Andy Begg (2001)
This easy to read article was recommended to me by a fellow student: Elaine A.
My thoughts are in bold throughout the thread:
I was immediately drawn to read the content of this article when I saw Begg’s interpretation of culture matches my own:
Any set of people who share a common language, belief, customs, or history. This definition is not limited to ethnic groups and includes all cultures and subcultures e.g. special interest groups, special needs groups, and genders.
Begg suggests that, essentially, ethnomathematics is about making connections:
– everyday world of the student
– prior knowledge of the student
– familiar contexts (school and beyond)
– other mathematics topics
– other schools subjects
– the past; and likely future
In this way, Begg has voiced the view that I have been considering. That although the overarching definition is ‘sets of people’ – culture is personal, and is based on prior knowledge and experience.
This version of ethnomathematics allows students to connect prior knowledge, which is every teacher’s intention. Begg refers to ‘schemas’ (mental maps) – a connection of ‘bits of knowledge’ and knowledge about the relationships between those ‘bits’.
Justification for Ethnomathematics in this context:
– beginning where the student is at
– starting with the student’s interests
– giving mathematics a more human (and for that matter – concrete) face
Begg posts two questions:
What do we think of mathematics within each culture?
Is including ethnomathematics enough?
Based on my reading so far; I would suggest that making mathematics to students’ individual, and social contexts would have more relevance, and make better connections than including mathematics which is a) removed from meaning of the historical cultural practice; b) Implemented as a cultural construct of a Western view of an historically constructed concept or practice; and c) ethnically and historically related, only if the student is considered to be a member of homogenous society.
So, in answer to his second question…
I think it depends on your definition of Ethnomathematics and Culture.
Enactivism (Davis as cited in Begg, 2001)
– doing without judging
– an embodied action – all responsible for our own actions
– thinking of knowledge as something connected to an individual and their environment – – not somethin that’s testable against external standards
Again; learning begins with the students…
Begg suggests, ‘being connected’ is much more important than ‘making connections’…
How do students learn? Are their ways of thinking different to those assumed by our Western teaching methods. Different ways of knowing …? Is Western schooling even appropriate?
What aspects of other cultures can be regarded mathematical?
And for me – What does this mean when we try to incorporate Cultural Aspects out of context? Mathematics is also about values, and ethics – we can’t just take sections of cultures, place our own understandings on what we think about them, and use them in a way which undermines their original cultural importance: ‘visible practices, displaced from underlying values”
For more information:
Schein’s definition of organisational culture: Underlying beliefs, Espoused beliefs, Artefacts
Schein’s theory of organisational culture
It’s not for us, as outsiders to try and determine mathematical concepts in another culture – that’s for the people to decide.
– once they’ve decided – we can support them: through Individual choices; or more broadly include it into curriculum’s and teaching practice
– relevant cultures must have opportunities to provide input into what they think about inclusion – what’s important, and how it should be incorporated.
Begg refers to other things which should be considered when making connections between mathematics and culture: history (cultural view towards a given historical event, or culture), first languages (because a) languages and culture are mixed and b) mathematics is largely language and symbols based)
Begg also suggests beliefs, language, and metaphors used in given cultures, help determine the way people think, and what they value.
Beg leads us to believe the issue is much bigger than the mathematics classroom – specifically; society at large!
Thankfully; Begg has provided some considerations for educators:
1) What elements from my student’s culture can introduce or enrich mathematical concepts
– How will I decide if they are appropriate? Who from the culture might help me to decide?
2) What can I find out about my students; how they learn, their interests, their beliefs
– Who can help me find out? How will I include them in my class?
3) Can I (and how) teach the current curriculum by integrating this knowledge, to help my students make more and better connections?
This post has asked a lot of questions – many I have asked myself: how do we decide what to include, without further offending people. Begg suggests asking people from the relevant culture; but as evidenced by the Mundine (2014) article – not all non-Western people agree about what or what not should be included in Western Schooling – some believe it’s not the job of schools to teach traditional culture – it is the school’s job to teach Western ways, to better help those children prepare for what IS a Western way of living.
So, what does it mean when inappropriate content is included – is it more offensive, and detrimental to learning, than not including it at all? How will I know if I have offended someone?
For example: many Ethnic traditions
1) have specific rules – women only, men only, initiated boys, girls only, kinship restrictions and relationships
2) have beliefs attached – dreamtime stories
And what of the cultures which haven’t been catered for?
In conclusion; what I’ve taken from this reading is a confirmation that INDIVIDUAL culture is important. Getting to know students, their families, and the background experiences is much more important than including token content for the sake of ticking boxes for a) inclusion or b) enrichment.
Having said that. I wonder if the information I have taken from the readings, is based specifically on my pre-conceived ideas that it is not reasonable to cover and include every student’s Ethnicity in whole class planning. And my belief that culture is more than just ethnicity.
Begg, A. (2001). Ethnomathematics: Why, and what else? ZDM, 33(3), 71-74. doi: 10.1007/bf02655697
Mundine, N. W. (2014). Teaching children Aboriginal kinship in maths does not add up. The Australian, (5 May, 2014). http://www.theaustralian.com.au/opinion/teaching-children-aboriginal-kinship-in-maths-does-not-add-up/story-e6frg6zo-1226906653349