Functional Skills? Chris Olley Blog: From Using and Applying to Functional Skills: Is Maths Actually Useful? So, why do we teach mathematics? Is it because it is useful? Can it solve real life practical problems? Are less successful mathematicians less able to function effectively in society? This session will set up a discussion to engage with the place of applied mathematics in the school curriculum.

Rock Concert

Managing Music Concerts Galbraith (P. Galbraith 2011) reports a question from the PISA project which provides a multiple choice set of answers to the question of how many fans could stand in a field at a concert 100m by 50m. The correct answer is given as C. 20,000. However, there is also an answer B. 5,000 which must be taken as incorrect. Galbraith says; “This sample item involves spatial insight, as students need to decide on a suitable model to quantify the amount of space occupied by a human, then perform an appropriate calculation to estimate how many people would fit into a given space. Only about 26% of the multinational sample of students answered the item correctly (C), illustrative of the depressed performance associated with contextualised problems.” Galbraith, P., Applications and modeling in mathematics education: Progress to celebrate-so much more to do. In 10th International Congress on Mathematical Education. pp. 1–17.

The Purple Guide The UK Health and Safety Executive publishes it’s Purple Guide (HSE, 1999, p.17) which says; “Generally, 0.5m 2 of available floor space per person is used for outdoor music events”.

Science in Maths A Straight Line Graph

Maths in Science A Scatter Plot with a Line of Best Fit

10cm 50cm 10cm 1cm You are a lab technician You are required to cut the large sheet of metal into as many of the smaller strips as possible. How many can you make? Maths Solves Problems Around the School

Discussion: Functional Skills? In groups: Share examples where you have worked through an activity with students in which some mathematics was applied in a realistic context… Or, if you have to, make one up! Critique the examples: – were the outcomes realistic (which you know from research) – would the professionals in the field solving the problem have done it that way?

What are we doing then? Ray Spradberry’s Pigeons Where does the point of evaluation lie? Pedagogic or exchange relations Stieg Mellin-Olsen’s Bergen Airport Project Who is it of interest to? What are we supposed to be doing? Carraher, Carraher and Schliemann: Sao Paulo Street Kids Selling bubble gum by the gross 100% success on the street Jean Lave: Cognition in Practice Best buy problems in the supermarket

Projects The Pizza Problem (Bowland) by KCL … develop the skills of constructing the model. Why do penguins huddle? See the Australian Antarctic Survey … to see how mammals vary their volume to surface area ratio. Work with biology. (Also: fridges vs radiators) Is the Chinese New Year animal designation (or star sign) accurate? Construct a statistical model. Designing an efficient car park for the school (and other packing problems) School finance (capitation in … salaries, buildings, equipment, … out). Work with Business Studies. Islamic Patterns (17 unique tesselations of the plain, start to develop a taxonomy, …)(Also, Escher tessellations for transformational geometry). Work with Art/Textiles. The Finances of the School Play. Work with Drama. Readability tests (well known readability models are available in MS Word … how is the model constructed and what is it good/bad for?) Work with English. What is the relationship between words and symbols for numbers in different languages? Why are some numbers special? What number base is being used? (Four score year and ten = Quatre-vingt dix) Work with MFL.

Applied Mathematics Each letter group divide into two subgroups. Elect a writer, a speaker, a timekeeper and designer/illustrator. Produce an activity in the form of an illustrated activity instruction sheet for school use. This must involve students engaged in an application of mathematics where the activity is done in a manner entirely recognisable to professional who would do this activity. Discuss (10 mins) Create (20 mins) Present (5 mins) Discuss (5 mins) Improve (10 mins) Discuss (10 mins) Create (20 mins) Present (5 mins) Discuss (5 mins) Improve (10 mins) Do a rough version, then a neat one. By hand is fine.

Realistic Mathematics Education “what is aimed for is a process of gradual growth in which formal mathematics comes to the fore as a natural extension of the student's experiential reality.” (Koeno Gravemeijer 1999) “… RME models are not derived from the intended mathematics. These models are seen as student generated ways of organising their mathematically grounded activity” (Koeno Gravemeijer et al. 2003).

Applied Mathematics “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” (Albert Einstein) “A system such as classical mechanics may be ‘scientific’ to any degree you like; but those who uphold it dogmatically — believing, perhaps, that it is their business to defend such a successful system against criticism as long as it is not conclusively disproved — are adopting the very reverse of that critical attitude which in my view is the proper one for the scientist”. (Karl Popper)

Mathematical Modelling The apprentice engineer/scientist

ProfessionalPedagogic MathematicalMathematics School mathematics Mathematical modelling School mathematical modelling