mathematical enrichment programme (ucc) maths …euclid.ucc.ie/mathenr/mathcircles_files/talk for...
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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
www.mathscircles.ie
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
www.mathscircles.ie
Mathematical Enrichment
NUI Maynooth
University College Cork
University College Dublin
NUI Galway
University of Limerick
www.mathscircles.ie
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
www.mathscircles.ie
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
www.mathscircles.ie
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
www.mathscircles.ie
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
www.mathscircles.ie
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!
= + + +
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.”
www.mathscircles.ie
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)
www.mathscircles.ie
April 2012: Maths Circles Open Day
www.mathscircles.ie
“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.”
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
www.mathscircles.ie
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
www.mathscircles.ie
1st year lesson plan Handbook
www.mathscircles.ie
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
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.
www.mathscircles.ie
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...”
www.mathscircles.ie
Student’s Perspective
www.mathscircles.ie
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.
www.mathscircles.ie
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.”
www.mathscircles.ie
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.”
www.mathscircles.ie
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.
www.mathscircles.ie
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.
www.mathscircles.ie
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.
www.mathscircles.ie
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.
www.mathscircles.ie
Teacher’s Perspective
www.mathscircles.ie
“...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
www.mathscircles.ie
“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
www.mathscircles.ie
“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
www.mathscircles.ie
“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
www.mathscircles.ie
“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
www.mathscircles.ie
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
www.mathscircles.ie
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
www.mathscircles.ie
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
www.mathscircles.ie
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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