Transcript Maths_Circle - Mathematical Sciences

Maths Circles
North Pres Pilot Scheme
Outline
• Programme for International Student Assessment (PISA)
• Mathematics in Schools
• Maths Circles
• What have we done?
• Outcomes
• What can you do?
Facts and Figures: PISA
• Developed by
• Administered to 15 year old students.
• 6 levels of proficiency: from the everyday to the unusual,
from the simple to the complex.
• Tests proficiency in : Reading, Science and Mathemtics
• Measures general mathematical literacy: An individual’s capacity to
identify and understand the role that mathematics plays in the world, to
use and engage with mathematics in ways that meet the needs of that
individual’s life as a constructive, concerned and reflective citizen.
• Multiple-choice questions or short written answers.
A result of global warming is that the ice of some glaciers is melting. Twelve
years after the ice disappears, tiny plants, called lichen, start to grow on the
rocks.
Each lichen grows approximately in the shape of a circle.
The relationship between the diameter of this circle and the age of the lichen
can be approximated with the formula:
where d represents the diameter of the lichen in millimetres, and t represents
the number of years after the ice has disappeared.
Using the formula, calculate the diameter of the lichen, 16 years
after the ice disappeared. Show your calculation.
the driver takes to begin to apply the
brakes (reaction-time distance)
· the distance travelled while the
brakes are applied (braking distance)
The 'snail' diagram right gives the
theoretical stopping distance for a
vehicle in good braking conditions (a
particularly alert driver, brakes and
tyres in perfect condition, a dry road
with a good surface) and how much
the stopping distance depends on
speed.
If a vehicle is travelling at 110 kph, what is the distance travelled while the brakes
are being applied?
Reading
Science
Math
In 2003, Ireland was ranked 17th with a mean score of 503
By 2009, we have dropped to 31st with a means score of 487
Losing Students Year by Year!
Higher Level Junior Cert Mathematics
2006 : 24,204
2007 : 23,804
2008 : 23,634
2009 : 23,592
2001 : 21,113
Higher Level Leaving Cert Mathematics
2006 : 9,018
2007 : 8,388
2008 : 8,510
2009 : 8,420
2001 : 9,938
Concerns:
• Performance of Irish students in international
standardized tests (PISA);
• Percentage of students taking on Higher Maths.
Irish Solution: Project Maths
Appendix 1 – Membership of the Project Maths Implementation Support Group
Frank Turpin (Chair)
Marie Bourke Expert Group on Future Skills Needs
Peter Brabazon Discover Science and Engineering
Sean Crowley National Association of Principals and Deputy Principals (NAPD)
Tony Donohoe IBEC
Aidan Farrell State Examinations Commission
Dr Sheila Gilheany Institute of Physics in Ireland
Margaret Kelly Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and Skills
Bill Lynch National Council for Curriculum and Assessment
Aoibhinn Ni Shuilleabhain Project Maths Teacher
Tom O’Connor Inspectorate, Department of Education and Skills
Professor John O’Donoghue National Centre for Excellence for Mathematics and Science Teaching
and Learning, University of Limerick.
Dr Diarmuid O Se Institutes of Technology Ireland
Lynda O’Toole Teacher Education Section, Department of Education and Skills
Ted Parslow Third Level Computing Forum
Lewis Purser Irish Universities Association
Dr James Robinson Engineers Ireland
Anne O’Mahony Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and Skills
Eve McKay Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and Skills
Is there something that we can do?
Maria Chudnovsky – Associate Professor , Columbia University, New York
Did you have a mentor? Who helped you develop
your interest in mathematics, and how?
Here I must mention a “math circle” I went to in 11th
and 12th grade. I lived in Haifa, and a friend from
school told me that on Thursday afternoons one could
go to the Technion and take this informal class run by
mathematics graduate students. It was an absolutely
amazing experience! Sometimes we would think about
problems, other times the teachers would tell us a
simplified version of a lecture that they themselves had
heard a few days earlier. Again, we all felt that nothing
out there could even compare to what we were doing.
That was when I decided that I would major in math in
college. As I studied more mathematics over the next
ten years, the problems got harder, the lectures got
more complicated, but the feeling that there is nothing
better I could possibly do with my time is still there.
What is a Maths Circle?
Mathematical circles are a form of outreach that bring mathematicians
into direct contact with pre-college students. These students, and
sometimes their teachers, meet with a mathematician or graduate
student in an informal setting, after school or on weekends, to work on
interesting problems or topics in mathematics. The goal is to get the
students excited about the mathematics they are learning; to give them a
setting that encourages them to become passionate about mathematics.
Primary
Junior Cycle
What are we doing for these students?
Senior Cycle
Mathematics Enrichment
Programme
Objectives of Maths Circle
• Offer an outlet for young students with an interest
in Mathematics
• Improve mathematical abilities in a relaxed, nonclassroom environment
• Engender and foster an enjoyment of Maths for
Junior Cycle students (mainly focused on 1st and 2nd
Year students for the time being)
Outside Involvement
• Anca Mustata – Lecturer Maths Dept UCC
• Julie O’ Donovan – Lecturer Maths Dept CIT
• David Goulding – Tyndall National Institute and
Maths Dept UCC
• Robert Linehan and Patrick Gorman – Fourth Year
Students UCC
• Additional support may be provided by
undergraduate students in UCC and possibly other
academic staff from the college as well
Structure of Maths Circle
• 1 hour Weekly Meetings (Thursday 4-5)
• 2 Adult helpers with a maximum of 16 students
• Introduce mathematical concepts using games and
activities in a relaxed, non-classroom environment
• Goal is enrich student’s wonderment of mathematics
not to supplement academic syllabus
• Additional help from parents, teachers and older
student pupils will be actively encouraged
• Pilot scheme ran for an initial period of 4 weeks
Sample Game
• Mastermind is a code-breaking
game, developed in the 1970s
• Two players – one sets the code,
the other tries to break it using
partial information given by the
other player
• This simple game can be used to
develop a student’s grasp of
logic, combinations,
permutations and probability
• Students initially unaware of the
underlying mathematics which
will be revealed
What is the largest number of
pieces we can get with only 4 cuts?
A mule and a donkey were stumbling along the road,
each carrying several identical heavy sacks. The
donkey started complaining, making a horrible
groaning sound, and eventually the mule got fed up.
‘What are you complaining for? If you gave me one
sack, I’d have twice as many as you! And if I gave you
one sack, we’d be carrying the same load’.
How many sacks were the donkey and mule
carrying?
Outcomes and Future Development of
Maths Circles in Cork/Munster Region
• Has the pilot scheme succeeded? If so what lessons have we
learnt from running it?
• Is it possible to develop circles in other schools without vast
input from us – i.e. can we develop a ‘recipe card’ for maths
circle success? (This is where we hope you will help us)
• Can we bring all maths circles together? Maybe once or twice
a year, bring groups together to meet and interact –
mathematical ability should not be exclusive, want students to
know it is instead inclusive and bring mathematically talented
students together
• From our point of view, this is a wonderful way for us to
develop, foster and nurture talented students looking towards
the Mathematics Enrichment Programme run in UCC
5. Did the maths circle change
your opinion of maths in any
way?
yes, that it can be fun too
ya you have to think about it
more 2* to get it right.
* (haha maths)
10. Have you any other
comments or advice to those
running the maths circle?
MATHS IS PUZZLING...! And
cool....