Session 2: School Wide Enrichment in Mathematics

Gwyn Jones, Bangor University gwyn.jones@bangor.ac.uk

Chris Olley, King’s College London chris.olley@kcl.ac.uk

Gifted and Talented in Mathematics

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

The apprentice mathematician

• Investigations and problem solving.• “... the global structure of mathematics to be

taught should be understood: it is not a rigid skeleton, but it rises and perishes with the mathematics that develops in the learning process. Is it not the same with the adult mathematician's mathematics?” (Hans Freudenthal)

1 21 7+7+72 22 5+5+5+73 23 4 24 5+5+7+75 5 25 5+5+5+5+56 26 5+7+7+77 7 27 5+5+5+5+78 28 7+7+7+79 29 All possible (+5)10 5+5 30 11 31 12 5+7 32 13 33 14 7+7 34 15 5+5+5 35 16 36 17 5+5+7 37 18 38 19 5+7+7 39 20 5+5+5+5 40

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)

Mathematical Modelling

The apprentice engineer/scientist

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