# Look around you!

You’re probably thinking how monotonous it is that I continue to repeat this, but maths is everywhere! Again.

I will never lose the amazement or curiosity I have filled with, at the fact that maths is the fundamental principle behind the creation and design of many things – and, much to your shock, as you are about to discover, it’s even on your face! Keep updated on my blog and have a look at my next blog post if you want to know what I mean by this. But really, your face is maths in practice.

In my last maths blog post: There’s no avoiding it – Maths is everywhere! (you can find this at:  https://blogs.glowscotland.org.uk/glowblogs/teachingjourney/2015/11/17/theres-no-avoi…-is-everywhere/)… I quite clearly conveyed my astonishment as I was discovering the honest truth that maths is everywhere. So, now it is my turn to shock you. Here are just a few places you’ll find maths…

Have a look at the tiles, perhaps in your kitchen or bathroom. This can be on the walls or the floor – if it’s the flooring, it may be wooden.
Like pineapples? If you do, you’re one step further. If you don’t like pineapples, look at a bar of chocolate.
If there happens to be a football kicking around – pardon the unintended pun – then you’ll find maths on that.
So that takes you outside – where you will see maths everywhere, but have a look specifically at cobbles, slabs or bricks on the pavements or roads – it’ll be there.

Tessellation is a mathematical concept which the construction of a multiple number of identical copies of one shape. I exaggerate ‘identical’, as this is the reason tessellation occurs. For a shape to become a tessellation, they must be the same size and shape, to fit more than one copy together.

Oxford University Press (2015) defines ‘tessellation’ as:
“An arrangement of shapes closely fitted together, especially of polygons in a repeated pattern without gaps or overlapping.”

To demonstrate this and lay it out, I have drawn a picture showing tessellation:

In this picture, you can see the triangular shapes drawn are clearly equal in size and they touch with no gaps between each shape. I could have continued drawing triangles until the page was full, but I wanted to write about it instead! Tessellations also work with hexagons, squares and many more. Any comments with how many shapes you can think of which can tessellate, would be great!

To further explain how tessellations work, below is what a tessellation is not:

In the above drawing are four circles, equal in shape in size. So, they are equal in shape and size – shouldn’t they tessellate when they are drawn next to one another? Well, no – looking back at the first picture, there are no gaps between each shape. Now looking at this picture, you can see gaps between each shape = no tessellation.

These are basic examples. More abstract designs using two or more different shapes can still tessellate, because they can be in order and start to design a pattern.

The fundamental mathematics behind tessellations is the shapes, sizes, scaling and quantity. The most basic idea is shape. In order to begin to tessellate a shape, you need to know the number of sides the shape has. For example, if I, at random, chose the circle to tessellate then began drawing it, I would soon discover it does not work – this is because it has one edge which is rounded. Therefore, clarifying my point that the fundamentality behind tessellations is shape.

UPDATE
A great discovery I have made… Have a look:

Harris, A. (2000) The Mathematics of Tessellation. [Online]. Available at: http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit9/Tessellation.pdf Last Accessed: Dec 5 2015.

References

Dickson, R. (2015) There’s no avoiding it – Maths is everywhere! Available at:  https://blogs.glowscotland.org.uk/glowblogs/teachingjourney/2015/11/17/theres-no-avoi…-is-everywhere

Oxford University Press (2015). Available at: http://www.oxforddictionaries.com/definition/english/tessellation?q=tessellations. Last Accessed: Dec 5 2015.

# There’s no avoiding it – Maths is everywhere!

Throughout my inputs in Discovering Mathematics, I’ve been thinking a lot about the links between maths are other curricular areas. I’ve been making connections more and more between maths and other subjects and, I have discovered something about maths that perhaps I hadn’t thoroughly thought about before… It is everywhere.

The idea to write a blog post centred around the fact that I am amazed elements of maths come in to everything, came from an idea I had to write an account reflecting on the connection between maths and one other particular topic which I knew linked and I had interest in. So, I started making a list and it went something like this…

• Maths and food;
• Maths and sport;
• Maths and the environment;
• Maths in literacy;
• Maths and music;
• Maths and dance;
• As well as the above, the connections between maths and all curricular areas is something I would like to explore further.

I looked back at this list and as I read over it, I realised one thing – that list would most probably never end. Why? Well, because everything we do, somehow connects to a way of mathematical thinking – numbers, time, money, patterns, sequences, routines, timetables, schedules, musical beats, distance, speed, shape… I could go on. Whether it is basic, simple, easy-to-understand fundamental maths, or even the more abstract concepts that challenge us to think, reflect and solve… It is everywhere.

I decided to look at her writings in an extract called ‘Learning together series’ (no date) where Carol Skinner wrote about maths, titled, ‘Maths is everywhere’. Carole Skinner is a former teacher, Maths Specialist in Early Years and a writer with the belief that teaching maths, learning maths and experiencing maths holistically should be an exciting for all learners. At her time teaching at Brunel University, London, she was a Numeracy Strategy Consultant and an Early Years maths lecturer. Upon reading ‘Maths is everywhere’, my understanding of where maths links in to other areas of learning became more profound. Carole Skinner suggests maths can be acquired, learned and developed more effectively if children have a good start in being confident with counting. She goes on to explain maths has involvement in the simplest of tasks. For example, changing the channel for the television, pointing at numbers on the clock after recognising that they are in fact numbers, and even saying things like, ‘1, 2, 3, boo!’ to babies, toddlers and young children (no date). On reflection of reading this, I realise that maths is not solely about addition, subtraction, equations and problems. I would argue that if we think deeper about where the fundamental maths is that these more challenging aspects stem from, we can identify the fundamental maths more recognisably.

• Understanding what numbers are – the fundamental maths in this is knowing that they are a way of keeping a count of the amount, quantity, value or measurement.
• Recognising a number when you see it – and knowing in what context the number is used and it’s meaning.
• Having ability to count – which, fundamentally, requires the learner to understand order, sequence and value; number patterns.
• Pairing socks or matching socks in the home environment – the basic maths in this is knowing that in order to have one pair of something, you must have two single items of the same, put together.
• Patterns and sequences – this can include in Art & Design; number patterns and sequences, which can entail having the ability to count and make calculations.
• Routines, schedules and timetables – to understand a routine, you would have to understand the time involved in structuring the routine; also incorporated in making plans on timetables and schedules.
• Keeping beats in music, songs, poems and dance – this entails having an awareness of timing, rhythm and regularity of beats in the tune, which most of the time – probably all of the time – entails the ability to count.
• Maths in the home – in weighing and measuring; cooking and baking entails many different aspects of fundamental mathematics combined and connected to each other; setting out cutlery for meals and knowing how many plates, knives, forks, glasses etc. to set out in accordance to how many people need them; having a fundamental understanding of volume, in order to be able to run bath water correctly; setting an alarm clock which requires an understanding of the basic maths of knowing numbers and calculating time; planning routines such as breakfast, lunch, dinner, television programme schedules and hobbies etc.
• Maths in the environment – environmental print can be largely beneficial to a learner’s developing understanding of fundamental mathematics and almost anything can be linked to maths.
• Classroom – in the classroom, things like arrangement of tables includes maths and knowing numbers, which effectively entails the ability to count; organising children into groups or pairs requires the children to have this understanding, if they are to manage this themselves, of quantity, number value, division calculations, counting and addition; reward charts; homework charts; diaries, schedules and timetables in school and in the classroom; also all curricular areas children are learning, I would argue, relate to fundamental mathematical principles in some way.

Gathering these ideas, on reflection, has also made furthered my awareness of how maths is all connected. To justify this, in order to know how to do or understand one thing in maths, you must have grasped and understood the basic maths behind it – the fundamental principles.

Carole Skinner has written for a number of publishing companies, including BBC. Her latest book is titled ‘Maths Outdoors’ and is available to order – https://www.waterstones.com/book/maths-outdoors/carole-skinner/9780904187434

References

Skinner, C. (no date) Early Education: Learning together series. London: British Association for Early Childhood Education. Available at:
https://www.early-education.org.uk/sites/default/files/Maths%20is%20Everywhere.pdf
Last Accessed: Nov 17 2015.

# Let’s talk philosophy… MA1

It is fundamental for any teacher to have their own philosophy of education, which is made up of their values and beliefs about learning, teaching and education, because this is an influential element of the learning, planning and reflecting process in the classroom, of which the teacher is responsible for.

Education is a never-ending, lifelong learning experience throughout which an individual to learn information, process knowledge and develop skills and abilities through experience and practice, which will develop the individual in becoming well-rounded. The value education holds is powerful and significant to many aspects of life including society, relationships and personal development; we develop by learning and being educated. Education and the value found in education is somewhat dependent around the individual’s learning experience.

To me, education is learning, knowledge, understanding, developing, experience and adaptation. I believe it is important for the teacher and the children to engage to their full capacity, always; be interested; and for the teacher to have and promote a ‘thirst for knowledge’. To experience valuable education, approaches and attitudes to acknowledge and portray are: mutual respect, equality, consideration, honesty, loyalty, integrity, justice, trust and fairness.

The teacher is the role model to the children he or she is responsible for; if the teacher portrays a thoughtful, considerate and interested attitude, the children will follow this. The responsibility the teacher holds for the learning and development of each child is highly important; the teacher must always ask, ‘what is the impact on learning?’, when he or she goes through the planning and assessing cycle. It is the teacher’s responsibility for the learning and education within the classroom – this is why it is of paramount importance the teacher has his or her own Philosophy of Education.

# “One child, one teacher, one book and one pen can change the world” – Malala Yousafzai

I’d like you to think back to your first years of education, a time when you were facilitated with materials such as pencils, pens and books. Something to write on, something to write with and someone to teach you how to write. Was this your introduction to an education?

Malala Yousafzai, a teenage girl from Pakistan, was victimised by a Taliban terrorist attack  on 9th October 2012. Despite her horrific injuries, Malala’s response may seem strange, as she did not seek revenge for those who attacked her. Not only did the incident strengthen her courage and her fight for every child’s legal right to an education, Malala shed light upon one of the world’s most powerful weapons, education.

Malala addressed the United Nations, including more than 500 students in New York on 12th July 2013: “One child, one teacher, one book and one pen can change the world.” Malala allowed many others around the world to join her in her fight for the right of every child to receive an education and following her speech, many children around the world have the growing confidence to begin their journey in education.

If we lack the support from a teacher and the essential materials, our education would not be enabled. Around five million children around the world are out of education, but this can be changed. Every child has the right to provision. Every child should have an equality of opportunity to receive an education. And every child has the right to learn of current and past world affairs, just like Malala’s story. With knowledge, society can be changed. Therefore, one child, one teacher, one book and one pen can change the world.

If I wasn’t given these essential materials, I would not be the person I am today. I would not be here today. This is Malala’s inspirational vision. What’s yours?