Using mathematics to change the world

1. Using mathematics to change the world Joan O’Hagan joanohagan@btinternet.com

2. ......the learner brings the context.... DfES, 2001 page 8

3. If the adult numeracy core curriculum is to be successful, it is important that: • The learner is clear about what they are learning and what the activities they are undertaking are designed to teach........ • the learner brings the context that will be the ultimate “proving ground” for their improved skills • the learner is sure that the skills and knowledge that they are learning are helping them to use their numeracy in the range of ways they want DfES, 2001 page 8, my emphasis

4. .....the learner is sure that the skills and knowledge that they are learning are helping them to use their numeracy in the range of ways they want DfES, 2001 page 8, my emphasis

5. The context which the learners “bring” is likely to include a cocktail ... • unemployment • or employment in jobs with poor pay and little access to training, • ill-health, • and low self-esteem.

6. And the range of ways in which they want to use their numeracy....? We don’t really know a great deal about this. What motivates learners? 16-19 year olds tend to be studying numeracy because they need it for another course, or because an employer want them to. Older adults tend to want to prove something to themselves, to become more confident, to improve their lives outside the classroom. But how good are we at finding out from the learners in front of us how they want to use their numeracy? And how do we help them explore various possibilities?

7. The ILP is king. But “individual” is the key word here. Most of our discussions are about the individual’s goals – learning goals, career goals, personal goals. All predicated on the idea that “individual skills lead to employability which leads to economic prosperity which leads to social inclusion etc”. Are we so sure about the “skills leads to happiness” argument that we can afford not to look outside it? Where might discussion about what maths is for come in? And where might discussion of societal as well as individual goals come in? Does this sound like educational old labour? If so, take a moment to wonder how we’ve arrived at a place where it sounds odd to invite adults to think, in an educational context, about big issues. Your future, it’s in your hands? Our future, it’s in our hands?

8. Three aspects of “Mathematics for social justice”. • Learning mathematics can enhance an individual’s life chances • People can use mathematics to change the world. • Learning mathematics is not a politically neutral activity. • The rest of this session will focus on the second and third points; note though that these can include the first.

9. My mother reported a lively discussion among her friends about washing-up liquids. They all accepted the TV ad story that the super-concentrated (and more expensive per millilitre) liquids wash more dishes per millilitre than the more dilute (and cheaper per millilitre) varieties, and that the cost per dish worked out less with the super-concentrated ones. Therefore, said her friends triumphantly, we should buy the super-concentrated ones. My mother argued however that if you are doing small amounts of dishwashing the TV ad scenario doesn’t work. She realised that there is a minimum amount of liquid which you use each time - a function of the size of the hole in the lid and of the squeeziness of the plastic bottle - and she suspected that this minimum amount of the super-concentrated stuff was far more than was needed at each of her small-scale washing-up sessions, whereas the minimum quantity of the ordinary ones was sufficient. Therefore, she hazarded, you were wasting the advantage of the super-concentrated liquids by in effect under-using them; super-concentrated manufacturers (like mustard makers) are making money from the stuff you threw away. By the way, she says she is lousy at maths….but maybe she is very good at numeracy. Adapted from O’Hagan, J. (1993). Can ordinary people do real maths? Viewpoints, 16. (Numeracy), 9-14. NIACE Power of Maths Stories

10. Mortgages • Smith requires a mortgage of £18,000 on which the interest is to be charged at 12% per annum. He agrees to pay regular monthly instalments. Find how much capital he still owes at the end of five years if his monthly instalments are (a) £180, (b) £240, (c) £300.

11. Worker Tung • When worker Tung was 6 years old his family was poverty stricken and starving. They were compelled to borrow 5 dou of maize from a landlord. The wolfish landlord used this chance to demand the usurious compound interest at 50% for 3 years. Please calculate how much grain the landlord demanded from the Tung family at the end of the third year. Maxwell, J., in Tomlin, A., (ed), The Numbers Game, 1982(?), Hammersmith and Fulham Council for Racial Equality

12. Freedom fighter • A freedom fighter fires a bullet to an enemy group consisting of 12 soldiers and 3 civilians all equally exposed to the bullet. Assuming one person is hit by the bullet, find the probability that the person hit is (a) a soldier, (b) a civilian. If instead the bullet hits 2 people find the probability that (c) both people hit are soldiers (d) both people hit are civilians (e) one of the people hit is a soldier and the other a civilian. • Maxwell, J., in Tomlin, A., (ed), The Numbers Game, 1982(?), Hammersmith and Fulham Council for Racial Equality

13. The Holborn escalator • The escalator at the Holborn tube station is 156 feet long and makes the ascent in 65 seconds. Find the speed in mph. Maxwell, J., in Tomlin, A., (ed), “The Numbers Game”, 1982(?), Hammersmith and Fulham Council for Racial Equality

14. “Well, my friends, in the research we had done in the townships and favellas where we were, we could observe the deficiencies among our comrades. Then, we realised that what our settlement companions really need is mathematics. They also need writing and reading, but, mainly mathematics. They look for mathematics the same way they look for a medicine for a hurt because they know where the hole of the projectile is, by which they are exploited”. Knijnik, G. 1997

15. Here Gelsa describes and comments on approaches to the measurement of land. An “academic” method – measuring the land in terms of hectares (squares of side 100 metres) – is contrasted with a measurement based on the length of time needed to work the land. The discussion took place in a context where ideas about the “size” of land are very significant for people involved in a struggle over control and ownership of land.

16. “…. others delimited the hectare of land to be farmed using the square “100 by 100” (i.e. 100 meters by 100 meters). Two of the peasants used as parameter to determine the size of a surface the “tractor time used to hoe”. One of them explained to the pupils“One places the tractor on the land. Working with it for 3 hours makes exactly one hectare”. The question of measuring the land with time was analyzed jointly with the pupils and the farmers. What, initially, as the pedagogical work began, appeared to be “inappropriate”, was then more clearly understood by the group, as examples of linear distances expressed by measure of time were examined….. For farming purposes, the hour of tractor use is more relevant data than the precision related to square meters of land. As a peasant said, “a few meters more, a few meters less, it doesn’t really matter too much.”

19. Munir Fasheh seeks to use local knowledges productively; rather than only celebrating local traditions, ..... [mathematics] can be used to make one aware of the drawbacks in one``'s own culture and try to overcome them. (Fasheh, 1997: 284)

20. ........He proposes international multicultural development of a syllabus based on the relationship between maths and cultural aspects: Students who go through such a syllabus will, I believe, be able to understand themselves, their beliefs, and their culture better. They will also be able to understand other people and other cultures better. ... Most important, it will help, I hope, in fighting three of the biggest evils in our time: absolutism, intolerance, and ignorance. (op. cit.: 289) This and previous slide are from Tomlin, A. B.,2001.

21. Knijnik, Gelsa (1997) 'Popular knowledge and academic knowledge in the Brasilian peasants' struggle for land', Educational Action Research,5:3, 501 - 511 To link to this article: DOI: 10.1080/09650799700200038 URL: http://dx.doi.org/10.1080/09650799700200038 DfES 2001, The Adult Numeracy Core Curriculum. London: DfES. NRDC 2008, Research briefing: Numeracy. London: NRDC Knijnik, Gelsa, 1999, ZDM (Zentralblatt für Didaktik der Mathematik, International Reviews on Mathematical  Education Volume 31 (June 1999) Number 3. Fasheh, M. (1997). Mathematics, Culture and Authority. In A.Powell and M.Frankenstein (eds0, Ethnomathematics: challenging eurocentrism in Mathematics Education (pp.273-290). New York: Suny Press. Tomlin, A. B.,2001. Participatory approaches to work with adult basic mathematics students. Unpublished PhD thesis.