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.

If a vehicle is travelling at 110 kph, what is the distance travelled while the brakes are being applied?

BRAKINGThe approximate distance to stop a moving vehicle is the sum of:· the distance covered during the time 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.

Reading

Science

In 2003, Ireland was ranked 17th with a mean score of 503By 2009, we have dropped to 31st with a means score of 487

Math

Higher Level Junior Cert Mathematics 2006 : 24,204 2007 : 23,804 2008 : 23,634 2001 : 21,1132009 : 23,592

Higher Level Leaving Cert Mathematics

2006 : 9,018 2007 : 8,388 2008 : 8,510 2001 : 9,9382009 : 8,420

Losing Students Year by Year!

• Performance of Irish students in international standardized tests (PISA);

• Percentage of students taking on Higher Maths.Concerns:

Irish Solution: Project Maths

Appendix 1 – Membership of the Project Maths Implementation Support Group

Frank Turpin (Chair)Marie Bourke Expert Group on Future Skills NeedsPeter Brabazon Discover Science and EngineeringSean Crowley National Association of Principals and Deputy Principals (NAPD)Tony Donohoe IBECAidan Farrell State Examinations CommissionDr Sheila Gilheany Institute of Physics in IrelandMargaret Kelly Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and SkillsBill Lynch National Council for Curriculum and AssessmentAoibhinn Ni Shuilleabhain Project Maths TeacherTom O’Connor Inspectorate, Department of Education and SkillsProfessor John O’Donoghue National Centre for Excellence for Mathematics and Science Teaching and Learning, University of Limerick.Dr Diarmuid O Se Institutes of Technology IrelandLynda O’Toole Teacher Education Section, Department of Education and SkillsTed Parslow Third Level Computing ForumLewis Purser Irish Universities AssociationDr James Robinson Engineers IrelandAnne O’Mahony Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and SkillsEve McKay Qualifications, Curriculum and Assessment Policy Unit, Dept. of Education and Skills

Is there something that we can do?

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.

Maria Chudnovsky – Associate Professor , Columbia University, New York

Did you have a mentor? Who helped you develop your interest in mathematics, and how?

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.

What is a Maths Circle?

Primary Senior CycleJunior Cycle

Mathematics EnrichmentProgramme

What are we doing for these students?

• Offer an outlet for young students with an interest in Mathematics

• Improve mathematical abilities in a relaxed, non-classroom environment

• Engender and foster an enjoyment of Maths for Junior Cycle students (mainly focused on 1st and 2nd Year students for the time being)

Objectives of Maths Circle

• 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

Outside Involvement

• 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

Structure of Maths Circle

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?

• 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

Outcomes and Future Development of Maths Circles in Cork/Munster Region

5. Did the maths circle change your opinion of maths in any way?

yes, that it can be fun tooya you have to think about it more 2* to get it right.

10. Have you any other comments or advice to those running the maths circle?

MATHS IS PUZZLING...! And cool....

* (haha maths)