This document discusses teaching mathematics from an Aboriginal and Torres Strait Islander cultural perspective. It begins by introducing Dr. Chris Matthews and the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA). It then outlines Dr. Matthews' journey developing the Goompi Model for teaching math in a way that connects to students' culture. The model emphasizes teaching math through patterns, storytelling, symbols and creativity. The document shares classroom examples of using the Goompi Model and its positive impacts on student engagement and understanding. It also discusses other models for culturally-connecting math, like those used at Yirrkala Community School connecting math to Yolngu kinship systems. Overall, the document advocates teaching math in a way that values

1. Teaching Culture = Deep Learning
Dr Chris Matthews
Chair
Aboriginal and Torres Strait Islander
Mathematics Alliance (ATSIMA)

2. Introduction
• Quandamooka Nation
• PhD in Applied Mathematics
• Chair ATSIMA and our vision is:
All Aboriginal and Torres Strait Islander Learners will be
successful in mathematics.
• Teaching from a cultural perspective is
paramount
• Mathematics is part of culture: it is a
cultural activity

3. Take you on a Journey….
• My journey…
• The Goompi Model
– Teaching mathematics from a cultural
perspective
• Explore Exemplars
– Development of new pedagogies
– Stories from the classroom: students,
teachers, principal and parent
• Where I’m going …

4. What is Culture?

5. Terra Nullius
Our Shared History Our Relationship
non-Indigenous
Indigenous
devalued
marginalised
dispossessed
primitive
valued
Knowledge holders No relevance
Advanced
No opportunity
Fear
Mistrust
Good Will
Silence

6. David Unaipon (1872 – 1967)

7. Maths
Numbers
Problem Solving
Measurement
Space etc
Fear and Anxiety
Love and Fun (Occasionally)
Who does Maths?
Everyone !
What Maths does
“everyone” do?
Money, Measurement,
Trades, Direction …
Number, Operations,
some algebra
What other Maths is there?
Matrices, Calculus, Numerical
Computation, Topology,
Number Theory …
Who does this type of maths?
Engineers, Scientists…
Picture a stereotypical
Scientist?
Nerd, social recluse, special
innate ability
What is Mathematics?

8. What is Mathematics?
Reality Maths
Abstraction
Creative
Critical Reflection
Symbols
Cultural Bias

9. Goompi Model: Keeping Connections
Reality Maths
Abstraction
Creative
Critical Reflection
Symbols
Cultural Bias

10. Linear Equations
𝑦 = 𝑚𝑥 + 𝑐
where y is the dependent variable, x is the independent
variable and m and c are constants
General form of a linear equation

11. Growing Patterns: Linear Equations
Number Sequence
Linear Equation
(𝑦 = 𝑥 + 5)

12. Goompi Model:
Transform Growing Patterns Pedagogy
Number Sequence
Linear Equation
(𝑦 = 𝑥 + 5)
• Connecting the Structure of
Pattern and Equation
• Numbers emphasize the
Structure
• Connecting the Symbolism

13. 0 1 2 3 4
Growing Patterns: Goompi Version

14. 0 1 2 3 4
Growing Patterns: Goompi Version
Constant 3 3 3 33
Growing 0 1284 16
S 3 1915117
+ +
++
+

15. 0 1 2 3 4
Growing Patterns: Goompi Version
Constant 3 3 3 33
Growing 0 1284 16
S 3 1915117
+ +
++
+
0 = 4 x 0 4 = 4 x 1 8 = 4 x 2 12 = 4 x 3 16 = 4 x 4
d
S = 4 × d + 3 S = 4d + 3
S = 5d + 2

16. Story from the Classroom
Amanda Pedder, Roma Mitchell Secondary College
• Never had this level of conceptual understanding
…
• Maths Class of disengaged Year 10 boys …
• “Remarkably they want to do this!”
• “I was astonished at what they drew.”

17. Students’ expressions …

18. Students’ expressions …

19. Story from the Classroom
Amanda Pedder, Roma Mitchell Secondary College
• Two days later, Amanda set a quiz …
• A questions was based on this idea
• They outsmarted me and asked really intelligent
questions
• It really helped break the deep cycle of
disengagement for many of them…
• made forming a relationship with each of them
much much easier …

20. Creativity
• Students need to be free to create
• Give Students time to create
• Students need to feel safe that they can express
their ideas in the classroom
• An expression of their culture
• Need to move away from right and wrong
mentality
• Do not say to the students you are wrong and
correct them

21. Creativity
• Talk with the Student(s) about their creation and
how it connects with the main concepts
• They will surprise you
• Allow students to share their ideas and creations
• Learn from the students
• Building positive balanced relationships

22. Elders Wisdom
Pattern thinking is Aboriginal thinking. There is no
big boss. Patterns are about belonging. Nothing is
separate from anything else
David Mowaljarlai, Elder from Derby
Aboriginality a Gift: Spirituality for a Nation

23. 3 + 5 = 8

24. Maths as Dance
• Make It Count Project
(2009 – 2013)
• Kargun Fogarty,
Songman
• Creating Stories
• Creating Dance
• STEM Congress 2017
• Bryce and Tamia
• Kite Hawk Dance
3𝑓+𝑠𝑤 3
3𝑠𝑙+𝑠𝑤 2
+ x 3
3 + 5 = 8
5 × 3 = 15
9 – 4 = 5
12 ÷ 4 = 3

25. Impact of the STEM Congress
Being cultural dancers, we thought “how can we
connect our traditional dancing in a way that Dr
Chris Mathews connected his patterns and stories
to STEM?”.
Tamia Blackwell and Bryce Cawte
Tal-Kin-Jeri
Woodville High School

26. Impact of the STEM Congress
Bryce and Tamia were sitting at the dining table
discussing an upcoming STEM congress that they
were presenting at…. There was a lot of debate,
questioning, curiosity and deep discussion … they
inspired each other to think deep and make
connections between maths and culture.
Karen Sinclair

27. Impact of the STEM Congress
I would not have given year 2 students a maths
problem such as (3h + 4d + 2P) X4 and they created
it themselves. Within their small group through
highly collaborative, creative and critical thinking,
they created a dance, performed then changed it
and explained its mathematical meaning to others.
Martine Turnbull
Aboriginal Education Teacher
Renmark Primary School

28. Impact of the STEM Congress
As a school we will ensure this strategy remains at
the forefront of staff and student minds. We will
create many opportunities to share it with our
school community i.e. assemblies, photos and
explanations in newsletters, students “performing”
to other classes/students and teachers learning
from each other.
Lyn Bretag
Principal
Renmark Primary School

29. Yirrkala Community School:
Garma Maths
• Kathy McMahon, Banbapuy Ganambarr-
Whitehead, Yalmay Yunupingu, Merrkiyawuy
Ganambarr-Stubbs;
• Garma: A metaphor for teaching and learning
• Value our Language = Bilingual Education

30. Elders Wisdom
Our mathematics, Yolngu mathematics, is Gurrutu.
Dr M. Yunupingu,
1st Yolngu Principal of Yirrkala Community School
Leader singer of Yothu Yindi

31. All
people
Yirritja Dhuwa
Red Yellow Red Yellow
Ŋarritj
Ŋarritjan’
Baŋaḏi’
Baŋaḏitjan
’
Buḻany’
Buḻanydjan
’
Gayak
Gutjan’
Gamarraŋ’
Gamanydjan
’
Balaŋ’
Bilinydjan’
Wämut
Wamuttjan’
Burralaŋ’
Galiyan’
Gurrutu: Kinship to all elements

32. Ŋarritj
Ŋarritjan
’
Gamarraŋ’
Gamanydjan
Y
D
Buḻanydjan’
Buḻany’
Y
Wamutjan’
Wämut
D
Balaŋ’
Bilinydjan’
Baŋaḏitjan’
Baŋaḏi’ Y
D
Gutjan
’Gayak
Y
Galiyan’
Burralaŋ’
D
Malk Cycles: Yothu Yindi

33. Why do we have circular kinship?

34. Why do we have circular kinship?

35. Why do we have circular kinship?

36. Gurrutu = Mathematics
• Circles is at the Centre of Yolngu Philosophy
• Knowledge is based on build kinship with all the
cycles of life
• Circles is also at the Centre of Mathematics
• Solution to equations always have some
representation of the circle
• As Aboriginal people we are deeply connected to
Mathematics