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Reflections on the mini maths camps

Monday, 27. February 2012 16:42

So we've finished our first run of ten schools (>2200 students!) and feel that we went some way towards achieving our aims of introducing the students to technology and giving them a taste of what we feel mathematics is really about.

We were suprised and pleased that there are mathematics clubs in many schools, and we tried to encourage, support and enhance these existing initiatives.  We recommended that the mathematics in these clubs should be extra curricular - e.g. games and puzzles - and left behind some resources to aid with this.

We tried to involve teachers as much as possible in these mini maths camps and discussed the possiblilty of an e-learning Masters course in Mathematics Innovation for school teachers at Maseno University.

A number of schools asked us to come back, and it is clear that we were apprectiated.  But as a volunteer group, this isn't sustainable, so what is the future of the mini maths camps?

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The reality!

Sunday, 19. February 2012 17:36

So last Thursday saw us at Rang'ala Girls High School near Ugunja, and for the last two days (three if you include being in a broken down car!) we've been in Kisii visiting four schools  - St Stephens Nyamware S.S., Riondong'a High School, Gianchere Friends S.S and Boruma S.S.

They are very different schools with different facilities - one with the no power and the rest with varying number of computers. Interestingly the one with no power has computers ready for when they do get power. We have interacted with a varying number of students in each school but our cumulative total of students so far is over 1300 students.

This, and other factors such as power cuts, room dynamics, projector issues, and changes in our team has meant that our program has varied greatly from school to school - I don't think any session as gone according to the program! - but we think the key messages have come across.

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Program for the mini maths camps

Sunday, 19. February 2012 17:25

Intros

Between the introductions from the team we hope the message comes across that maths is something you can enjoy, it is a subject that you can get 100% in at school, there is so much more to mathematics than what you learn in school, computers have changed the way we do maths and computers can be used to learn mathematics.

Introduction to Maseno Maths Camp

19th -25th August

Learn how maths is used in the real world.
The beauty of mathematics - more than calculations
A whole week with access to computers.
Learn how to use new software.
Meet mathematicians and teachers from different countries.
Card games every evening

Games

Shall we play a game? (obligatory joke about not bringing sports kit as the word 'game' is mainly used in a sports context)

Play 21's at the front and then ask students to play

What has this got to do with maths?  Maths is all about learning the rules.

First session

[...]

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Idea behind mini maths camps

Sunday, 19. February 2012 16:30

The mother of one of the students of the 1st Maseno Maths Camp telephoned the week after the camp asking what we had done to her daughter. She said that she had been round at a friend’s house every day since she got back as this friend had a computer and she wanted to carry on exploring the mathematics she had learnt. A week later, when school term started, we received a telephone call from one of the student’s teachers asking what we had done to her. The teacher asked if we could come to his school and do a one week mathematics camp there for all his students.

Unfortunately we don’t have the resources for this, but what we have decided to do is a series of ‘mini maths camps’ – half day taster sessions in schools where three of the sessions are given and the key software introduced. All the resources that we created during the week long camp will be left behind in DVD format for the school and students to use.

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Geometry

Monday, 30. January 2012 13:33

We used Geogebra to allow the students to create geometrical functions, and see the links between geometry and algebra.

One activity used this starting point in Geogebra:

Parabola

and asked the students to plot all the points that were equidistant from the line and the point.  It is set up so that the students create y=x^2.

The students had a lesson on spherical geometry - showing them that the angles in a triangle do not always add up to 180, and a lecture on reflectional symmetry in euclidean geometry, spherical geometry and hyperbolic geometry.

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Computer based statistics

Monday, 30. January 2012 12:15

This theme showed the power of computers in understanding statistics and in analysing huge amounts of data in an easy visual way.

The students were introduced to CAST, an online statistics textbook which uses interactive applets for explanations and practice and for student practice.

Students watched Hans Rosling's fascinating video showing 200 years of history in four minutes, and had the opportunity to use the Gapminder software for themselves.  Students explored worldwide trends, but were able to focus on Kenya using the trace function.  The software initiates mathematical discussions such as "What is a logarithmic scale, and why is it often used instead of a linear scale?"

 

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Game Theory and Modelling

Monday, 30. January 2012 11:50

This theme was probably the most fun - from Prisoners Dilemna to Monty Hall to running outside in a group trying to mimic the behaviour of swarming birds; there was certainly lots of hands on action.

Students watched a TED talk by Steven Strogatz explaining the basic rules that can be used to model how each bird flies in a swarm.

1. Only aware of your nearest neighbour
2. Fly in the same direction as your neighbour
3. Maintain the same distance from your neighbour
4. Fly away if you see a predator

Easy to understand, hard to enact!

The main idea we were trying to get across was that maths is all about sets of rules.  Once you understand the rules you can do the maths.  We played card games every evening which reinforced this idea of being able to operate within rules.

 

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Number systems

Sunday, 29. January 2012 13:14

This theme grew from the film "The Story of 1" narrated by Terry Jones of Monty Python fame, which we showed the students in the middle of the week.  We looked at counting in binary, helped by the Mathematica applets Binary Card Game (you may have seen this in a Christmas cracker!), Counting in Binary, and Binary Counting Sequence.

The story of Pythagoras and his denial of irrational numbers was discussed, and the existence of irrational numbers was proved using this Geogebra applet:

Pentagram

 

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Number Theory

Sunday, 29. January 2012 9:47

During the maths camp last summer we used Simon Singh's excellent website The Black Chamber after introducing the students to the concept of codebreaking by splitting them into groups and asking them to create their own codes.  We looked at the frequency distributions of letters in English and Kiswahili and how you could use these to crack certain types of code.

We followed this with a session on modular arithmetic, leading to the use of primes in codebreaking, via inverses.

In the final two sessions we showed the students three problems  and asked the following questions:

Fermat’s Last Theorem (with n=3)

x3+y3=z3

and asked students if they could find any integer solutions.

Hendrik Lenstra sequence

$latex x_{0}=1$

Etc. etc.

Are the solutions always integers?

3n+1 Problem 

Take any positive integer, if it is odd: multiply it by 3 and add 1, if it is even: half it.

Keep following these steps, stopping if you get to 1.

e.g. 5 – 16 – 8 – 4 – 2 – 1

Are there any numbers which don’t go to 1?

Students had time to explore these using pen and paper and then used Mathematica applets to explore further

We then used these problems to discuss the difference between an unsolved problem, a counter example and a proof.

See the 3n+1 it described here by Stephen Wolfram

Fermat's Last Theorem - see Simon Singh's site (the book is brilliant)

Lenstra ...

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Current themes

Friday, 27. January 2012 19:30

In the inaugural maths camp in 2011 we decided to structure the week according to mathematical themes.  The logic was that the themes would run through the week, with roughly one lesson per day in each theme.  This wasn't made explicit to the students, but the idea was that the lessons and activities would build up in difficulty during the week and come together at the end.

Initially this blog will describe the themes we used to introduce our students to extra curricular mathematics in 2011, and then add to these themes and develop new ones through interaction for 2012.

 

 

 

 

 

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