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Mundane Maths?

I will not take this for an answer. Maths is not mundane. It is not tedious. Most of all, it is not boring! I have learned this only from teaching maths in my professional practice and still then I was not 100% confident maths could be full of fun and adventure. However, now, having completed the Discovering Mathematics module, my fun with maths is only just beginning.

Maths does not have to be a chore. It does not have to be the dreaded subject for a learner to approach. But this is up to you, the teach, the educator, the facilitator, the mathematician! I think it is important that in order for a learner to enjoy learning mathematics, the content delivery should be engaging, intriguing and taught with an approach oozing motivation and love for learning maths. Otherwise, what’s the point? You’ll be bored teaching it and you’ll be fed up learning it. Make it fun, it’s down to you to get involved.

Piaget (1953) expresses his view of learning maths:

“It is a great mistake that a child acquires the notion of number and other mathematical concepts just from teaching. On the contrary, to a remarkable degree he develops them himself independently and spontaneously. When adults try to impose mathematics concepts on a child prematurely, his learning is merely verbal; true understanding of them comes only with his mental growth.”
(p. 74)

My interpretation of this, is Piaget is saying maths does not solely have to be learned from the teacher teaching the subject content; honest understanding and real learning of maths happens through experience out-with the classroom, as well as in the class environment. I can vouch for this and state that I completely agree with this statement. I have learned through the course of Discovering Mathematics that maths can in fact be discovered and learned successfully by independent research and development. By development, I mean I have developed an appreciation for maths more than I had prior to this module. The way I have learned maths and been taught maths has made it intriguing maths rather than mundane, which is immensely important to note.

Bruner (1964) makes a valid point:

“Any idea or body of knowledge can be presented in a form simple enough so that any particular learner can understand it”.
(p. 44)

To me, this summarises and clarifies what fundamental mathematics is all about – why we talk about it, why we learn about it and why we use it to teach. It is so important to know about.
Prior to this module, I did not have a clue what ‘fundamental mathematics’ was. I mean, I could take somewhat-aimless guesses at what it meant, but I did not know how to approach understanding what it entailed and meant in the classroom context. Bruner (1964) suggests any content of learning has the ability to be translated in its notion, in order to allow learners to understand it at the appropriate level. In other words, abstract and ‘scary’ maths – which is commonly the root of maths anxiety (pardon the pun) – can be taught, delivered or learned in a different form, one that is more simple or fundamental, for the learner to have an easier understanding.

References

Bruner, J. S. (1964) Some theorems on instruction illustrated with reference to mathematics. In E.R. Hilgard (Eds.), Theories of Learning and Instruction: The sixty-third yearbook of the National Society for the Study of Education (NSSE) Chicago: The University of Chicago Press.

Mason, J., Burton, L. and Stacey, K. (2010) Thinking Mathematically (2nd ed.). Harlow: Pearson Education Ltd.

Piaget, J. (1953, reprinted 1997) The origins of intelligence in the child. Abingdon: Routledge.

First position – Dance and Maths

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First position. Second position, third, fourth, fifth position. Wall one, two, three, four. Corner five, six, seven, eight.

Maths, believe it or not, is a large fundamental element underlying choreography and dance.
From the age of two years and for the most-part of my teenage years, I was, unbeknown to my senses, experiencing mathematical thinking during rehearsals and practising dance. My passion for ballet, Scottish dance, jazz and tap meant I was dancing for years without consciously recognising the patterns of maths evolving. Now, since starting the Discovering Mathematics module, I have come to realise maths is monumental in its involvement in dance.

I first realised this whilst sitting in a Discovering Mathematics workshop, where my astonishment was rapidly growing about the connections maths has, to everything. I decided at that moment, to reflect on this. This led me to write about the links between maths and tasks we complete day-to-day. However, in hindsight, I realise I did not actually write about a specific link I’ve made to maths.

Generally, maths is in dance if you think about counting beats, speed, shapes made with the body, angles, position, timing in music and patterns in the choreography itself. For example, in the dance studio, you will, most of the time, be surrounded by four walls and four corners. You must learn the number each wall is labelled as and understand the directions in which you must face. To face whichever numbered wall or corner, you must understand the mathematical concept that is ‘rotation’ by understanding clockwise and anti-clockwise. Mathematical vocabulary is widely used in dance, as well as in drama and theatre performances:

CS – centre stage
CSL – centre stage left
CSR – centre stage right
USL – upper stage left
USR – upper stage right
USC – upper stage centre
DSL – down stage left
DSR – down stage right
DSC – down stage centre

These are named ‘stage directions’ and usually your choreographer or director will instruct you in accordance to the space. To be able to dance in accordance to this, you must understand the maths vocabulary used, which, in this example, is direction.

Dance does not require mathematical problem-solving or making calculations. Instead, it is simpler. More fundamental. It requires you to think mathematically. What I mean by this is you need to be able to have a sense of pace, time and speed in dance routines and therefore counting beats is a mathematical strategy in practice. It is debatable that counting beats is a musical skill, however I argue that this is mathematical, as well as musical.

Additionally, symmetry is largely used in dance. Numbers of routines and choreographed sequences are designed around the principle of symmetry – this requires the understanding of what symmetry is, what symmetry looks like and how symmetry is created. The fundamental understanding of symmetry is key in dance. Symmetry is also in occurrence when a dancer is balancing, because keeping the body symmetrical or in other words equal, aids balancing.

Dancers make shapes with their bodies in dance. Specifically, in ballet, dancers create triangular shapes and angles with their legs and arms. An understanding of straight, parallel, horizontal, and curvilinear needs to be understand, as this is important in ballet. Dancers should understand the fundamental learning of angles – specifically, understanding 40, 90, 180 and 360 degrees, in order to accurately use their bodies in pirouettes and developpes.

In summary, I have discussed the links between maths and dance, a real passion of mine and as dance as always been a strong commitment of mine I was enthusiastic about sharing its interconnected relationship with fundamental maths.
In terms of pedagogy, I aspire to learn about teaching maths through dance in my professional practice. Dance is an expressive art which is not implemented sufficiently in schools and I definitely intend on it having more consistent and regular involvement in aiding children’s learning.

Any fellow dancers, I would love to hear your thoughts on dance and maths.

Roman numerals, Ishango and all things prehistoric…

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Firstly, I’d like to you imagine something. Something unusual for many, but perhaps not so much for others. Imagine you had more than ten fingers. More than ten toes. More than two eyes, two ears, one nose and… Actually, imagining you had more than ten fingers will suffice.

We use methodology to take account of the value of things and this methodology is using number systems. Number systems provide symbols which represent digits which symbolise the value. This may seem confusing, but bare with me.

The terminology available to describe numbers, counting, digits or mathematical values, proves to be of a broad essence.

Cardinality – the number of elements in a set or other grouping, as a property of that grouping;
Ordinality – ordinal number;
Integer – a number which is not a fraction – a whole number;
Numeral – a figure, symbol, or group of figures or symbols denoting a number/ a word expressing a number.
– Oxford Dictionaries: Oxford University Press (2015)

So, it appears that numerals are symbols which represent the value, which fundamentally, is a number. Each symbol denotes a digit and looks something like: 0, 1, 2, 3, 4, 5, 6, 7, 9… (do bare in mind that number symbols do not look like this in particular countries… For example, have a look at the number symbols in the Chinese language).

How old are you, numeral?

Roman numerals is a number system going back to 3500bce, which makes it 5500 years old.
However, number sequences are suggestively not the same age. Take a look…

http://africanlegends.files.wordpress.com/2013/08/ishango_bone.jpg

This is the Ishango Bone is a mathematical resource, a ‘tool’ if you like, which was used to make tally marks to keep count. It is 22, 000 years old and in its original use, it did the job for people tracking environmental occurences, such as the factors indicating season changes, or light and dark weather. Today, clocks tell us the time and so if it is 11pm, we know, without looking outside, there will be a dark sky. Vice versa, if it is a dark sky outside, we will know, without checking the time, it will be somewhat late in the evening. Back when the Ishango Bone was used, there were no clocks to distinguish the time – the hours, days, weeks, months and seasons going by.

http://www.math.buffalo.edu/mad/Ancient-Africa/ishango_bone.jpg

Tally marks were notched into the bone to count or symbolise the number value. For example, one line = 1, two lines = 2, three lines = 3, and so on – each line is one tally mark. Amazing, isn’t it?

Back to Roman Numerals

Perhaps Roman numerals is an easier way to educate learners about what a ‘numeral’ actually is, because Roman numerals, apart from the numerals we use today, are well known, so much so that they are still used on clock faces.

Here is an example of this! Roman numerals on the clock at The Steeple Church, Dundee. This picture was taken by myself.

These are fundamental elements in maths – number recognition, counting, values and number

systems. Yet, it is so astonishing how number systems have evolved throughout the years of

maths going on, almost in a subconscious behaviour. I mean, when people used the Ishango

Bone, did they have the understanding they were using mathematics and, more amazingly, they

were practising and demonstrating an understanding of fundamental mathematics?

References

Mastin, L. (2010) Prehistoric Mathematics. Available at: http://www.storyofmathematics.com/prehistoric.html. Last Accessed: Dec 5 2015.

Ishango Bone – http://africanlegends.files.wordpress.com/2013/08/ishango_bone.jpg

Ishango Bone (2) – http://www.math.buffalo.edu/mad/Ancient-Africa/ishango_bone.jpg

Look around you!

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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.

And you’ve got your answer…
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.

Unimaginable Imagination

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Imagine an unimaginable imagination. One that no teacher, educator, facilitator, parent, caregiver or learner sets expectations for, standardises for, or… imagines.

Sarah Maxine Green, an American educational philosopher, author, social activist and teacher, stated,

“We want our classrooms to be just and caring, full of various conceptions of the good. We want them to be articulate, with the dialogue involving as many persons as possible, opening up to one another and to the world. We also want our students to be concerned for one another as we learn to be concerned for them. We want them to achieve friendships among one another as they move to a heightened sense of craft and wide-awakeness and a renewed consciousness of worth and possibility.”

Following an input in Education Studies: Historical and Comparative Perspectives on Education module, I thought about this quote from Greene and I reflected on what it means to be in a classroom. What is our purpose of schooling? What is the need to teach such human traits as to be caring, respectful and open-minded? I argue that it is to broaden the mind of our learners. To allow them to visualise, to imagine their potential and teach them the skills they need to turn that imagination into a reality. Schooling is to support and encourage our learners in becoming well-rounded individuals.
I analysed this quote from Maxine Green and recorded a few key points I interpreted from it:

Click on the picture for better quality.

Many of the traits Maxine Green talks about in the above statement, I interpret to making a number of links to the Curriculum for Excellence (2009), and in particular, the four capacities: successful learners, confident individuals, responsible citizens and effective contributors.

This just highlights to me that even though Maxine Green does not base her work in Scotland, around our Scottish Curriculum, based on our learners, our expectations and our way of working in schools, the idea and the imagination and thoughts are still on the same wavelength. We want our learners to achieve potential, bring their own views and to have the confidence to express them. Most importantly, for our learners to have an awareness and an imagination for what is possible.

In response to Greene’s statement, she is talking about creating an ethos and an influential environment in classrooms and amongst children as learners and individuals – one that demonstrates respect, appreciates friendships and understands voices and opinions. I strongly agree with what Greene pushes for by saying this, as she shows understanding of the profound importance of capturing the essence of the holistic child.

References

Greene, M. (2000). Releasing the Imagination. Essays on Education, The Arts and Social Change. San Francisco, CA: Jossey-Bass. Page 155.

Scottish Government (no date) Education Scotland: The purpose of the curriculum: The four capacities. Available at:
http://www.educationscotland.gov.uk/learningandteaching/thecurriculum/whatiscurriculumforexcellence/thepurposeofthecurriculum/. Last Accessed: Nov 17 2015.

There’s no avoiding it – Maths is everywhere!

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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.

Profound Understanding of Fundamental Mathematics

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Four Properties – to ensure a profound understanding of fundamental mathematics

Liping Ma (2010) believes in four properties in teaching and learning which sum up the way in which a teacher’s profound understanding of fundamental mathematics can be represented in the classroom. By this, Ma means a teacher will demonstrate the four properties and if this is successful, he or she has a profound understanding of fundamental mathematics.
– If you are unsure about what this is – profound understanding of fundamental mathematics – scroll to the bottom to read quotes extracted from Liping Ma’s ‘Knowing and Teaching Elementary Mathematics’ (2010). This may aid your understanding of the Four Properties in this post.
The first, connectedness, occurs when a learner has the intention of making connections between mathematical concepts and procedures. In pedagogical terms, the teacher will prevent the learning from being fragmented and instead, learners will develop the ability to make connections between underlying mathematical concepts that link.
The second property, multiple perspectives, is practised when a learner is able to take into account various perspectives when thinking in a mathematical way. This includes addressing pros and cons of all different viewpoints considered. In pedagogical terms, the teacher provides opportunity for their learners to have a flexible way of thinking and understanding concepts in maths.
Thirdly, basic ideas, is a way of thinking about maths in terms of equations. Ma refers to basic ideas as, “simple but powerful basic concepts and principles of mathematics” (2010, p. 122). Ma suggests, when practising the property ‘basic ideas’, learners are guided to conduct ‘real’ maths activity rather than just being encouraged to approach the problem. I suggest this means if a teacher is effectively implementing this property, he or she will be not just attempting to motivate the learners to approach the maths work, but instead, providing a solid and secure guide to the learners understanding the maths themselves.
The forth and final property, longitudinal coherence, is when a learner does not have a limit or boundary of knowledge. In other words, it is not possible to ‘categorise’ the learner or identify the learner as working at a specific level or stage in maths. Instead, he or she has achieved a holistic understanding of maths – a fundamental understanding. In pedagogical terms, Ma suggests a teacher who has achieved a profound understanding of mathematical understanding is one who is able to identify on demand the learning that has been previously obtained and will be learned later. Subsequently, the teacher will lay the fundamental maths as a foundation for later learning.

A few quotes extracted from Liping Ma’s Knowing and Teaching Elementary Mathematics (2010) that I feel define and summarise profound understanding of fundamental mathematics…

“The term ‘fundamental’ has three related meanings: foundational, primary, and elementary.”
– Ma (2010, page 120)

“By profound understanding I mean an understanding of the terrain of fundamental mathematics that is deep, broad and thorough. Although the term ‘profound’ is often considered to mean intellectual depth, it’s three connotations , deep, vast, and thorough, are interconnected.”
– Ma (2010, page 120)

“As a mathematics teacher one needs to know the location of each piece of knowledge in the whole mathematical system, its relation with previous knowledge.”
– Tr. Mao (2010, page 115)

“I have to know what knowledge will be built on what I am teaching today.”
– Tr. Mao (2010, page 115)

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics 2nd edn. New York: Routledge. Pages 115-122.

‘The Secret Life of 4 Year Olds’

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I recently watched ‘The Secret Life of 4 Year Olds‘ broadcast by Channel 4 on Tuesday 3rd November (Watch here – http://www.channel4.com/programmes/the-secret-life-of-4-5-and-6-year-olds). As the episode progressed, I found myself realising I have definitely been underestimating children as young as four years old. The hour-long duration of the programme was enough to capture the essence of the life of a four-year-old and the day-to-day thoughts, activities and behaviour of the children – not to mention, the emotional roller-coaster they endure because their ‘best friend took their toy or decided to play with someone else.
Oh, to be four.

A number of key points initiated…

Children, at 4, 5 and 6, are at a partial age;
Futures are formed from this young age;
These ages are a crucial stage for a child’s development – what they learn now is the ‘blueprint’ for adult life;
Moral argument can quickly become coercion;
Supportive friendships have the ability to rapidly change;
A history of friendships create expectations of behaviour;
Ambitions from the four-year-old children in the episode include, ‘save the planet’, doctor and hairdresser – at the same time, and ‘jelly maker’.

Dr. Sam Wass, Educational Psychologist – MRC Cambridge quotes,

“To establish and maintain relationships, one of the key tools that children need is language. And at four, the average girl tends to be five months ahead of the average boy, in terms of their language skills. This can put some boys at a disadvantage in their social interactions.”
On reflection, what is meant by ‘average’? Every individual child is different and unique in the way they learn. Therefore, arguably, we cannot generalise, label or categorise children’s abilities, to give us a specific indication of ability.

“They’re beginning to learn to regulate their emotions, to interact with each other and to understand that other people have feelings, too. These are lessons that will inform a lot of their future interactions.”
On reflection, children respond in a variety of ways in different situations and therefore express a range of emotions. For example, experiencing a tragic incident, being vulnerable to an unsafe environment, bullying, winning or losing, achievements and many more. I believe it is not possible to teach a child these emotions because to do that would mean telling or showing a child which emotion ‘matches’, if you like, with which situation. Emotions are a natural human trait – they are intrinsic but often influenced by extrinsic factors. Therefore, we can only teach children how to cope with and respond to their emotions, by being a supportive role and most importantly, by understanding. This is a learning process which children are still going through at a young age.

He continues,
“You give a child a new abstract concept to play with such as the concept of a friendship, and the natural instinct of a child is to want to prod and explore what that idea means. They tug it around a bit, see if they can break it and by doing this, they learn more about what the concept of friendship means.”

Professor Paul Howard-Jones, Educational Neuroscientist – University of Bristol quotes,

“Competition is motivating, it’s exciting, but it’s also great learning experience.”
On reflection, competition is an issue that is widely debated: is competition a good thing? My viewpoint is that is can introduce diversity, which may be viewed as a positive. However, I think competition is an important thing to teach our children to deal with, by teaching coping strategies.

“Children at this age self-segregate on the basis of gender.”
On reflection, I remember at primary school having to choose partners, groups or team leaders and the majority of the time, boys would choose boys and girls would choose girls. It was rare that opposite genders would be paired together. What does this say about our society? If anything, what does it tell us about our teaching strategies? As teachers and educators, the fundamental basis of our teaching and learning is around equality of opportunity and inclusion. We teach children the morality that everyone is the same, despite gender, race or religion. So, why do children self-segregate on the basis of gender? I would be interested to see any comments on this post regarding this issue.

And one final thought I will leave with you – extracted from The Secret Life of 4 Year Olds:

“It’s really striking how much children have to achieve at four years old. It may look like play, but actually they’re working really, really hard and they’re having to learn an awful lot. The way that they’re communicating with each other, the way that they’re experimenting and finding things out is really, really important for them.”

– Professor Paul Howard-Jones, Educational Nueroscientist (2015)

Watch ‘The Secret Life of 4 Year Olds’ – http://www.channel4.com/programmes/the-secret-life-of-4-5-and-6-year-olds

Let me speak!

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Yesterday, in my place of work, I found myself astonished by the sight and sound of a mother silencing her child.

Allow me to contextualise the situation for you. I work in a restaurant located in our City Centre. It is always busy with guests coming in for the first time, the second time, or coming in for their weekly order. So yesterday, work was extremely busy and therefore the noise levels were expectedly high. However, I could not ignore what I heard one woman say.

I allowed my eyes to glance across tables and they stopped on one table in particular. At this table sat eight guests who had come in together and going by first judgement, they were a family – made up of what I can only presume was two brothers, around three and five years old, along with their parents, grandmother and perhaps other relatives or failing that, family friends.

Now, in my place of work is one huge stone oven which does not ignore the flames that provide it with a warm glow and extreme heat. The boy, of about five years of age, sat at the table and was staring at this oven in absolute amazement. Of course he would be – it’s an enormous oven and most definitely is not your standard oven in your kitchen at home. He was amazed. It was something new to him. Something wonderful and exciting.

He turned to his mother with absolute excitement lighting up his face, wide-eyed and open-mouthed and said,
“Look! Mum, look at that!!! Our pizza is in that oven, look!”.
At that moment lay an opportunity for the mother to endlessly discuss the most exciting thing this boy had discovered – the oven!

Instead, she turned to him, ignoring the subject that provided him with such amazement, and silenced him with,
“Sssh, be quiet.”

I was in shock. You may be wondering why I was left feeling shocked and quite simply empathetic towards this boy. You see, this child should be immersed in language. Engaged with language. Not silenced when something is open for discussing, explaining and being interested in. His mother could quite easily have turned to her son and described the oven, asked him questions about it, used language to indicate a sharing of excitement and amazement about what her son had sighted.

I am fully aware the oven is not the most exciting thing for an adult to lay eyes on. However, as teachers, parents, educators or caregivers, it is crucial that we recognise children’s learning is embedded from a young age, they are learning all the time; and that is what we need to get right – we need to identify the gaps for learning and fill those gaps with knowledge, vocabulary, insights and perspectives. With language, there are a mass amount of opportunities to do this.

It is moments like this when children are surprised, amazed and intrigued about something at which it is necessary to capture this interest and go with it. Silencing a child when they show interest in something can only teach them not to display signs of true hysteria.

Celebrate this, engage this, and most importantly ask questions. Be involved by talking, discussing and conversing using your language skills and understanding, in order to facilitate the child’s learning and awareness of language. Show emotions with language and use words the child will question the meaning of; use terminology to challenge the child appropriately and broaden the vocabulary of the child.

As cited in The Really Useful Literacy Book (3rd edn.), it is suggested that children learn by understanding and remembering, which is essentially achieved effectively by ensuring application and regular revision (Martin, T., Lovat, C., Purnell, G., 2012). I agree with this and I suggest that in order for children to learn, understand, remember and progress language skills, it is profound that they are immersed in a language-rich environment,

The focus of this reflection is not about the oven. It is about spoken language.

The Meaning of Mathematics – Maths defined

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Numbers, sums, equations, patterns, sequences, problem-solving, formulas, confusion…

What comes into your head when you think about ‘maths’? Should we think more about ‘mathematical concepts’ and look deeper into what maths is all about, rather than accepting maths as being solely about numbers and work books?

‘Mathematics’ is defined as,
“The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics) or as applied to other disciplines such as physics and engineering (applied mathematics)”. (Oxford University Press, 2015)

So, what is maths? Maths can be confusing for many people. Many people believe you either have a ‘maths brain’ or you do not. I believe maths can be confusing, however I passionately argue that maths, the majority of the time is equations and formulas to follow. My view is maths can be straight-forward, if you allow it to be, or as the teacher, if you facilitate it right; it’s made up of steps and strategies. The difficult concept to grasp in maths is understanding those strategies, formulas and equations. Given you have that understanding, you are able to follow the steps and reach your solution – your answer.

However, saying that, is maths all about finding an answer? The problem-solving involved in mathematics is easier for me personally, because I enjoy being challenged to think and to think about problems from various perspectives. So, I enjoy the aspect of thinking about maths in contexts, as it has a purpose. I like to think of this as meaningful learning. In summary, I view problem-solving in mathematics as meaningful learning.

That’s not to abolish that other elements of mathematics are not intended purposeful learning. As stated by Scottish Government,
“Mathematics is important in our everyday life. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.” (Scottish Government, Education Scotland, 2015)

I agree with this – maths is important. Maths can be used everywhere in situations, without us recognising that we are using our mathematical understanding. How would we be able to tell the time? How would we be able to implement time management skills? How would we know to recognise significant dates? Would you know when your own birthday is approaching? How would we manage finances and handle money? I could not think of one occupation or career that does not involve mathematical elements in some way. Could you?

Maths is fundamentally important in every day life, I agree.

References

Oxford University Press (2015) Oxford Dictionaries: Language Matters. Available at: http://www.oxforddictionaries.com/definition/english/mathematics. Last Accessed: Nov 5 2015.

Scottish Government (2015) Education Scotland: Mathematics. Available at: http://www.educationscotland.gov.uk/learningandteaching/curriculumareas/mathematics/. Last Accessed: Nov 5 2015.

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