Talk at Mathematics Education meets the Philosophy of Mathematical Practice https://yhamami.github.io/mathed-pmp-workshop/program/

1. Every
Classroom is
Multicultural

2. Every
Classroom is
Multicultural
Ten years ago, the AHRC funded
the Mathematical Cultures
Network. I will briefly recount
some of the contributions that
made a difference to the way I
think about culture and education.
I will present and argue for a
general model of culture and
describe some of the things I
have tried to do with it.

3. 3
BAmaths & philosophy (1988)
MAphilosophy (1990)
DPhil philosophy of maths (1994)
Who is this talking at us now?

4. 4
How I became an expert on
culture
With help from
Benedikt Löwe &
Thomas Müller

5. 5
How I became an expert on culture
(2012) “The Mathematical Cultures Network Project” Journal of Humanistic Mathematics 2
(2): 157-160.
(2016) Mathematical Cultures: The London Meetings 2012-2014 Edited collection,
Birkhäuser, Basel
(2016) “What are Cultures?” in Cultures of Mathematics and Logic Selected papers from the
conference in Guangzhou, China, 9-12 November 2012. Shier Ju, Benedikt Löwe, Thomas
Müller, Yun Xie (eds.) Birkhäuser, Basel
(2016) with Karen François “Cultural and Institutional Inequalities: The case of mathematics
education in Flemish schools” Journal of Mathematics and Culture, 10(2), 37-54.
(2018) with Karen François “The concept of Culture in Critical Mathematics Education”. In P.
Ernest (Ed.), Philosophy of Mathematics Education Today Springer Verlag.

6. 6
Some of the papers that made me think about culture
Understanding the Cultural Construction of School
Mathematics—Paul Andrews
Creative Discomfort: The Culture of the Gelfand Seminar at
Moscow University—Slava Gerovitch
Mathematics—and First Nations in Western Canada: From
Cultural Destruction to Re-Awakening of Mathematical
Reflections—Tom Archibald and Veselin Jungic

7. 7
Culture? What’s that?
• Non-biological reproduction
• Bigger than the individual,
smaller than the species
• Expressed in practices and
artefacts
• Something to do with values

8. 8

9. 9
What is the unit of cultural analysis? What is
a culture anyway?
Chemla & Fox Keller against
cultural essentialism (even though
actors are often keen on it esp.
national or religious cultures).
Cultures are internally diverse,
changed by their own products
and interactions with others,
dynamic and actors are often
relatively self-aware.

10. 10
What is the unit of cultural analysis? What is
a culture anyway?
D’Ambrosio: any collection of people can be an ethnos for
the purposes of ethnomathematics—if they share some
mathematical practices.

11. 11
Essentialism: what is the unit of cultural
analysis? What is a culture anyway?
Makenzie (in Chemla & Fox Keller p. 38) presents
four criteria for cultural distinctness:
Different practices associated with different
 Ontologies
 Processes of socialisation
 Mechanisms of interaction among participants
 Path-dependent patterns of change (i.e. different
histories)
Makenzie requires all four…

12. 12
Essentialism: what is the unit of cultural
analysis? What is a culture anyway?
Makenzie requires all four, but is this too much? The
last one is probably redundant—if you have the first
three, there must be different histories.
If you had two, would that be enough?
Do we need different ontologies every time?
(Notice: all Moscow maths seminars had the same
four Makenzie elements.)

13. 13
Understanding the Cultural Construction of School
Mathematics—Paul Andrews
Cultural forces inside and outside schools “determine what
is to be taught, to whom it is taught, how it is to be taught,
and where it is taught” (p. 11, quoting himself)
But learners arrive in class with values and practices of their
own! (most obviously First Nations and Brazilian indigenous
peoples—everybody).

14. How to think about culture
(From a talk with Karen)
• Not as distinct, discrete, fixed units e.g. the Navajo
culture, the Mundukuru culture, British culture, etc..
• As a material-ideal pair: artefacts & practices ~ values
• As a mass-noun, not a count-noun
• As a task for the individual, not a property
• Why?
 It’s the truth a model that captures what I care about
 Allows overlapping and common spaces
 Allows change
 Allows recognition of shared values

15. 15
For example, convicts
Have a meetings
culture rooted in
rehab.

16. 16
Why should we learn maths?
We can think about student motivation in
terms of values and identity rather than
(distant) external and (invisible) internal
goods…
…without falling into essentialism or
culture-monadology (the fate of
ethnomathematics)

17. Thank you
Every classroom is multicultural: Loughborough June 2023 17