## Maths Memos

## Mathematics on my mind

I would like to share my last week in March where mathematics came up every day. I adopt a diary format.

*Sunday*. Spent a couple of hours helping my 35-year old
older son with his maths A level. He is working full time, did not
take A level Maths at school and wants a career change. As he works
full time, he is taking modules. As Chair of ACME I wonder how easy
it will be in the future for adult learners when A levels become
linearised with end of course exams? Settling down for the evening
with a glass of Bordeaux to watch a TV detective drama when Andrew
phones me for help with factorising a tricky trigonometric
function.

*Monday*. Down at the London offices of a major mining
company with the Head of their Risk Department. Can the methods
used to assess risk and uncertainties on volcanoes be adapted to
help reduce mine accidents and assess the risk of ships sinking in
port facilities to disrupt ore exports? The underlying statistical
methods and mathematical modelling for risk assessment are the same
so the answer is affirmative.

*Tuesday*. Do a bit of maths myself in a project to
constrain the magnitudes and frequency of global volcanic eruptions
from an incomplete and time-biased dataset.

*Wednesday*. ACME business in London. Enjoyed a very
positive discussion about A level reform with Professor Richard
Craster (Imperial College) who chairs the Russell group committee
advising Government on maths A level content. There are clear
synergies between the new Committee and ACME, not least a strong
view by both that assessment is crucial. Contemporary assessment
tests speed and accuracy but does not promote understanding or
replicate how maths is actually used to solve problems. In the
afternoon meet MP Caroline Dinenage, who chairs the newly formed
All-Party Parliamentary Group on Maths and Numeracy with an
encouraging 50 members already. Discussed the 35% of children who
currently do not attain grade C in GCSE. Will the reforms to GCSE
make is more difficult for these groups without an obvious
alternative qualification?

*Thursday*. Listen to excellent lecture by Seth Stein, a
Professor of Seismology from Northwestern University. He is
interested in deep uncertainty and concludes that many mathematical
analyses of complex systems like earthquake hazards, climate, and
diseases fall short in not properly characterising uncertainty.
Science loses credibility when forecast events fall outside the
supposed calculated uncertainties. I agree.

*Friday*. Finished the week at a performance of Tom
Stoppard's brilliant play Arcadia. Three of the major characters
are mathematicians and the play includes a wonderful explanation of
non-linear dynamics applied to records of grouse shooting. One of
the characters is a precocious and mathematically gifted girl and
is Stoppard's homage to Byron's daughter Ada Lovelace. Ada is
credited as writing the first computer code in 1842-43. Babbage
described her as the *"Enchantress of Numbers."* Now here is
a role model for girls in our schools.

**Professor Stephen Sparks CBE FRS is the
Chair of ACME and a Professor of Geology at the University of
Bristol.**

The 35% who do not get a C in GCSE Maths are ALWAYS a worry for me and alternative qualifications may always be needed. We have to encourage a growth mindset and the fact that Maths, like reading and writing, is a basic requirement for all. As for the Maths A Level content and its current assessment, perhaps, in the future, a PBL approach to A Level Maths can help students understand how it is actually used in the real world? Try convincing us teachers about PBL when we are always under stress tick-boxing, target setting, having ofsteds and mocksteds and teaching Maths for 7 hours a day (unlike our colleagues in Shanghai). The exam boards will have to buy into PBL too, but surely they will do what the Govt. says? BTW, I had my students use calculus to do a project on the quantity and rate of expulsion of materials from a volcano, great stuff! Prof. Sparks, you can always tell your son to ask me for help if he is ever stuck, ok?

I wonder where you got 35% from? I think the figure is more like 50%. The numbers who achieve a grade C post 16 are very small and we should be creating a climate in which a resit of something 'failed' at 16 is not the automatic option! I'd like to see a world in which there are good and equally valued qualifications for those who have finished KS4. This is potentially a huge job - especially making them engaging and interesting (well taught of course) to encourage attendance and success. Just making maths compulsory is only the first step - we need to get those kids in the classroom enjoying maths!