YuMi Deadly Maths is an educational program developed over 20 years for indigenous and low SES schools. It is based on the RAMR (Reality-Abstraction-Critical Reflection) teaching framework which uses a constructivist pedagogy cycle. The RAMR model begins with introducing mathematical ideas through local cultural knowledge and hands-on activities. It then develops representations of the ideas through physical, pictorial, and symbolic means to build student understanding. Students reflect on the ideas by applying them back to real-world problems and discussing their validity. The program has been shown to improve teacher and student attitudes towards math by emphasizing active and culturally relevant learning.

1. YuMi Deadly Maths
What Is It and How Does It Work?

2. YuMi Deadly Maths
• Grew out of over 20 years work in low SES and
Indigenous schools
• Related to whole school change and takes
account of culture
• Based on big ideas, connections, sequences &
pre-empting
• Based on active constructivist pedagogy cycle:
reality  mathematics (RAMR)
• Empowers teachers and students
2

3. Ensuring high
expectations in
leadership and high
expectations in terms of
student attendance,
engagement and
performance.
Building and maintaining
strong community and
school partnerships.
Cycle of school change and leadership
Acknowledging,
embracing and
developing a positive
sense of Aboriginal
identity and a positive
Torres Strait Islander
identity.
Acknowledging and
embracing Indigenous
leaderships roles in
schools and their
communities.

5. • RAMR Model

6. Development of the RAMR teaching framework
Perceived
Reality
Creativity & problem
solving
Symbolic language &
structure
Cultural bias
Critical Reflection
Invented
Mathematics
Abstraction
Chris Matthews 2010

7. RAMR
CYCLE
Reality
Abstraction
Critical Reflection

8. RAMR
CYCLE
Reality
Abstraction
Critical Reflection

9. Reality
• Identify local cultural and
environmental knowledge that can
be used to introduce the idea.
• Ensure existing knowledge
prerequisite to the idea is known.
• Construct kinaesthetic activities
that introduce the idea (and are
relevant in terms of local
experience).

10. Abstraction
• Develop a sequence of representational
activities (physical to virtual to pictorial
materials to language to symbols) that
develop meaning for the mathematical
idea.
• Develop two-way connections
between reality, representational
activities, and mental models through
body  hand  mind activities.
• Allow opportunities to create own
representations, including language
and symbols.

11. • Enable students to appropriate and
understand the formal language
and symbols for the mathematical
idea.
• Facilitate students’ practice to
become familiar with all aspects of
the idea.
• Construct activities to connect the
idea to other mathematical ideas.

12. Critical Reflection
• Set problems that apply the
idea back to reality.
• Lead discussion of idea in terms
of reality to enable students to
validate and justify their own
knowledge.
• Organise activities so that students
can extend the idea (use reflective
strategies – being flexible,
generalising, reversing, and
changing parameters).

13. RAMR
CYCLE
Reality
Abstraction
• Identify local cultural and
environmental knowledge that can be
used to introduce the idea.
• Ensure existing knowledge
prerequisite to the idea is known.
• Construct kinaesthetic activities
that introduce the idea (and are
relevant in terms of local
experience).
• Develop a sequence of representational
activities (physical to virtual to pictorial
materials to language to symbols) that
develop meaning for the mathematical
idea.
• Develop two-way connections
between reality, representational
activities, and mental models through
body  hand  mind activities.
• Allow opportunities to create own
representations, including language and
symbols.
• Enable students to appropriate
and understand the formal
language and symbols for the
mathematical idea.
• Facilitate students’ practice to
become familiar with all aspects of
the idea.
• Construct activities to connect the
idea to other mathematical ideas.
Critical Reflection
• Set problems that apply the idea
back to reality.
• Lead discussion of idea in terms
of reality to enable students to
validate and justify their own
knowledge.
• Organise activities so that students
can extend the idea (use reflective
strategies – being flexible,
generalising, reversing, and changing
parameters).

14. Reality
Decimal match and
order: using existing
knowledge, money
Decimals -Whole to part for
measuring

15. Abstraction
Decimals-whole
to part,
measurement

16. Mathematics
Matching
decimals
Decimals-whole
and parts
(measurement)

17. Reflection
Measurement-time
Read, write
and say
large
numbers,
compare
and order
Decimals, whole to part

18. Changing mindsets
Teacher 1
Beliefs
Teacher 2
‘One of the most powerful influences that Yumi has given my class and I, is that
now when I say we are about to do maths, the children are excited. They know
it’s not just pen and paper, that they will be manipulating objects, exploring and
involved in some hand and body activity. My attitude to teaching maths has also
changed and I relish the new ways I can explore it with the children. This by far,
has made the whole experience particularly valuable for my classroom, practices
and pedagogy.’

19. Links
 Yumi on You tube Sharing summit 2013: reflections from Principals & teachers
https://www.youtube.com/watch?v=6e0SRwknWQE
• Chris Matthews: Culture and Mathematics
http://www.qsa.qld.edu.au/3035.html
 Maths Fun with Yumi- Teaching Angles
https://www.youtube.com/watch?v=twbDN_8B2a8
 Yumi pedagogy Professor Tom Cooper explaining the RAMR
https://www.youtube.com/watch?v=9FAntCEMyjQ
 Article Dr Bronwyn Ewing
http://www.minnisjournals.com.au/educationtoday/article/YuMi-Deadly-Maths-Program--690
 Yumi Deadly Maths Professional Learning
http://www.teachlearnshare.gov.au/File/7ebe8916-bb8d-49c4-8cdb-a27b00c89f1e

20. Abstraction -body

21. Abstraction Body-Hand-mind

22. Abstraction student model

23. Abstraction- hand &mind