2009 Study Tour

Dan Hellerich & Kevin Fusselman (2001) enthusiastically set up an official website for Pi day. Their site celebrates Pi in various ways and provides some interesting classroom ideas for teachers.

Some Pi facts – did you know?

Pi, Greek letter (), is the symbol for the ratio of the circumference of a circle to its diameter. Pi Day is celebrated by math enthusiasts around the world on March 14th. Pi = 3.1415926535…

With the use of computers, Pi has been calculated to over 1 trillion digits past the decimal. Pi is an irrational number meaning it will continue infinitely without repeating. The symbol for pi was first used in 1706 by William Jones, but was popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737.

World Maths Day is all over! However, a new World Record has been achieved with 1,133,246 students and 56,082 schools from 235 countries uniting to  correctly answer 479,732,613 questions online at World Maths Day.

Channel 9 Today show presented a feature story about World Maths Day on Tuesday 4 March 2010. The show commented that: “World Maths Day 2008 is a free web-event where kids from six to 16 years old can compete in live competitive challenges with other kids from around the world in answering mental arithmetic questions”.

There are many other interesting web links and articles about World Maths Day that provide information about how people across the globe involved themselves in lots of mathematical problem solving and fun experiences.

Do you know of any links that are worth sharing here?

I first met Geogebra at the 2009 ATM conference in Swansea, Wales. Presenters demonstrated various uses of this open-source software, providing examples of practical uses in the mathematics classroom.

But … what is it?

GeoGebra is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. It offers multiple representations of objects in its graphics, algebra, and spreadsheet views that are all dynamically linked. While other interactive software (e.g. Cabri Geometry, Geometer’s Sketchpad) focus on dynamic manipulations of geometrical objects, the idea behind GeoGebra is to connect geometric, algebraic, and numeric representations in an interactive way. You can do constructions with points, vectors, lines, conic sections as well as functions and change them dynamically afterwards. Furthermore, GeoGebra allows you to directly enter and manipulate equations and coordinates. Thus you can easily plot functions, work with sliders to investigate parameters, find symbolic derivatives, and use powerful commands like Root or Sequence.

I would be interested to hear how other mathematics educators are using this product in classrooms with learners, and to see examples of what you are doing too.

Hands-on mathematics at the mathematikum in Giessen, Germany

Challenging puzzles, giant soap bubbles, deceiving mirrors, mysterious bridges and more: Check out the fun side of mathematics and put your hands on more than 100 interactive exhibits. The Mathematikum in Giessen appeals to people of all ages and is the perfect destination for a family weekend. Experience a different side of mathematics! “Hands-on” is our first objective, which will allow you to really get involved and experience surprising phenomena yourself. How can a bridge be constructed not using any nails, glue, ropes or other tools? How is rolling dice related to Mozart’s compositions? Our whimsical way of dealing with mathematics helps overcome any reservations people might have facing the subject they most love to hate. Being amazed is the first step to getting behind mathematical secrets.

All exhibits are labeled in German and English. The Mathematikum is located in Giessen, in the centre of Germany 60km north of Frankfurt/Main.

An interesting practical use of mathematics relates to the area of campanology (ie. bell ringing). Polster and Ross (December, 2009) have written an article entitled ‘Ringing the Changes‘. They start by asking whether or not you “prefer your maths in exotic locations?” They then go on to suggest that “perhaps you should join a band of bell ringers, engaged in the grand old practice of ringing the changes. You could then employ your art in churches throughout (mainly) the English speaking world”.

But what does bell ringing have to do with mathematics? As they continue to go on and explain, a lot!

Their article goes into detail about the complex patterns and changes involved in ringing both large church bells and the much smaller hand bells. The language proves to be interesting, as the reader learns about the intricacies of the ringing patterns and sequences and comes across names that are described as being ”quintessentially English”. Examples include:

• Plain Bob Minimus,
• Plain Bob Doubles (on five bells),
• Plain Bob Minor (on six bells),
• Reverse Canterbury Pleasure Place Doubles,
• Grandsire Triples, and
• Cambridge Surprise Major.

There is lots to do with number and geometry in bell ringing including examples such as symmetry, sequencing and patterns. This article proves to be an interesting read involving an alternative practical area to consider the concepts related to Mathematics in. A fun and different way to consider sequences and patterns for students in your learning spaces! Maybe there is room to visit a few churches and to see the ringing in action?

The Millennium Mathematics Project (MMP) is a maths education initiative for ages 5 to 19 and the general public, based at the University of Cambridge and active nationally and internationally. The project group have stated that they “aim to support maths education and promote the development of mathematical skills and understanding, particularly through enrichment activities”. More broadly, they want to “help everyone share in the excitement and understand the importance of mathematics”.

The project consists of a family of complementary programmes including the NRICH website, and the STIMULUS programme. An array of different resources can be found on the project website. The MMP offers a range of  experiences for students and staff to engage in rich and authentic learning tasks. A recent update of a practical programme circulated by the MMP is detailed below.

Hands-On Risk and Probability Show

What are the chances of winning the lottery? How much of a football
team's league position is due to luck and how much is due to skill? What
are the chances of a false positive test result in security or medical
screening? Which newspaper headlines are telling the truth? Can you spot
a scam before you fall for it? 

Probability and statistics help to provide answers to questions like
these, forming a strong foundation for mathematics education. 

The Hands-On Risk and Probability Show addresses the importance of
probability and statistics through an interactive presentation and 'Who
wants to be a Mathionaire' Gameshow workshop. Students participate in
various activities and use voting technology to respond to multiple
choice questions. The questions are designed to teach them key
principles involving probability, statistics, problem solving and
lateral thinking. 

To find out further information, or to make a booking, please see
www.mmp.maths.org/risk

An extra session that was slotted into the busy schedule of the 2009 ATM conference at Swansea was given by a group of extremely enthusiastic and energetic mathematics teachers from Nova Scotia, Canada. They came dressed in black and green ready to share their ‘Math-On‘ experience with anyone willing to listen, solve problems and compete! In the short space of 60 minutes the 20 willing participants who came to this extra hands-on workshop had solved numerous problems and experienced a condensed version of what Math-On was.

The Math-On team described the Olympiad as being “an opportunity for middle school students in our school to grow and excel in their mathematical thinking. Students will experience a sense of teamwork and enjoyment while engaging in stimulating mathematical challenges”.

Check out the Math-On website for some interesting, innovative and engaging ideas to inject some fun into your lessons or student year groups.The website contains information on how to setup and organise your own Olympiad experience. There are practice questions to test yourself and others with too.

Maybe you will be as adventurous as the teachers from Nova Scotia and create a broader experience involving other schools too!! Whatever you choose to do, remember to have some fun and, Math-On!his is a competition for students who are willing to work together and who enjoy problem solving.

Maths is fun! Many would not agree with this statement unless they were in some way associated with the learning, teaching or research involved with mathematics or some similar area of study and/or focus. Attending a workshop given by Rachael Raed at the 2009 MA conference reminded me of the creativity, engagement and fun that mathematics can inspire within learning spaces and individuals. She found that pupils in her classes wanted activities that were:

• varied;
• competitive;
• collaborative; and
• didn’t involve textbooks.

Like her pupils, the delegates attending Read’s workshop also wanted to “soak up” a variety of different, practical and engaging activities. For 50 minutes we were tantalised by coloured paper, shapes, thought provoking problems and lots, lots more … We were made to think, discuss and challenge one another with the answers that we came up with individually and then had to share with the rest of our group.

Activities included:

• walk-a-bout-maths;
• drawing tasks;
• talker drawer cards;
• jenga;
• fractals;
• dancing patterns;
• angle pictures and transformation jigsaws;
• tumbling blocks;
• match-up exercises;
• and, lots more …

Each of the tasks that we worked on was rich and authentic in structure. Everyday items were utilised in the mathematical problems being solved.

I left this workshop reflecting on my early days as a mathematics teacher and the methods that I  had used and which often brought fun and excitement to my students learning. I realised that with the pressure of external examinations and having to get through a lot of content for regular tests that some of this “fun” had been lost. Now, I have the challenge of bringing the fun, creativity and excitement back into my lessons through the old fashioned way of concrete materials, and the 21st century way of using and embedding technology to provide variety and engagement for my learners.

A second workshop that provoked a lot of mathematical and deeper thinking; presented by Anthony Robin at the 2009 MA conference held at Robinson College, Cambridge; focused on the connections between some statistical distributions. Robin’s (2009) workshop blurb stated that:

“If you know the distribution of children in a family, what is the number of siblings a person has? If you know the age distribution of people on the street, what is the distribution of the age at which they die? and some other related problems”.

Heavy in statistical analysis and formulae but extremely thought provoking in terms of the analysis and the outcomes.

Check out the workshop presentation notes for further details to see what you think.

An interesting workshop presented by Anthony Robin at the Swansea 2009 ATM conference considered the everyday calendar. Robin’s (2009) workshop blurb stated that:

“We shall look at finding the day of the week of a given date, by both a mental method, and a method easily used on a machine. We shall see how the latter can be adapted to count the number of days between two historical events, using both Gregorian and Julian calendars. We shall also look at the moon’s motion and how this affects the tides and Easter. A range of mathematics involved, especially modulo (clock) arithmetic. Some of the ideas could be used in primary, but most in secondary”.

Lots of delegates came away talking about this workshop because of the many facts and figures that they hadn’t realised about the simple calendar. Many had not considered also the many mathematical calculations and problems that are associated to this time recording device.

Need more information about ‘What is a calendar?‘ then follow the hyperlink.

Workshop presentation notes