercise after exercise.
We try and get the right answer or the wrong answer.
Sorry, we try to get the right answer.
We usually get the wrong answer.
And that sort of dynamic feeds into this fear and anxiety.
‘Cause, if you’re continually getting the wrong answer, then you’re continually being wrong.
That’s not a nice place to be.
You’re also one of those people who maybe get things right.
Most of the time.
So, you can develop a love for mathematics.
So, this nature that we get in here, these two here, is a direct reflection of how we teach mathematics is my thing.
Ask any child who does maths and they’ll say everyone.
And we carry that with us all the time.
Everyone does mathematics.
But the majority of maths that we get taught is this stuff here.
We spend probably all of the primary school and, also, for some kids, high school in that space generally.
We do have this problem within maths education that we then try and take this cognitive jump into this space around year seven to year eight, usually.
Where they’re thrusted into algebra all of a sudden.
And you get these kids who are saying, “Why am I doing this?
I’m never going to use it again.
Where’s the numbers?
I’ve got letters.
Why are there letters?”
All that sort of stuff.
And there’s no real conversation or teaching within that space.
And then these become unobtainable for a lot of people.
And I’m talking about students in general.
This stuff here.
And, even when we perpetuate the stereotype, I even challenged you.
Do we actually perpetuate this all the time within our system?
When we perpetuate this stereotype here, is it just a way of rejecting being a mathematician or a scientist?
Do we hold onto that because we wanna keep it special and an expert field?
What is it that why we got this vision, this view here that sits there?
Maybe it’s true.
I’ve been to a lot of maths conferences before I was doing maths education.
And it does fit with some people.
But it’s not always true.
And it doesn’t have to be true.
Now, this is a problem for all kids in maths education.
But, now, when I start to think about Aboriginal kids within the classroom, this is a story that generally means that, like Tom was sort of asking me at the start, in a way, that people don’t necessarily believe that we can be good at mathematics within the classroom or within our lives.
And I believe that the root of that really comes down to this notion of terra nullius.
Where we started as a history or the relationship between our two peoples.
It’s our shared history.
And I just put some words around this thing, because we’ve basically got the two spheres of non-indigenous people and indigenous people.
And I’ve just used some words around there that’s sort of in that relationship space.
The one here that, you know, is perceived, especially within the scientific fields, that sort of Darwinian idea, is that the non-indigenous people have a more advanced culture than what we had.
That’s the sort of belief that sits in that space.
That their culture is the one that’s actually valued here in that space.
That they’re the knowledge holders and they were there to teach us about stuff.
And I’ve got this thing here called no opportunity, because terra nullius is a relational thing.
And part of that relationship is there was the dispossession of Aboriginal people.
But the other part of that is that it’s actually developed a deep ignorance for non-indigenous people.
‘Cause, if you believe that the land belonged to nobody beforehand, then how can you engage in that culture or those people?
How can you actually develop some sort of understanding of those people?
So, again, on our side, we actually got the usual words.
Our culture has been devalued.
We’re usually relegated as a primitive people.
For many years, that was written in the textbooks that we are the most primitive people on the planet.
Using that Darwinian idea.
I actually keep old textbooks.
And one I had, it was a geography one and it was written for students in the 1930s.
But it actually states in that geography book that Australia is a white country.
That’s what it says.
And the population is predominately in the south.
Meaning Sydney and Melbourne.
So, that’s how much it filters in through that education system.
That we do not have any relevance at all and that, as a people, we actually are devalued, as well.
So, these sort of ideas are pushed onto us as Aboriginal people from this space.
From the coloniser.
But we do push back.
And, within that sort of space, we do get this notion of fear, mistrust.
And, if you actually read the reconciliation barometer, that’s the one thing that really comes out of that.
You know what the barometer is?
It’s actually a survey run to ask about our relationship between each other.
Aboriginal and non-Aboriginal people.
And there’s a whole range of things.
But the one that sticks out for me was that it says “Do you think there’s trust in the relationship between Aboriginal people and non-Aboriginal people?”
And, the last time I looked, about 90% of the people says no.
There’s no trust.
That’s one of the things that really sticks out.
That we don’t have a solid connection at all.
‘Cause of this history that sits behind us.
And fear is a real thing.
I mean, I’ve talked to teachers about connecting with the Aboriginal community.
And they actually say “We are too frightened to.”
That’s what they actually say.
We might get something wrong.
We might get in trouble.
We might be called a racist.
Or whatever it is, the fear in the back of their mind.
I say to them toughen up.
If you get in trouble, you get in trouble and move on.
Learn from the experience if that’s what you’re gonna do.
But there is a real fear that exists.
There is good will in that space.
And there are a lot of good people that want to work with us in that, as well.
I’m sure there’s many in the room who work in that space who are non-indigenous people working with Aboriginal people.
But, sometimes, this good will can be very much tainted by these ideals.
Because they become paramount.
And the last thing I’ll say about this sort of slide is that there is a huge silence around anything to do with Aboriginal people and science, as well.
Which now it’s starting to change.
If people haven’t read the book yet, please read Dark Emu, because it’s actually looking at how Aboriginal people were growing crops.
I always knew that, as a people, we actually use grains and made bread and all that sort of stuff.
But I didn’t really understand the extent of the grain belt that we had in Australia.
And how many hectares of grains that Aboriginal people were actually growing and harvesting at that time.
They made structures to store these things and so forth.
It’s a really good book.
I usually talk about silencing in here, because most people never even heard of David Unaipon.
How many people, just out of curiosity, knows who David Unaipon is?
So, not everybody.
Only a few people really still.
And I won’t go into the story, ’cause I’ll take too long.
But look up David Unaipon.
He actually revolutionised the shearing industry.
Aboriginal man born in about 1890s.
Lived to about 1960s.
Revolutionised the shearing industry by inventing the hinge for the two blades to go like this.
So, every time you get your hair cut, that’s thanks to David Unaipon.
The other silencing there, too, is I never even heard of John Cusack until I had to do this lecture.
And I think that’s a shame.
Most people wouldn’t know who Eric Wilmart is.
Anyone know who he is?
Anybody heard of his name?
There’s one person.
So, these are actually Aboriginal people.
Sadly, men at this point.
But people like Carly are changing that.
Who actually entered the scientific community in some sense.
Or are actually engaged in the world of science.
And they did amazing things.
But we still don’t know about them.
Kids aren’t taught about them.
David Unaipon was from the Ngarrinjeri people down in South Australia.
And I was in Adelaide not long ago and I was asking Aboriginal kids down there “Who’s David Unaipon?”
And they didn’t even know.
‘Cause it’s not part of our education system.
And you just gotta ask the question why.
So, we need to overturn the mindset of terra nullius.
And we ask the things does maths education and research devalue indigenous people and cultures?
We need to build positive relationships with the indigenous communities.
And we also need to build connections between culture and curriculum, including mathematics.
So, for me, most of my talk will be focused on that bottom line, really.
I wanna talk about how to make those connections and what I do with that
in actually teaching maths to Aboriginal kids.
So, I really have to ask myself this question again.
What is maths?
So, what is it really about?
Where does math come from?
And, for me, maths really is observing our reality that’s around us.
The world that we see perceived through our own lens.
Our own worldview.
We actually select part of that reality and we actually go through an abstraction process.
We create this thing called maths.
And then, once we create this thing called mathematics, we have to, then, critically reflect on that.
‘Cause what we’re actually doing is we’re actually taking a part of our reality that we’re perceiving.
We’re actually making a model of that or an abstraction of that.
And we then need to really ask the question, “Is this really a good representation of what we are doing there?
Am I actually learning something about my reality by doing this?”
So, that critical reflection is very much important.
Now, I’ll argue that most of our education just sits in this maths cloud.
We don’t get any experience of moving from thinking about the world around us.
Thinking about how that builds into the maths world.
And then, from this cloud, we don’t really think critically about what does that mean back in our reality.
‘Cause, if we did, then we wouldn’t have kids in algebra class saying, “Why am I doing this?
Why is there an x?
When am I ever gonna use a quadratic?”
And so forth.
I didn’t wanna show that word.
Now, what also struck me is that, if I cancel out that maths word, what else could you put in there?
Anyone yell out something?
That’s the things I stated to think of.
Music, art, dance.
And those are things that we put this word against.
It’s called creative.
But, if you ask anybody about their experience with mathematics, they won’t use that word.
And, for me, a key part of that, too, was this abstraction process, ’cause what we do is to carry meaning from our reality into the maths world, we actually create some symbols to do that.
And we don’t teach, explicitly, what those symbols actually mean within our maths education.
We just let them sort of sit there and say “Now, I’m gonna use an x.”
Or whatever it is.
This is an integral sign.
Whatever it is.
We don’t really teach what those symbols actually mean.
And the other part of that is that it’s all culturally biased.
And that’s okay, because that’s what we do.
Any piece of artwork, any piece of music is all culturally biased.
It comes from the point of view of the person that created it.
But we don’t really look at that within maths world.
And, if you throw up a theta or an alpha, that’s when people start vomiting.
It’s when they start to have convulsions.
‘Cause they can’t understand why that symbol sits there.
It’s foreign to them.
That’s ’cause it has that cultural history.
And this is the basis of the Goompi Model.
So, the reason I call it the Goompi Model was that I created it to think about maths education from my own community.
And I was actually sitting on my country.
Sitting in the land that we used to call Goompi.
It’s now called Dunwich.
And I created that model.
So, I wanted to do that to keep connection with where I come from and where’s the model was created, but also that notion of keeping connections means that, when we’re actually teaching maths, we should be keeping all these connections alive for our students.
And that is a real challenge to do that.
To break that sort of mould and actually work within those connections.
So, I wanted to show you an example of that.
Before I move on, I just want to put up this thing here.
What I’m talking about, too, that people are using this word called culturally responsive pedagogy.
And this is where I think a lot of this thing fits.
It’s from this paper down here.
And there’s two main points here that I wanted to highlight, too.
That indigenous learners are more vulnerable to bad pedagogy.
Where good pedagogy will benefit all learners.
So, I’m finding that the work that we do is, I believe, falls in the realm of good pedagogy.
And actually does benefit our children, but also benefits other kids within the classroom.
I always get that thing.
If it’s just for the Aboriginal kids, what about the other kids?
But this is still good stuff.
And, also, all children in Australia should know more about Aboriginal people, anyway, and cultures.
So, I have no qualms in that.
And, also, this paper here says the secret is the ability to link principles of learning with deep understanding and appreciation for culture.
What I actually wanted to say there, as well, is that I think, when you actually delve into that sort of cultural model, you are actually pulling out the deeper learning anyway.
‘Cause you’re really teaching that notion of what maths is.
You’re coming from that deeper understanding.
Not the surface level procedure, structure-type stuff.
Anyway, there’s something beeping.
So, my promise to you was, in the abstract was I’ll talk about New South Wales STEM camps that we do.
And there’s a collaboration between New South Wales Aboriginal Education Consultative Group, the New South Wales Department of Education and Communities, and ATSIMA.
I also want to talk to you about garma maths eventually.
At Yirrkala Community School.
Two way learning.
And I will talk a little, only a tiny bit, about the Indigenous STEM Congress.
I’m just putting them up there ’cause I actually put in my abstract, if you wanted to know what’s going to happen.
But I’ll try and get to most of those.
I’m probably running out of time already.
I talked too much.
Before I get into looking at a pedagogy around that model, I just want to talk a little bit about the STEM camp.
We held the very first STEM camp in 2015.
And we held it in Dubbo in New South Wales.
And it was a bit of a test case, really.
Because the STEM camps…
You know, when black folks get together and do something, they usually have a flashy name.
They wanna have usually an Aboriginal name from an actual community.
And we did talk about that.
But what we settled on was that we wanted to make sure the kids know they’re coming to a science and maths camp.
So, it is boringly called The STEM Camp.
Science, Technology, Engineering, Maths Camp.
So, I didn’t know how it was going to go.
We put the idea out there.
And we were overwhelmed by applications from Aboriginal kids.
So, the first time we did it, we had about 130 Aboriginal kids.
They come in to Dubbo in New South Wales.
We had multi-age groups from years five to 10.
And they travelled from a huge radius.
The reason I’m over here…
I wanna read.
They actually travelled from Bobobilla, which is near the top of Queensland.
From Burke, Borornia, Collianembroy, Kernobul, Inverell, Moree, Neramoyne, Tirie, Toronto, Waldut, and Wakenia.
Some of those kids were travelling nine hours.
Just to get there.
So, one thing that struck me about that is the thirst for it.
They wanted to do it.
They wanted to be part of it.
And that’s not strange growing up as an Aboriginal person, because what we do as Aboriginal people is we actually consider the world around us.
We think about what’s happening.
We look at the patterns of environment.
We understand when certain things are happening and not gonna happen.
So, we’re part of that culture of observing, looking for patterns.
Growing our understanding of the world around us.
That’s what, for me, what science really is about.
I actually wanted the camps to be a celebration of Aboriginal people.
Not just them to come and blow something up and walk away and everyone clap.
I want to get away from that sort of idea.
I wanted Aboriginal people up there presenting to them.
So, I actually put the feelers out there for as many Aboriginal people as I can get to come and do presentations for these kids.
The very first STEM Camp we had the majority of the presenters being Aboriginal people.
And we’re doing stuff like the maths of fire with Associate Professor Jason Sharples who lives down here.
And he was at the back burning fire and looking at what the patterns were doing.
And then, from that pattern recognition, talking about how it changes with different conditions.
And then looking at how it’s produced in mathematical modelling.
Hell even talk to the kids about that arrow you see in the road and what actually goes into actually changing that arrow.
I was ignorant enough to think that some bloke just come along and went like this.
Looks about that.
But it’s not.
This is actually a complex mathematical model that goes on behind it before someone moves the arrow.
So, he was going through all of these things that the kids see every single day.
That they engage in fire in their own communities.
They knew the patterns anyway, but you can actually see the connection between maths and fire.
And then Jason went into showing how he models really big massive things that causes storms and all that sort of stuff.
So, it’s quite exciting.
We had down Cass Hunter.
Who’s a CSIRO person.
Who has done one of these lectures.
And she was looking at the notion of quantifying the value of resources.
And she does that with different Aboriginal people around Australia.
We had Professor Rowena Ball.
Who’s also a professor down here.
And she was teaching kids fractals by actually making fractals by cutting a card somehow.
I’m not quite sure how she does it.
But she does it.
But what she’s doing, first of all, is she’s actually relating the idea of fractals to rivers and mountains and stuff like that.
To get them a clear picture of how these patterns exist within the environment.
And from that workshop, we had a lot of kids running around picking up things.
Saying “I think this is a fractal.
Look at this.
This is a fractal.”
You know, they’re engaged in that idea.
And I boringly did stuff on linear equations.
Which I’ll show you in a minute.
It doesn’t sound as dull as you think it might sound, hopefully.
So, I will talk a little bit about that later on.
And it fits in with that model I was talking about.
They did have other experiences.
The one was the robotics workshop that was done by the first crew in Macquarie University.
And what I found interesting about that is that the kids didn’t listen to any of the instructions, which is fine.
And they were challenged to get a robot through a maze.
To build a robot and get it through a maze.
So, they had to know how to turn it certain degrees and all that sort of stuff.
So, the instructors were trying to teach the kids how they would turn the robot 90 degrees.
Whatever it is.
But, invariably, these kids were coming up with their own solution to that.
They weren’t listening to the instructor.
They wanted to do their own way of doing it.
And they actually said to me that…
‘Cause we only give them an hour to do each of the workshops.
And they even said to me “Look, we go to expensive schools.
And most of those kids can’t get through the maze.”
These kids were getting the robots through the maze.
So, they’re really, really impressed by the ability of these kids.
You gotta be the best in the science community.
We just wanted to get any Aboriginal kid that wanted to come.
So, there’s no sense of this you’re the best in your grade.
And we also had Engineering Without Borders, as well.
And they did workshops where they’re looking at constructing boats from materials and who could make a boat that could have the biggest load, basically.
So, that sense of competition there was engaging for the kids, too.
They really got stuck into that.
Want to know if I can be the one to get 50 marbles or 120 marbles to be part of my boat and not sink.
They’re really engaged in that idea.
But I think the strength here is we’re actually changing the view of what maths and science is for our kids.
We’re actually showing them there are Aboriginal people out there.
They’re doing it for a particular reason.
A lot of them are working with our communities.
And there’s other ways of thinking about what maths and science is.
So, I’m gonna talk a bit about growing patterns, which is what linear equation stuff is.
And I did…
I said, boringly, I did linear equations.
This is all to do with growing patterns.
And the common approach that we usually have is that people usually give a teacher-constructed growing pattern.
Something like that.
And it’s always invariably squares stacked on top of each other, as well.
Which is interesting.
The kids used to have to transform that into some sort of number sequence.
And then, from that, they usually have to then change that into a linear equation of some form.
Now, the thing I found interesting about that…
The first time I really saw an academic talk about these sort of ideas was I went to a maths education conference in Seoul called PME.
That’s right, isn’t it, for the maths educators here?
And there was a talk done by an American academic talking about they called it the jumps between the pattern, number sequence, and the equation.
That there is a jump.
They have to really think about what that means and how they construct those things.
And, some things, maybe that’s not a bad thing, but I was sitting in the lecture thinking “Instead of studying how the students made the jump, why don’t you actually just teach them?”
There was a sense, for me, that they weren’t teaching children the full story.
Or teaching how it’s connected.
So, what I want to do is I want to take any growing pattern and explicitly connect it to the different parts of the linear equation.
And what I did is I looked at the linear equation as something that had a constant bit and something that had a growing bit.
So, those two ideas, you can actually use that to look at how those patterns are constructed.
So, what I was interested in doing was…
My idea was, if you actually taught that properly, you should be able to give any child any linear equation and they should be able to draw a pattern for you.
They should be able to go from pattern to equation and equation to pattern.
If they truly understand those ideas.
So, I wanna go through the full thing with you.
But what I did was I actually…
What I’m doing is I’m actually really explicitly looking at this reality stuff.
And what I do is I actually do, usually on the floor, chalk drawings or bits of paper, whatever it is.
But then look at something that’s growing.
And I generally do, when I do it, I generally do a spiral.
‘Cause the kids can actually talk about what the spirals are and how it relates to the world around us.
And a spiral grows over time.
So, they talk about hurricanes.
They talk about water going down the plug hole.
They talk about shells, starfish, all sorts of things.
While they’re looking at that spiral.
And what I’m doing is I’m doing part of this abstraction process where I’m actually doing the pattern, talking about how it’s constructed, and how it’s connected to the mathematics.
And also encourage them to think about what I’ve just done and reflecting back on the reality again.
And see how things that they see.
But I really want to do this thing here.
I’m connecting the symbols.
Allowing kids to create for themselves.
So, after doing that…
I just want to give you some examples of what they actually do.
I hope you can see that all right.
But these patterns are for, say, one is equal to 5x plus two.
And solve the linear equation.
And these are the different patterns the students come up with.
I do like this one here a lot.
This one that’s over here.
I like all of them, really.
I like this one here, because they really wanted to be part of the picture with their hands.
To actually own that.
This one here, too, they wanted to put their names on it.
And they even hashtagged it.
And I think that’s significant.
But this one here has done some interesting grouping.
‘Cause I actually couldn’t see what the two part is.
‘Cause the two part’s gotta stay the same across the whole pattern.
And it grows up by five each time.
But he does a bit of artistic stuff here.
But his two part was that dot in the middle and the blue circle on the outside was his two across that whole patterning.
And he could tell me all about this.
Talking it through to me.
If you get to this one, here, on the yellow ring, you can see he put five dots around that.
And, on the same yellow ring, he put another five dots to make the group of 10.
And then he starts expanding the circle out.
And so, he’s grouping by 10 on the circle each time.
Each second time.
I did a STEM Congress in Adelaide.
You can’t really see that very well, can you?
But you can always come back and have a look later, if you’re really interested.
But you can sort of see the different patternings that are happening here.
Just to give you an indication, too, that this one here, if you can see it, it’s sort of like a square growing outwards.
And the student has actually said to me that this is our Aboriginal unit at the school.
And that unit is growing now as we get more kids engaged with the activities in there.
That’s what they wanted to model.
They wanted to really connect it with part of who they were and what they were doing.
Now, I wanna put these ones up, because this was a bit of a surprise for me.
This whole thing.
I did a professional development in Perth at Curtin University, actually.
And they had their very last cohort of Aboriginal education workers who were trying to become teachers.
And, unfortunately, they were shutting down the programme, which I don’t understand.
But it happens a lot.
The pathways that Aboriginal people have to become teachers, as Aboriginal education workers in their community, are getting shut down by universities.
Probably because of economic reasons and budgets and so forth.
But, besides all that,
I was doing a PD with that group of people, but also other teachers around the area of Perth.
They’re coming from different communities.
And there was a group of kids that come with the parents of the Aboriginal education workers.
And one of them was a girl who was in grade three.
And she engaged in the activity with us.
And did some fantastic drawings within activity.
But this drawing here, she actually went with her auntie after that.
And her auntie had another class.
And, when she was in that other class, she got the pen and started to do this.
Independently from the workshop.
So, she was making up her own linear equations and started to draw them out in the ways that she wanted to do that.
And she was in grade three.
So, she did this beautiful linear pattern here.
And she did this four star plus three.
So, x here is actually a star.
Because she made her own symbol for that unknown quantity.
And she says here that maths is easy.
And she got another one to the side with five star plus four.
And she got a few words.
I don’t know what she was thinking there.
But, then, after that, she actually writes this statement.
She says, “I love maths because I know it.
And it’s really easy.
But sometimes a little hard.
Which I thought was cute.
But I was really impressed with the fact that she just went independently by herself.
Actually engaged in this idea of creating these patterns and understand them through that maths lens.
I won’t go through those points.
Basically, what I’m trying to do here is on last.
Students express their understanding for themselves.
Drawing who they are as a student.
Hopefully, they’re making connections between the reality patterns and mathematics in a two way connection.
Not just learning the maths for maths sake.
And, again, that’s pretty much the same sort of point, expressing themselves.
I just wanna go on to talk about Yirrkala Community School and garma maths.
Yirrkala is supposed to have an indigenous cross curriculum priority that sits within it.
It’s not mandatory with cross curriculum priorities, but they try and put this things that’s called elaborations within them.
So teachers, if they decide to, can actually do stuff in their mathematics.
And there’s not much in the maths curriculum at this point in time.
But there is one.
They actually refer to kinship systems as being a mathematical thing.
And I’ve actually had emails from people understanding this and so forth.
And what I actually believe is that this actually comes from Yirrkala garma maths.
The Yirrkala garma maths was something that was started in the late 80s/early 90s.
And it really came down to one man.
I will tell that story in a minute.
Before I do that, I just wanted to acknowledge these people.
Katherine McMahon, in particular, on behalf of the community, actually invited me up there.
I read about garma maths years and years and years ago.
And there hasn’t been much progress, unfortunately.
For a whole range of reasons I don’t think I need to go into.
But them inviting me, actually being part of it, was something snivving it for me.
And I’ll tell you in a minute.
Banbapuy Whitehead, Yalmay Yunupingu, and Merrikiyawuy Ganambarr is all people that are my teachers there.
I’ve actually been adopted into the Ganambarr family.
And that really has to happen for those people to build a relationship with me.
So, they’ve become my uncles and my aunties.
And I acknowledge their knowledge and wisdom.
Now, really, the story I want to talk about was from Doctor Yunupingu.
He was the lead singer of Yothu Yindi.
I won’t say his first name, ’cause that’s not still talked about in the community.
And that’s out of respect for that community.
But he was a lead singer of Yothu Yindi.
He was also the first Aboriginal principal of Yirrkala Community School.
And he had a vision of that two way education system.
And he did name that two education system garma after a…
It’s a metaphor.
Garma is the place where saltwater and freshwater meet.
So, they’re actually two different things that come to meet that don’t mingle, but they meet to create something new.
So, the idea was that we can learn from each other.
We can have western science sitting alongside Nungal understanding of the world.
And build a relationship with that to create something new and different and an education for
all those Nungal kids.
So, he had that vision.
When he was down in…
Learning to become a teacher in one of the universities, he come across mathematics fairly strongly.
And, from his view, mathematics was the first one that they should do in terms of a two way education system.
And I found that interesting that he thought maths was the key to connecting these two cultures.
And that he believed that because of gurotu.
Gurotu is, in an English translation, means kinship.
But, usually, you only think of people.
Really, it’s not.
And I’m no expert on gurotu.
I’m only just starting to learn a lot of stuff from these people.
But, really, gurotu is how everything is related in the world.
And what our Aboriginal community’s done, across Australia, I believe, is we all had a similar structure.
And that structure of that is that we actually split the world into two.
So, we have two parts of the world.
And everything fits within those two parts.
So, there’s people that sits in their two parts.
Same with animals and plants and water and all sorts of land and everything.
Everything sits within these two halves.
And the reason that that binary is created is because it’s used to balance the world around her.
So, there’s a boundary between things.
There’s a binary that needs to be balanced.
And, for me, that’s a very mathematical idea already just from that part of it.
Then it gets really complicated after that.
‘Cause people are then classified into colours, which gives you certain social responsibilities in different contexts.
And then, after that, you are broken down into…
So, from your binary, you’re broken down into two colours.
So, your two become four.
And then each of those peel off into two again to give you eight at the bottom.
And that, in Nungal language is called malk.
In English version, they call them skin names.
Those names give you who you are in the world.
Who your mob is, who your clan is, and all that sort of stuff.
And that skin name is given to you by your mother.
So, depending on who your mother is gives your skin name.
Or your malk.
And that actually sits in the circle.
So, it actually goes back around in a circle.
So, you actually have two circles of relationships that exist.
So, you’re moving away from an idea of a linear grandmother, grandfather, mother, father, child.
To something that is actually in a circular pattern.
And the main philosophy of that, for me, is everyone has a responsibility to everyone, first of all.
When you’re in a circle, you have to have responsibility to everyone.
It’s like when you’re standing in a circle.
You have a responsibility to everyone.
Whereas, if you have a linear pattern, you don’t necessarily have to have a responsibility.
You do, in a sense.
But not for everybody in that line.
But, if you have a circular one, you have a responsibility for everybody.
And that was significant for me, ’cause, when I start reading stuff like Dark Emu and even Bill Gammage’s book Greatest Estate on the Earth, I think the basis of that philosophy is why we could sustain a culture over 50,000 plus years.
It’s our relationship with everything.
Now, what I also found exciting about that discussion is that, once you set a structure like that…
Once you set a relationship like that, it actually gives way to a structure.
And that structure was actually…
The name they give their structure is jacre up in that community.
And the way I think about things in terms of mathematics is that we do have these rules
and patterns, if you like, that then give the structure that we engage with within algebra and so forth.
So, I can actually see how that old man was thinking that this fits within mathematics.
And I also get excited that the basis of the whole philosophy is a circle.
Because, from my years of being a mathematical modeller, you’re always dealing with sine, cos, pi.
Circles are bloody well everywhere in mathematics.
So, there’s a strong connection with all of that stuff, as well, that I still want to engage with.
I just wanna show this one more slide, ’cause I’ve actually been given the bell.
And part of the story is that, one of the first trips I went up to Yirrkala Community School, I actually had a teacher approach me and saying his frustrations.
He’s a non-indigenous teacher.
Saying that his frustration about these kids don’t seem to be able to understand how to times.
They can’t understand multiplication.
In the back of my head, I’m thinking,
“How can that be possibly true?”
‘Cause all you’re talking about is groupings.
There’s just groups.
That was that sort of frustration that this student had.
I wasn’t out to prove that person wrong or do anything about it.
But the opportunity come up when I was working with Banbapuy.
My uncle, he was a teacher in the school.
And I sat down and talked about how we can actually look at equations as a bunch of symbols put together to tell a story.
‘Cause that’s all they really are.
They’re just a bunch of symbols put together to tell something about the world around us.
So, she got quite excited about that idea.
What she did is she went and did a brainstorming with the kids in their own language.
So, she sort of, half broiling, in a way, put up all the math symbols that she wanted to put up there, those ones up there, and got the kids to express their understanding in their own language about each of those symbols.
You can see, they couldn’t do much about divide.
There’s not much to understand there about divide.
But what they clearly want to understand…
Why they want to understand multiplication was groups.
And the language word they use, mittji, which means clan.
If you have anything to do with Garma Festival or been up there, you’ll know that everyone sits in their clan groups.
They want to see it as that.
The subtraction they want to see as take away or take it or steal it, which I thought was funny.
Your equals sign, you want to see it as how many.
It gives you a sort of an answer.
But also plus was also about sitting together.
Everyone sitting together, all together.
They want to see it like that.
So, once Banbapuy hooked onto this, she actually started writing up multiplication symbols like this.
So, in their own language, they were actually saying how many.
Like how many in each clan?
And this is the number of clans.
So, kids were doing these extra drawings like this and then coming up with the answer.
And, in their own wording, the actually said this to her, it’s like storytelling.
They said that in their own language.
It’s like storytelling.
And, again, they did another multiplication.
Again, talking about the number of clans and how many are in each clan.
Banbapuy then gave them a whole list of multiplications to do.
And they were doing the multiplications like this.
They were circling the numbers and writing the language words next to them.
And then writing…
Sometimes doing a drawing.
But definitely writing the right answer.
And, eventually, those drawings disappeared and they’re just writing the right answer.
And this is with kids who couldn’t do multiplication.
And the only thing that changed…
There’s only one lesson that changed.
And that was ’cause they had the opportunity to talk within their own language.
And, also, part of that is perceiving maths differently, too.
See everything as something you can relate to the way you see the world.
And not the way the teacher wants you to see the world.
So, in quick summary, we need our cultures valued in maths and science education.
We need more indigenous educators in maths and science.
‘Cause that is a real problem.
And, especially at Yirrkala, ’cause they actually had a whole cohort of Aboriginal teachers at one point.
But their pathway to university got shut down ’cause of funding or whatever it was.
And that cohort is getting older and older.
And there’s no one following them through.
And that’s a real shame, ’cause they actually were making great leaps in that school until this lack of teachers were coming through.
We need to really overturn the mindset of terra nullius.
Really think about what that means and how that infiltrates into the world that we operate in.
And then we need to work together to build a better future for all of our kids.
To build that relationship that’s lacking.
To build that trust again.
For all of us.