Alan J Bishop
Bishop’s paper “presents the results of a series of analyses of educational situations involving cultural issues. Of particular significance are the ideas that all cultural groups generate mathematical ideas, and that ‘Western’ mathematics may be only one mathematics among many. The values associated with Western mathematics are also discussed, and various issues raised by these analyses are then presented”
I was really keen to read this article because it specifically talks about the idea of implementing ethnomathematics into educational situations.
Bishop explains that it is through sustained, conscious use of certain activities that mathematics becomes culture. This supports Howard Groome’s assertion that culture is dynamic, and is constructed by individuals as they live their day to day lives (as cited in Herbert, 2006, p. 78). With several different cultures in one’s class, how would we as teachers decide what content, or processes, to include in an attempt to avoid total acculturation to a ‘western’ way. Bishop recognises that we see possible cultural conflict as an outsider, and that it isn’t for us to assume what the right answer might be to incorporating culture into mathematics. (This supports Mundine’s (2014) statements).
Bishop ponders whether the mathematics is an international language to be used and understood by all? But, if we consider Bishop’s statement below, that mathematics exists differently for people worldwide; how would / does acculturation feel to students who are asked to forgo their cultural knowledge and understanding?
Bishop suggests that there are universal mathematical activities, which all cultures have, but may do, value and represent differently:
His cultural definition is based on another researcher’s paper, in which it suggests the function of culture is to connect human’s to their environment and vise versa
and it exists of 4 main things, 3 of which are values:
Sentimental values – attitudes, feelings, behaviours
Idealogical values – beliefs, symbolism, philosophies
Sociological values – customs, institutions, rules and patterns, interpersonal behaviours
Technological – manufacture and use tools
Whilst recognising that different cultures may have unique values, Bishop notes that it’s worth teaching students about values, without trying to force our own upon them.
The paper suggests we can conceptualise maths as a cultural construct by considering values in pairs of conflicting ideas:
Control vs Progress – stable, stay the same, secure, right answer!
vs. generalising, using new knowledge in new ways – New
ways of thinking – becomes a new culture
Logic vs Objectivism – ways of thinking, and rationalising – such as causation arguing
not based on seniority, status or experience
vs. dealing with the abstract as if it were an
object – such as letters and numbers
Openness vs Mystery – openness refers to the ‘truth’ of maths –
open to scrutiny by all – as long as the person has maths knowledge
vs. despite the openness – surprise discovery, abstract reality, and context. Yet mathematics is it’s own context
So what have I learned?
I actually feel that this has been the most enlightening reading so far. It supports much of what I have been thinking; and questioning.
Although the author suggests many maths classes do not balance out the complementary values listed above, I feel that the Australian Curriculum has, at least at face value attempted to address these ‘Western values’, while incorporating suggestions for ‘token’ content inclusion: specifically Asian and Aboriginal content and perspectives.
What this tells me is that we, as teachers, definitely need to take the time to understand the mathematical, social, and cultural backgrounds of our students, not so much to consider what we can do FOR our students, but more so that WE can understand their ways of thinking, and doing, and to plan to teach and assess accordingly.
Mathematics is more than what Bishop calls ‘meaningless pushing around of figures’; maths is a socially constructed process.
A.C.A.R.A. (2013). F-10 Curriculum English Rationale. v7.3. Retrieved 25 April, 2015, Retreived from http://www.australiancurriculum.edu.au/english/rationale
Bishop, A. J. (1988). Mathematics Education in its Cultural Context. Educational Studies in Mathematics, 19(2), 179-191.
Herbert, J. (2006). Indigenous learners, language and identity: implications for educators. In K. Cadman & K. O’Regan (Eds.), Tales out of school: identity and English language teaching (pp. 72-85). South Adelaide, SA: Australian Council of TESCOL Association.
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