The Value of an Engaging Learning Environment

by Tom Krueger

Fig. 1

I am in a fortunate position to have my own classroom in which I teach all my lessons. I am even more fortunate because the person in charge of the timetable is a fellow maths teacher (they usually are, aren't they?) and upon my very polite request my classroom is not often used by other teachers, allowing me to use it also as my office, marking preparing-thinking-creativity space. In short, I spend most of my working day in one location and I want that one place to have a good feel to it. I want to feel 'at home' in a way and I certainly want my pupils to feel that I not only care for their mathematical progress but also about their learning environment. So, it was a logical step to start decorating my classroom and over the years I have run out of wall space and soon the ceiling is full too, as you can see in Figure 1, the photograph above.

I think that most people would agree that a stimulating learning environment has benefits for the general classroom conduct of young people. They see the teacher taking pride in their shared working environment and wall or table graffiti is kept very well at bay. I think it is also possible to draw parallels to note taking and general neatness. My colleagues also feel (or is that only wishful thinking) that maybe their rooms could do with the occasional 'spark of colour'. New teaching recruits at the interview stage will teach their observed lesson in my classroom to offer a 'subtle' hint as to how a classroom should look. But most

importantly of all I would like my charges to stop and look at the displays or, if I dare going further, to engage and think and even get excited about them.

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Fig. 2

Mathematics in School, September 2010 The MA web site www.m-a.org.uk 3

Now, I don't just want to write about the value of engaging, intriguing or merely beautiful and eye-catching displays but explain a few in detail and what use I get out of them with my pupils. So, let's start with the one I use most often (Fig. 2). It's a simple percentage chart where a pupil puts on a red counter (with blue tack) on a field in the top half of the chart and the class calculates the according percentage of 650. It is much better to use pupils here because they just love to be the teacher for a short while. Once they have all grasped the idea I now ask another 'teacher' to put the first counter onto a field in the bottom half...that normally earns some 'moans'...

Fig. 3

My most recent display is shown in Figure 3. Some of you will recognize it as being very similar to the final page of Issue 37 of Symmetry Plus. The pattern, painted on a rainy afternoon during the Christmas holidays, represents to ten significant figures - 3.141592653 (truncated rather than rounded) using concentric circles. The tiny red section in the middle represents three tenths of a circle (3.141592653), followed by the dot and then the slightly bigger green section represents one tenth (3.141592653) etc. The length of each word in the mnemonic underneath gives correct to 14 decimal places.

I picked up the idea of a 'Challenge of the Week' (Fig. 4) at last year's Annual Conference and have successfully run it

Fig. 4

since. All it involves is a short problem printed out and put on a wall. My junior classes can choose to solve it and whoever gets a correct answer gets a piece of paper with their name on put into a little sealed bucket (an empty 500 ml yoghurt pot works for me). At the end of each term I draw a winner for each class and usually present them with a small game from the 'Happy Puzzle Company' (www. happypuzzle.co.uk). My senior classes enjoy the problems too!

And whilst we are at the topic of 'time' have a look at Fig. 5 and convince yourself of what time it is there.

Fig. 5

And what's the time in Figure 6?

Fig. 6

I must confess that my pupils do get confused when trying to work out how long it is until the end of the lesson (the only thing they ever want to know, it seems...). In case they ask me my usual answer is: "Well, you are here to think ..."

Some good questions have emerged from using these two rather weird clocks, like "How often during the day will they show the same time?" - in fact, they always do but what I mean here is that you will see the 'same' picture on the clock face - or "At what times is one clock a mirror image of the other?" [Find these clocks online at:

www.iwantoneofthose.com/backwards-clock/index. html www.officeclocks.com/24_Hour_Clocks.html]

Some beautiful wall displays emerged from teaching about areas of regular shapes and symmetry. We worked out the area of all the ATM mats (Fig. 7) and then the task was to produce a shape of area 0.5 m2 (or as close as possible; note the potential for area scale factor here) and rotational symmetry order of at least 3.

The winner is shown in Figure 8.

Some other displays include the following:

4 Mathematics in School, September 2010 The MA web site www.m-a.org.uk

Fig. 8

Figure 9: Just a 3D presentation of the K?nigsberg Bridge Problem on the ceiling - the 'solution' is also on the ceiling but in a different corner .

Fig. 9

Figure 10: A graphical representation of the different types of numbers - very useful when solving equations or working on proofs and the question states 'for all g IR' or similar.

Fig. 10

Figure 11 : A good lesson idea for the last period on a Friday or just before long holidays. On my ceiling I have Roman Numerals, The Greek Alphabet, Names of large numbers, Conversion facts and Prime numbers.

Fig. 11

Figure 12: An eye-catching poster from Tarqu?n Publications (www.tarquin-books.demon.co.uk) - it provides many ideas for 'curve stitching' work using

MSWLogo (www.softronix.com). My classes never thought that trigonometry could be so beautiful.

Figure 13: Another idea for Friday afternoons - this time based on trigonometric identities. My classes are allowed to 'look around' the classroom during tests and if they can find useful information they may use it - "C'est la vie."

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Curve Stitching

Fig. 14

Fig. 15

Figure 14: Pupils have asked me about the meaning of Vedic Mathematics and when I show them what the symbols here mean they normally go "Ahhh..." (Maharaja, 2009).

Finally to Figure 15, which is not a display but an origami calendar that sits on my desk (www.accordpublishing. com). Pupils love to be rewarded for good effort and enjoy making these paper airplanes.

The display work doesn't stop in a classroom of course but continues throughout the maths department for very much the same reasons: we want 'Regulars' and 'Visitors' to be inspired by the mathematics around them and from the

moment they walk into 'our quarters' feel that we mean business. You can ask many young mathematicians here what is 8x8x8x8 and they will correctly say that it is 4096. Why? I hear you ask. Well, it is one of the Problem Pictures in the Mathematics Department foyer (Richard Phillips, at Phillips@badsey.net). M

References

Maharaja, . . . 2009 Vedic Mathematics, Motilal Banarsidass, New Delhi. ISBN: 81-208-0164-4.

Williams, K. R. 2005 Vedic Mathematics, Teacher's Manual Vol. 3, Advanced Level, Motilal Banarsidass, New Delhi. ISBN 81-208-2787-0.

Both books are in print only in India and may take a little while to arrive once ordered.

Keywords: Learning environment; Displays.

Author Tom Krueger, Head of Mathematics, Bradfield College, Reading, Berkshire RG7 6AU. e-mail : TKrueger@bradfieldcollege.org.uk

6 Mathematics in School, September 2010 The MA web site www.m-a.org.uk