Transcript Mathematical Modelling

Functional Skills?
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.
Chris Olley
[email protected]
Blog: www.themathszone.com
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., 2011. 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,
0.5m2 of available floor
space per person is
used for outdoor music
events”.
Science in Maths
Volume (cm3)
Volume of Gas Produced
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Time (sec)
A Straight Line Graph
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Maths in Science
Volume (cm3)
Volume of Gas Produced
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Time (sec)
A Scatter Plot with a Line of Best Fit
Maths Solves Problems
Around the School
10cm
50cm
1cm
10cm
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?
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.
• 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?
Paul Dowling:
Domains of (Pedagogic) Action
Dowling, P. (2002). The sociology of
mathematics education: Mathematical
myths/pedagogic texts. Routledge.
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)
The apprentice engineer/scientist
Mathematical Modelling
Professional
Mathematical Mathematics
Pedagogic
School
mathematics
Mathematical Mathematical School
modelling
modelling
mathematical
modelling
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.