Mathematical enrichment programme (UCC) Maths …euclid.ucc.ie/MATHENR/MathCircles_files/talk for ims 2012.pdf · Develop problem solving skills based on an investigative method,

Dr. Anca Mustata (UCC) Dr. Andrei Mustata (UCC)

Dr. David Goulding (Tyndall Institute & UCC) Mr. Ciaran O Conaill (Douglas Community School)

Julie O Donovan (CIT, CMC)

Nairtl funded

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Maths Circles After school maths club for junior cycle secondary school students

Designed specifically for students who enjoy mathematics

Aim to provide extra challenge of exciting topics that are normally outside the school curriculum.

Enrich student’s wonderment of mathematics

Introduce mathematical concepts using games and activities

A relaxed, friendly, mathematical environment

Run by third level maths students with the help of a maths teacher from the school

Communication between different people with interest in maths

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Mathematical Enrichment

NUI Maynooth

University College Cork

University College Dublin

NUI Galway

University of Limerick

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http://www.irmo.ie/

1 hour Weekly Meetings

Takes place in students secondary school

After school or at lunchtime

Maths games, puzzles. General mathematical activities.

1 or 2 tutors (third level maths students)

1 teacher

Usually about 10- 16 students

Students interested in maths – often picked by teacher Teachers Workshop

Lesson plans and activities for the circle are prepared by the tutor in advance of the circle for that week.

Structure of Maths Circle

1st year Maths circles: Encourage an appreciation/enjoyment of maths.

Develop problem solving skills based on an investigative method, pattern guessing, trial-and-error,

Develop independent and team working skills.

Develop an intuitive understanding of some mathematical concepts (e.g. limits, Combinatorics)

Give students a setting that encourages them to become passionate about mathematics

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2nd-3rd year Maths circles Encourage an appreciation/enjoyment of maths. Develop critical thinking – a wish to understand rather

than accept rules blindly Teach a structured programme which includes extra-

curriculum concepts/methods as well as developing curriculum concepts through problems and examples, in a natural and systematic way, and aligned to requirements of international curricula for that age

Prepare the grounds for sportive Maths –team contests, Olympiads

Open up horizons to the larger mathematical context – an intuition for how vast and rich it is

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The Team

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The Team Students

Tutors

Teachers

Organisers

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Students: 1st year secondary school (2nd and 3rd years to follow)

Tutors: 2nd -4th Mathematical Sciences (4 1h1, 2 2h1, 1 2h2)

Maths Research students

(2 teachers)

Teachers: Secondary school maths/science teachers

Organisers Third level Maths lecturers and a teacher

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Maths Circles – timeline Discussions at Maths Enrichment meetings

Oct 2010: Anca’s Maths week talk and tea

Jan/Feb 2011: North Pres Pilot scheme

March 2011 Teacher workshops (tea included)

Sept 2011 NAIRTL funding

Oct 2011 Maths fest

Oct 2011 Second Teacher Workshop (tea included)

12 Maths Circles in Cork Region

April 2012 First Maths Circles Open day

Summer 2012 Major Lesson Plan Development

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www.mathscircles.ie

Motivation:

Support network for youth (11-18 year old):

Math

circles Math

Olympiads

Math

camps Math

journals

School Town/city County National

- motivation

- perseverance

- a sense of community

- knowledge

- adventure

- math skills

- an ethos of giving!

= + + +

Talk by Anca Mustata aimed at secondary school teachers

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North Pres Pilot Scheme - 4 week pilot scheme

- Robert Linehan, Patrick Gorman, 4th Year UCC

“I helped run the pilot scheme and was surprised by the ability of the students and also their enjoyment of the circles...the students returned each week eager to again get involved in the circle, this showed great promise for the scheme and gave us great encouragement to advance the scheme.”

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www.mathscircles.ie

March 2011: First Teacher Workshop

March 2011: First Teacher Workshop

Oct 2011: MathsFest (CMTA)

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Second Teacher Workshop

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Maths Circles 2011/12 Douglas Community School - Ciaran O’Conaill and JP McCarthy

St. Aidan’s Community College – Joan Hough and Gráinne Walsh

Nagle Community College, Mahon– Ciara Twomey, Kathleen Cronin, Sinead O’Sullivan and Meabh Kennedy

Colaiste An Phiarsaigh – Sian Joyce and JP McCarthy

Scoil Mhuire Gan Smal, Blarney – Sean Foley, Joe McEniry and Sinead McCarthy

Hamilton High School, Bandon– Eoghan O’Leary and Aodhan O’Leary

Bishopstown Community School – Mary Sheehan, Vahid Yazdanpanah and Phillip O’Mahony

Mount Mercy – Mary Cowhig, Ann Sullivan, Sophie Daly and Sophie Scannell

Gaelcholáiste Mhuire, – Valerie Mulcahy and Eoin O’Mahony

St. Mary’s Secondary School, Macroom – Sharon O’Connell, Deirdre Van Der Krogt

St. Aloysius – Sarah Moore and Sorcha Gilroy

North Presentation School (Pilot Scheme) – Julie O’Donovan, David Goulding, Robert Linehan and Patrick Gorman

(Sacred Heart Secondary School, Clonakilty – Colm Kiely)

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Maths Circle in Blarney, Co. Cork

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Maths Circles 2011/12

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April 2012: Maths Circles Open Day

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April 2012: Maths Circles Open Day

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April 2012: Maths Circles Open Day

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April 2012: Maths Circles Open Day

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“I really enjoyed the open day for the students and found all of the students to be excellent and their willingness to get involved and their mathematical talents surprised me. I was not expecting such a highly talented group of students for our first open day so was delighted with that outcome.”

Lesson Plans

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1st year lesson plan content: List of activities

Presentation of activities and required materials in ready-to-go (student oriented) format

Hints

Solutions

Take-home problems

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1st year lesson plan Handbook:

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Ciaran O Conaill, Douglas Community School

1st year lesson plan Handbook: Introduction

Week 1: Nim, Magic Squares, and Filling

Week 2: Matchstick Mania, Dastardly Diagrams and a Crazy Fly.

Week 3: Mastermind, Mobius Strips, and some Brainteasers.

Week 4: The Flummoxed Flea, the Money Muddle Puzzles.

Week 5: Stand Up For Your Rights, X’s and O’s, and the Number of Possible Paths

Week 6: More Brainteasers, Taxicab Challenge, and the Towers of Hanoi

Week 7: Leaping Lizards, Cup Conundrums, and Safe Queens..

Week 8: Crafty Card Tricks

Week 9: Elfen Fun (Logic game), Christmas Tree Combinations, and Festive Brainteasers

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1st year lesson plan Handbook

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Week 10: Commencing Combinatorics: nCr

Week 11: Continuing Combinatorics: “Sober or Blotto, Remember the Lotto”

Week 12: Confounding Combinatorics: Hands at Poker

Week 13: Confirming Combinatorics: Repeated Elements, and Stars and Bars

Week 14: Nasty Number Tricks, and Devious Divisibility Tests

Week 15: Nefarious Number Tricks: 1089 And All That, and Why A Square Number Can Never End In 7

Week 16: Gruesome Games

Week 17: Ghoulish Games: Working From The

Week 18: Gargantuan Games

Take-Home Problems

Examples of 1st year lesson plans

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Examples of 1st year lesson plans

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Examples of 1st year lesson plans

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Examples of 1st year lesson plans

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Examples of 1st year lesson plans

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Examples of 1st year lesson plans

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2nd- 3rd year lesson plan content: The first part models a teacher- classroom discussion

on a given theme, developing the theme through examples, questions, hints, solutions, explanations of concepts, practice exercises.

Second part – more practice exercises. Solutions of these can be discussed in a subsequent hour.

Kieran Cooney, Ryan McCarthy, Anca Mustata, Ciaran O Connaill.

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Perspectives

Students

Tutors

Teachers

Organisers

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Student’s Perspective Did you enjoy the Maths Circle? 8 yes, 1 ya, 1 yah What part did you most enjoy? Different people different things (2 matchsticks, 4 tricks, 1

puzzle, 2 calculations, 1 mastermind) Did the maths circle change your opinion of maths in any way? "it can be fun", "i like maths", "ya you have to think about it more to get it right” “MATHS IS PUZZLING...! And cool...”

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Student’s Perspective

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Maths Circle in Douglas, Cork

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Tutors University students have the drive, enthusiasm, talents,

and skills set necessary as well as being able to relate well to the secondary school students. The maths circles team tried to channel this energy in the maths circles project. The students were fundamental in the development of resources.

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Tutor’s Perspective How did you find the exercise of producing lesson

plans/lesson reviews? “Grand, no trouble.” “I found it quite challenging in a lot of ways and I was very

grateful for the resources already in place.” “It was easier over time as I got to know the girls and what

types of maths they enjoyed.” “ This was a fairly ok job after we got used to what the

students could handle but it got difficult as time went on due to the lack of an idea of what the kids knew and what they’d understand. Perhaps some list of what would be suitable and what the kids knew would help.”

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Tutor’s Perspective Which activities worked best/worst and why? “Riddles and logic worked worst, they all shouted out answers messing

and then they lost interest. They enjoyed the hands on games the best like brainmaster, match stick puzzles and number problems.”

“They especially enjoyed matchstick puzzles. I think puzzles where you can use your hand and eye are much appreciated.”

“Logic problems (Einstein puzzles, problem solving, etc.), match stick puzzles and sequences seemed to work well. They seemed to like to sit down and start to try and work things out. Anything to do with areas or angles was a waste of time as the kids didn’t even know how to calculate the area of a circle. Splitting them into groups was a nightmare as we couldn’t watch all groups and it ended in a mess.”

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Tutor’s Perspective Did the students in any way direct what you did with them in class?

Yes they told us what puzzles they liked and wanted to make everything a competition because they all wanted to be the smartest.

Yes their interest in sequences is what guided me to include more... Yes, the students had a big impact on what we did with them in class. We

constantly asked them for feed back and usually asked them if they had any preference on what we did the following week.

Yes. If the students liked a problem they would ask for more like it and I would try to find some. Also if I thought they were struggling with something we would dedicate more time to that. At one stage we noticed they didn’t know anything about sequences and series so we did them for a few weeks.

Well they said that they enjoyed the games such as capture the fort so we tried to find more of those type puzzles for them.

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Tutor’s Perspective Would you consider making teaching a career? Why? • Yes definitely, it’s more entertaining than working in an office

and holidays are great. • I would consider it, as I find it to be very rewarding, however, it

wouldn’t be my first choice. • Yes it has made me consider teaching as it was a pleasant

experience. I would rather teach at a higher level though. • I wouldn't mind being a teacher, I like teaching and the maths

circles have thought me a lot about presenting something to a class room of people.

• No. I wouldn’t be able to deal with the “messers” and kids that have no interest in the subject in secondary school. We had the cream of the crop in this project which was a huge advantage over actual teachers.

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Tutor’s Perspective Did you notice any change in the way participants reacted to

given tasks in the last sessions as compared to the first? If so, how would you describe these changes?

They were less shy and more out spoken and really improved, they became way

better problem solvers. Yes the girls became a lot more confident. They were shy at the beginning esp

when answering questions. In the last few weeks they would shout out the answers.

Definitely. Students participated a lot more. In the first few sessions they were very quiet and afraid to shout out an answer or idea but by the end of it they seemed at lot more relaxed and more confident in their abilities.

Not really, the students were enthusiastic from beginning to end, which I was surprised and pleased to see.

Definitely. Students participated a lot more. In the first few sessions they were very quiet and afraid to shout out an answer or idea but by the end of it they seemed at lot more relaxed and more confident in their abilities.

At the start the kids would just sit there and look stunned when presented with something they didn’t understand but, towards the end, they were able to sit down and work out a difficult problem either by themselves or as a group.

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Tutor’s Perspective Did anything about the students during the maths circles

project surprise you? Yes, how intelligent they were Some of them were much quicker on the uptake. In one class, one

student correctly identified that any number divided by infinity would be 0.

I was impressed by how intelligent some of the students were. Once you got the kids to give things a try they figured out puzzles faster

than me most of the time and the answer sheet saved me from becoming a laughing stock more times than I’d care to admit.

That they kept showing up every week. I honestly thought that short of parents dragging them or the school forcing them they wouldn’t bother but they showed up every week and were always enthusiastic.

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Teacher’s Perspective

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“...students come from large classes with mixed range of abilities. So, as a teacher it is not easy to give individual attention ... Maths Circles provided these more-able students an opportunity to look at more challenging aspects of Mathematics.” Joan Hough, St. Aidans

“I found that the Maths Circle helped students gain more confidence in both their Mathematical ability and ability to express themselves to their class mates. Students developed new methodologies which they brought to their Maths classes but most importantly they found that Maths is fun!” Joan Hough, St. Aidans

Teacher’s Perspective

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“So many programmes focus on weaker students and this was a great opportunity for the better students.” Sarah O Donovan, St. Als, Cork City “Students developed their mathematical skills in a very different learning environment from the classroom ... It was really interesting to see students completing the same problem using very different methods.”

Sarah O Donovan, St. Als, Cork City “In our school 21 students started and 18 of those students attended all sessions ...” Sarah O Donovan, St. Als, Cork City

Teacher’s Perspective

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“In Blarney we found that it was a great boost to the students that had a real interest in problem solving and lateral thinking. Within the regular maths course these students do not normally get the opportunity to enjoy the fun and thrill of solving puzzles that require an understanding and sometimes unusual application of mathematical principles.”

Sean Foley, Scoil Mhuire gan Smal, Blarney “Maths Circles are an excellent way for students to feel good about their maths ability and themselves, it gives them a like-minded social group and the freedom away from class to become excited again about maths.”

Celeste Quinlan, Colaiste Daibheid

Organiser’s Perspective

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“In the past few years the demand for high quality graduates in high tech industry has seen a huge increase in Ireland, as a result immense focus has been put on mathematics education in this country. I feel that the maths circles initiative can provide an opportunity to increase student's enjoyment of the subject while at the same time improving their logic and problem solving abilities”

Organiser’s Perspective

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“I was surprised by how many university students wanted to get involved in the math circles as tutors and how enthusiastic they were”

“Don’t feel like you have to start big – one school at a time is ok”

Organiser’s Perspective

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Anything surprise you? The students' enthusiasm was surprising, in a very positive way!

Improvements? Have resources available to schools - lesson plans / worksheets. This will hopefully lead to both greater tutor and teacher involvement.

Advice if starting a maths circles hub... Make it as easy for the instructors involved as you possibly can!

How did you find working on the project? Great, to be honest.

Organiser’s Perspective Benefits of Maths Circles for students

a support network for those students with an interest in mathematics, both at an educational and at a social level – it’s always good to discover, and spend time with people who share our own interests

being exposed to deeper, more varied and more enjoyable aspects of maths than the school curriculum, children have more chances of preserving a keen interest in it throughout their development

problem solving skills

increase the percentage of time spent by these students on learning maths

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Other Perspectives: “It’s fantastic to see those very good students so engaged in the Maths Circle,

clearly enjoying the experience of being challenged mathematically.”

Jim Long, Principal Douglas Community School

“Engineers Ireland’s STEPS programme is delighted to support Maths Circles. This initiative is a terrific way for Junior Cycle students to gain an appreciation for the creative and aesthetic sides of maths, and to develop problem-solving skills in an environment that celebrates investigation for its own sake. It is students with these skills that will make great engineers of the future.” John Power, Director General - Engineers Ireland

“The Maths Circles Initiative provides students with an opportunity to build their self-esteem in a relaxed and supportive atmosphere. The Maths Circles make available a safe environment for students to realise their mathematical talents and perspectives that no one else has.” Noel Brett, Project Coordinator, Eureka Centre, UCC

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What we’ve learnt: Good will for maths - at all levels student, tutor, teacher, lecturer Energy and talent of Third level students Start small, think big. - Possibly even a four week programme in one school.

Make it as easy as possible for teachers

Communication is key Build rapport with schools/teachers

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How to start a maths circle hub? Website www.mathscircles.ie and Lesson Plan Handbook Tutors

Mention in lectures Survey (contact details, times avail, area they live, marks,...)

Workshop for teachers/tutors: Tutors prepare activities. Maths teachers association Hdip Students (in lecture) Any other links to teachers (graduates, ex schools,

enrichment links,... )

Students – Teacher helps coordinate in schools Tutor meeting Introduce teacher and tutor

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Dr. Anca Mustata (UCC)

Dr Andrei Mustata (UCC)

Dr. David Goulding (Tyndall Institute)

Mr. Ciaran O Conaill (Douglas Com.)

Julie O Donovan (CIT, CMC) Nairtl funded

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