Transcript Session 1: Accelerated Support Programmes

Gifted and Talented in Mathematics
Session 2: School Wide Enrichment
in Mathematics
Gwyn Jones, Bangor University
[email protected]
Chris Olley, King’s College London
[email protected]
Session Outline
•
•
•
•
•
•
Towards pure mathematics
The apprentice mathematician
Towards applied mathematics
The apprentice engineer/scientist
Identification, selection and grouping
Discussion and Feedback
From School Mathematics
to Professional Mathematics
• The aim is to allow the engineers, economists,
scientists and mathematicians of the future to
flourish.
From School Mathematics
to Pure Mathematics
• “A mathematician, like a painter or poet, is a
maker of patterns. If his patterns are more
permanent than theirs, it is because they are
made with ideas”
(G.H. Hardy)
From School Mathematics
to Professional Mathematics
“I am not an educationalist. I am a
mathematician. But I know what turned me on
to the subject. It was being shown what
mathematics is really about. It was being
exposed to the big stories, the Shakespeare of
mathematics that inspired me”
(Marcus de Sautoy)
Some big stories of mathematics
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
7+7+7
5+5+5+7
The apprentice mathematician
5+5+7+7
5+5+5+5+5
5+7+7+7
5+5+5+5+7
7+7+7+7
All possible (+5)
5
• Investigations
and problem solving.
7
• “... the global
structure of mathematics to be
taught should be understood: it is not a rigid
skeleton, but5+5it rises and perishes with the
5+7that develops in the learning
mathematics
process. Is it7+7not the same with the adult
5+5+5
mathematician's
mathematics?” (Hans
Freudenthal)5+5+7
5+7+7
5+5+5+5
The Apprentice Mathematician
• Nrich Trails
– Generalising
– Working Systematically
– Visualising
The Apprentice Mathematician
• If a group of people shake hands with each
other. What is the relationship between the
total number of handshakes that take place
and the number of people?
The Apprentice Mathematician
• From transformation geometry
• To groups
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)
Applied Mathematics
• “Science no longer is in the position of observer
of nature, but rather recognizes itself as part of
the interplay between man and nature. The
scientific method ... changes and transforms its
object: the procedure can no longer keep its
distance from the object”.
(Werner Heisenberg)
STEM (Science Technology
Engineering Mathematics)
The apprentice engineer/scientist
Mathematical Modelling
Identification and selection?
• “Gifted adults were seldom child prodigies”
• “We need an approach which will recognise and
nurture signs of high performance wherever, and
whenever, they might occur”
• “The ‘human capital’ approach, which has
become dominant in more recent decades,
suggests that we should not be trying to ‘find’ the
gifted, but trying to create high performers”.
(Deborah Eyre)
• Jaime Escalante. ‘Stand and Deliver’
Summary
• An enriched mathematics curriculum rooted in the
big ideas of mathematics, it’s history and application.
• A systematic development of skills in pure
mathematics.
• A systematic development of the skills of
mathematical modelling (STEM)
• A curriculum for all.
Discussion and Feedback
• What view do our students get of
mathematics in schools under the current
curriculum?
• What view to they get of maths as a
component of STEM (with science,
engineering and technology)?
• What would be needed to begin the journey
of engaging school students with the
professional practice of maths and science?
Information
•
•
•
•
•
Go to http://www.themathszone.com/
Illuminate
Wondermaths
The Pizza Problem (Bowland Maths)
Gifted and Talented