As evidenced by my posts so far, I believe effective teaching recognises and embraces individual student cultures. While it is not reasonable to think that a single teacher could produce individual ‘contexts’ for each child, they must recognise that students can learn from the diversity within the classroom (school community); and should therefore aim to provide meaningful learning opportunities which do not cater only to the majority. Zevenbergen, Dole and Wright (2004) suggest that learning environments which match the learning needs, backgrounds and interests of the students; have high expectations for student success, and encourage deep learning, about and through mathematics, ensure all students can learn mathematics. Further; Smith, Ewing and Le Cornu (2007) recognise the importance of providing opportunities for learning in everyday situations; and connecting to student backgrounds and practices in order to build student self esteem.
In this post I will demonstrate some small examples of mathematics ‘taken from systems which are part of students’ realities’ (Rosa and Orey, 2010). Using my interpretation of culture, which is not limited to ethnicity; I will demonstrate Ethnomathematical examples of drawing on knowledge from traditional cultures, sport, and music.
In this ethnomodelling example the teacher has provided an open ended activity which allows the students to demonstrate their understanding of one concept (solids) by incorporating something they are familiar with, and using that knowledge to build on other content knowledge. This example demonstrates how incorporating ethnomathematics does not require the teacher to decontextualize culture (in contrast to my previous understanding), because the children are bringing it to the classroom (rather than the teacher including it in a worksheet or something). Students are able to use the artefact as a foundation for learning, until such time as they can move beyond the concrete and move on to the symbolic and the generic.
By providing opportunities for students to incorporate items which are familiar to them, students are able to: a) develop self esteem, and cultural pride, b) verbalise cultural component, and connections between cultural and mathematical content and c) make meaning through building on prior knowledge.
Talking about these items allows students to strengthen their understanding of social and mathematical concepts in what is a vastly technological and multicultural world.
This is not the whole article – it is just the appendix, but it really demonstrated to me how easy to think about incorporating cultural knowledge without prejudice or stereotype:
Abiam, Abonyi, gama and Okafor (2015) explain that their example was from Africa, where although they do have vernacular terms for circles and curves, they are spacial rather than geometric references (note that Aboriginal Cultures are also highly spatial … see below).
Many times during my degree I have heard the mantra “AFL will get them engaged in maths!” Putting aside any obvious issues with that comment – such as stereotyping the ‘them’ in that statement (gender? race? cultural group? students?); what is it about Aussie Rules/Australian Rules Football/AFL that is engaging, and mathematical?
Before learning about Ethnomathematics, I had thought the engaging part is making connections to lives outside of school – but I recognise not everyone plays AFL. Maybe that’s another mathematical consideration – comparisons between different sports, for example, scoring systems in AFL (6 points for a goal (grouping/multiplication/division), 1 point for each netball goal (tallying), 2 points each for basketball (or one for a foul (vertical number line/addition/subtraction), number of people on a team, times for quarters/halves/breaks (fractions – also field division), average number of times a whistle is blown in a game (did you know netball just changed the rules to reduce the whistle blowing by 30%?)… the list goes on and on. A ‘Google search’ of Aussie rules math brings up a plethora of examples of how to use AFL in the mathematics classroom.
One author, Christine Nicholls (2013), suggests Aboriginal culture is centred around spatial relationships (like the African example above), which is ideal for a game like football which requires a 360 degree perspective of the field. Rather than focussing on left and right, which depends on the way the body is facing; Aboriginal cultures focus on cardinal directions – north/south/east/west; connecting to things like the sun, and the horizon. Spatial awareness is a coveted skill; and directional awareness is cited by many involved in Aboriginal research, but understanding the directionality of Aboriginal culture is beyond the scope of this post. You can read the article for more information, where even Nicholls acknowledges there is more to learn.
I refer to above cultural knowledge to demonstrate possible differences in perspectives about what children may bring to, and get out of, cultural inclusions in mathematics lessons. Another consideration is that children become engaged because it is something they understand and are good at; and feeling successful is something which can encourage further participation. It also helps students to understand that mathematics is all around us in various forms – it is not just a classroom concept.
But did you know Aboriginal people have played games, similar to AFL for many hundreds of years?
By highlighting the connection between traditional games, and AFL; students may also feel their culture is being respected, and consequently more connected to the learning environment. Meanwhile, non-indigenous students learn about other cultures, whilst connecting to something they are already familiar with.
Two examples of traditional Aboriginal ‘football’ games:
Marngrook, Marn Grook: A traditional game from the Gunditjmara people in Victoria. The name comes from a corroboree by the Djabwurrung and Jardwadjali clans in Victoria’s Western District. Marngrook is said to be the Aboriginal game that provided the first lawmakers of football with some of the fundamentals of the game millions know and love as Australian Rules (Aussie Rules) Football, a view which is not totally undisputed
PurljaPurlja: A game like football that the Warlpiri Aboriginal people (north-west of Alice Springs) played for thousands of years.
We often hear that music and mathematics are connected. That makes a lot of sense when you think about it – patterns, fractions, comparisons, categories – all mathematical concepts! And add to that the social and cultural elements of music, and the way people in different communities value and use music, I feel that it is reasonable to include it in this discussion about Ethnomathematics.
According to Johnson and Edelson (2003) music allows students to connect to the symbolism language of mathematics, and to understand that humans use many symbols to express themselves in different ways. Chahine and Montiel (2015) suggest that analysing the mathematical structures of music provides meaningful learning opportunities. And, because ALL of Bishop’s mathematical concepts are present in music, I tend to agree with them!
As noted previously: Alan Bishop (1988) suggests there are six mathematical concepts counting, locating, measuring, designing, playing, explaining, sentimental values – attitudes, feelings, behaviours, idealogical values – beliefs, symbolism, philosophies, sociological values – customs, institutions, rules and patterns, interpersonal behaviours and technological – manufacture and use tools… .
As noted by Pais (2011) there are also opportunities to miss the connections between social and mathematical world views, if the teacher does not understand the cultural relevance (for example, Pais suggests using flute from a given region could just as well be any other instrument if the cultural aspects are missed). Despite this, Pais suggests test results improved through the inclusion of a culturally responsive artefact.
Johnson and Edelson provide a lot of examples of how to incorporate music into mathematics lessons here. Although these activities are not Ethnomathematically centred; they do provide starting points through which culturally responsive mathematics activities could be developed. Some examples might include specific types of music, instruments and songs, comparisons between and discussions about the similarities and differences, and a combination of visual, aural and practical activities which develop socio-cultural, mathematical and cross-disciplinary learning.
Drums to engage students – patterns (Aboriginal school in Alice Springs):
Fractions in musical symbols:
Abiam, P. O., Abonyi, O. S., Ugama, J. O., & Okafor, G. (2015). Effects of Ethnomathematics-based instructional approach on primary school pupils’ achievement in geometry. Journal of Scientific Research & Reports, 9(2), 1-15. doi: 10.9734/JSRR/2016/19079
Aboriginal culture – Sport – Traditional Aboriginal games & activities. Retrieved from http://www.creativespirits.info/aboriginalculture/sport/traditional-aboriginal-games-activities#ixzz4AV2CfYyS
Bishop, A. J. (1988). Mathematics Education in its Cultural Context. Educational Studies in Mathematics, 19(2), 179-191
Chahine, I., & Montiel, M. (2015). Teaching modeling in algebra and geometry using musical rythms: teachers’ perspectives on effectiveness. Journal of mathematics education, 8(2), 126-138.
Groundwater-Smith, S., Ewing, R., & Le Cornu, R. (2007). Teaching: challenges and dilemmas (J. West Ed. 3rd ed.). South Melbourne, VIC: Harcourt Australia.
Johnson, G. L., & Edelson, R. J. (2003). Integrating music and mathematics in the elementay classroom. Retrieved 31st May, 2016, Retreived from lesage.blogs.uoit.ca/wp-uploads/2010/08/Integrating-Math-Music-2003NCTM.pdf
Nicholls, C. (2013). It’s time we draft Aussie Rules to tackle Indigenous mathematics. Retrieved 31st May, 2016, Retrieved from http://theconversation.com/its-time-we-draft-aussie-rules-to-tackle-indigenous-mathematics-15032
Rosa, M., & Orey, D. C. (2010). Ethnomodeling: an ethnomathematical holistic tool. Academic Exchange Quarterly, 14(3), 1-5.
Zevenbergen, R., Dole, S., & Wright, R. J. (2004). Teaching mathematics in primary school. Crows Nest, NSW: Allen & Unwin.