Author Archives: Emma Kilpatrick

The Enormous Turnip

 

  1. MUSIC AND STORYTELLING (3 hours)

Choose a well-known children’s story and dramatise this, using musical motifs, sound effect, character songs and instrumental music to accompany the drama/narrative.  This can take the form of a stage production or a radio version of the story.

Music beyond sounds

CROSS CURRICULAR LEARNING IN MUSIC (3 hours)

Consider how you can make links between music and other curricular areas.  Choose as many subject areas as you wish, and for each, create activities that draw upon musical knowledge to enhance the learning. 

Music and Art – Create a picture to go alongside the piece they have created in music.

  • Consideration of key (major or minor = happy or sad) and what colours could represent that
  • Is this piece slow and graceful or quick and jumpy? What sort of lines and shapes
  • could represent this?
  • Musically, this develops the skill of appreciation, and being able to identify themes and techniques used in the music. Artistically, this allows the children to create an explorative piece, where they are free to express themselves, and justify their use of materials and artistic techniques
    • Art – Through observing and recording from my experiences across the curriculum, I can create images and objects which show my awareness and recognition of detail. EXA 2-04a
    • Music – I have listened to a range of music and can respond by discussing my thoughts and feelings. I can give and accept constructive comment on my own and others’ work. EXA 1-19a / EXA 2-19a

 

Music and Science – Waves and Vibrations

  • Use scientific skills of hypothesising and experimenting to investigate:
    • Which instruments make vibrations and how?
    • Which instruments make the most vibrations? Why?
    • Do higher or lower pitches make more vibrations? Why? (wave lengths)
    • Can you always see vibrations?
  • How do different materials allow vibrations to pass through them? Which would be the best material to use for music room? Why?
    • Music – I can use my voice, musical instruments and music technology to discover and enjoy playing with sound, rhythm, pitch and dynamics. EXA 1-17a
    • Science – By collaborating in experiments on different ways of producing sound from vibrations, I can demonstrate how to change the pitch of the sound. SCN 1-11a

 

 

Music and HWB/Drama – Music linked to emotions

  • Examine major and minor chords and scales. Ask the children how the sounds make them feel, contrasting the two. Also play with spooky and dreamy scales. Also look at pieces of music, having the children close their eyes and use their imagination to pick out the emotions present in the music.
  • This can then link to drama and characterisation, with the children creating/developing characters and their traits, based on a piece of music. This reinforces the skills of identifying themes and emotions portrayed in music.
    • HWB – I am aware of how friendships are formed and that likes, dislikes, special qualities and needs can influence relationships. HWB 0-44a / HWB 1-44a
    • HWB – I am aware of the need to respect personal space and boundaries and can recognise and respond appropriately to verbal and non-verbal communication. HWB 0-45b / HWB 1-45b / HWB 2-45b / HWB 3-45b / HWB 4-45b
    • Music – I have listened to a range of music and can respond by discussing my thoughts and feelings. I can give and accept constructive comment on my own and others’ work. EXA 1-19a / EXA 2-19a
    • Drama – I enjoy creating, choosing and accepting roles, using movement, expression and voice. EXA 1-12a

 

 

 

Music and Literacy – Music and Poetry

  • After looking at poems in class (potentially about their topic), let the children listen to different pieces of music and have them decide which piece fits the poem(s) best. (appreciation)
  • Then the children would work in groups to create their own music piece to match a poem, thinking about the techniques the pointed out in the previous examples. (composition)
  • If the children are enjoying these activities, they could be developed further, with the children writing their own poems and music to go alongside them (which could link with topic) – with the final product being performed, bringing in the final aspect of music. (performance)
    • Music – I have listened to a range of music and can respond by discussing my thoughts and feelings. I can give and accept constructive comment on my own and others’ work. EXA 1-19a / EXA 2-19a
    • Music – Inspired by a range of stimuli, and working on my own and/or with others, I can express and communicate my ideas, thoughts and feelings through musical activities. EXA 0-18a / EXA 1-18a / EXA 2-18a
    • Music – I have experienced the energy and excitement of presenting/performing for audiences and being part of an audience for other people’s presentations/performances. EXA 0-01a / EXA 1-01a / EXA 2-01a
    • Literacy – Having explored the elements which writers use in different genres, I can use what I learn to create stories, poems and plays with an interesting and appropriate structure, interesting characters and/or settings which come to life. ENG 2-31a
    • Literacy – I can: · discuss structure, characterisation and/or setting · recognise the relevance of the writer’s theme and how this relates to my own and others’ experiences · discuss the writer’s style and other features appropriate to genre. ENG 2-19a

 

 

Music and Maths – The Sound of Shapes (reinforcement exercise)

  • When learning about 2d shapes, the more corners a shape has, the higher the note they should play i.e. triangle would have a low pitch but an octagon would have a high pitch, whereas a circle would be silent – use boomwhackers or similar
  • This tests their knowledge of shapes and their ability to distinguish low and high pitch and how to make those sounds.
  • This activity can then be used to teach about music notation. Instead of notes on a stave, the children could use shapes to know which note to play. This can allow them to create rhythms and patterns without knowledge of how staves work.
    • Maths – I have explored simple 3D objects and 2D shapes and can identify, name and describe their features using appropriate vocabulary. MTH 1-16a
    • Music – I can use my voice, musical instruments and music technology to discover and enjoy playing with sound, rhythm, pitch and dynamics. EXA 1-17a

Say Cheese!

Using Photography in teaching (4 hours)(Art)

Digital photography can be a useful tool and activity in the primary classroom.  Almost everyone uses it, often without any formal teaching.  Produce an illustrated guidance poster, video or hand-out for primary teachers and or pupils in the use of this medium.  Consider aspects such as image quality, subject matter, composition, inclusion, accessibility, potential health and safety risks, privacy, storage, printing and compile a list of potential uses around the school.

 

The use of photography in the classroom is all too often limited to the teacher, usually taking pictures of the children working or what they create. These pictures are then used in displays and often little learning is taken from them. While it is good to document and evidence the children’s work, there are so many more learning opportunities to use photography in the classroom.

 

 

Using cameras as a medium for art allows children to expand their thoughts about art, and changes their perspective. This strategy can be useful in including children who feel that they are “not good at art”, as they can feel less pressure by using photography. They can capture the beauty of what they see without worrying about drawing properly etc.

 

There are also other uses for photography which draws links between art and the artistic nature of photography (angles, lighting etc), and other areas of the curriculum – some ideas are shown in the leaflet I have created for the TDT.

 

 

 

The Blue Lights of Pizza Express

Task 2: SCOTTISH COUNTRY DANCING (1 hr)
Go to http://www.scottishdance.net/ceilidh/dances.html. Choose a dance and teach it to someone.

Being a passionate Scottish Country Dancer, the task to learn and teach a Scottish Country Dance as part of the Expressive Arts elective thrilled me immensely! I have been dancing as a hobby from the age of 5, and for the past few years have been assisting in teaching the younger class, and it is still a hugely enjoyable pastime for me, however, I believe that schools take the joy out of it.

The dance I chose to learn and teach to my class is “The Blue Lights of Pizza Express” (yes, it is a real dance). The picture shows the dance crib (instructions)(click to view clearer), which is written using dancing terms, which we know, but would need explaining to a beginner. This dance is a Strathspey (slow dance), in a square set, the type of which is not taught in schools. The dance is quite complex, and took a good deal of explaining to my class, and therefore I certainly wouldn’t use anything near as difficult with a primary class. We did get a video of us dancing it, however, the file is too large to be uploaded to the site. If anyone would like more beginner-friendly instructions for the dance, just comment.

 

As my love for Scottish Country is so well established, I am of the opinion that it is taught completely wrong in schools, to the extent that our national heritage is loathed and comes with such a stigma. Whenever I tell anyone I do dancing, they usually ask which kind, to which I reply Scottish Country. The sheer comments and questions that follow highlight my point precisely. They ask “Why?”, or sometimes simply just laugh or look confused, a reaction which I argue would not be given had the answer been Ballet, Hip Hop or even Highland.

Schools teach the same 6-8 dances throughout primary and secondary, and in an attempt to make it more fun, have begun to use modern music. While this is a good strategy, and one we use in dance class ourselves, it is only the beginning. Children are forced to dance with classmates they would rather not, which starts the lesson off poorly. Children should be able to choose their partners, boy or girl, and, as long as there are clear rules about expectations of behaviour, there will be less misbehaving to warrant partnering children up. There should also be a range of dances taught, as well as step practice. We would not give children the task of playing football or basketball without teaching them some core skills they would need to play. Therefore, why do we partner children off and tell them where to go – usually by walking – and let them get on with the “dance”. There needs to be a shift in the thinking of teachers who teach Scottish Country Dance, before there will be a shift in attitude towards it.

 

 

 

Looking Back, Looking Forward

One learning experience I particularly remember from school was from our topic in Primary 7. Like many in our final year at primary school we studied World War 2, and I remember very little of the worksheets or textbooks we read from about the subject. The activities I remember are the ones where we were actively involved and excited about the learning experiences – an idea I believe would still be true in a classroom today.

2 activities from this topic stand out in my mind, both centred around learning about Anderson Shelters.

Within the class, we created a somewhat lifesize model of an anderson shelter use wire, tarpaulin etc. As much as we could we were allowed to help construct the model, and seeing the finished product allowed us to appreciate the cramped conditions families would be subject to during an air raid. We also transformed a cupboard into what the inside may look like, complete with books and an old style radio. No technology was allowed in there, and in pairs we would each take turns to spend time in the “shelter”. This particularly stands out to me as you were living as people would have lived during that period in history. Getting children consumed in the learning and feeling like they are truly within the era is usually an idea reserved for Early Years classes, as their imagination is still wild and they are more inclined to believe the imaginary context the teacher has set up for them. In the upper stages, this imagination is almost taken out of the classroom, as the pupils are much less inclined to believe in a fairy leaving notes in the class or an alien visiting the school. Using the learning context in a mature way – allowing the pupils to discover the experiences and understand the emotions of someone living in the era/place they are studying – can reignite a love for learning in a creative way, which seems to get abandoned somewhere in the middle years of primary.

The other activity I remember was a homework task we were set to build our own model of an Anderson Shelter. I fairly standard task, I know, however, I remember working on the project with my grandad. I remember putting loads of effort and commitment into the project – using real soil for the garden etc – and I remember the pride I had in showing it off in class. Getting the family involved in the children’s learning, I believe, can be so rewarding and highlights to children the importance of learning and can motivate them to want to do work. However, I do understand the practical implications of tasks such as these. I am extremely lucky to have a hugely supportive family network who value my education very highly, however, some children will not have this luxury. While I would love to see a bigger focus on learning with the family – where I mean fun activities, not taking textbook work home – I understand that this would be dependent on the children in my class, and the knowledge I have of their backgrounds and family situations.

Even from simply analysing these two memorable learning activities from my schooling, I can see how my education and background will influence the teacher I will become. The fact that I remember the more active, involving activities is testimony to the benefits of active learning. Children who are engaged in their learning are more likely to tell parents when they get, and they are more likely to remember these fun activities. The influence of my family in my education and my life in general will also influence how I teach and how I see the role of the family in the classroom. While I understand that family life will vary hugely between children in my class, it is important to try to include them as much as is possible to show the children the intrinsic value of education.

Images from https://www.pinterest.co.uk/debpooll/anderson-shelter/?lp=true

Can’t sleep? Count chicks!

I have chosen to look at the picture book “Six Chicks” by Henrietta 1Branford in terms of the mathematical learning involved in the book.

The book tells the story of Red Hen, who is trying to get her 6 chicks to sleep. Red Hen tries many strategies to get her chicks to sleep, however, only one chick falls asleep at a time.

The book will familiarise children with number words up to 6 in a descending order, allowing them to practice the backwards sequence, which is often overlooked and is trickier for children to master.

While reading the story, the adult should try to get the children to count the chicks on the page – which should always be six – and the amount that are sleeping and awake. This will familiarise the children with numbers that add up to 6. For example, there are 3 chicks awake and 3 chicks sleeping; there are 6 chicks in total, therefore 3+3=6.

The adult could also use numerals alongside the story, as the book does not show the numeral with the number word. Every time the number word is said either point out the numeral to the children to highlight the connection between the two, or have the children point to the numeral if they are familiar with the numeral and number word connection.

I’m a Scientist!

We conducted an experiment to see which material was the most absorbent.

1We decided to change the type of material used (the dependent variable) and keep the amount of liquid used, the type of liquid, the surface and the size of the material the same (the independent variables). We measured the time taken for the liquid to be soaked up by the material.

Using the planning sheets prior to the investigation helps focus in on what you are looking for in your experiment. They also ensured that you had a controlled experiment, as it made sure you only changed one variable. This would be particularly helpful for children to begin the process of planning controlled investigations. 

We predicted that the thinner materials would soak up the water quicker and the thicker materials would soak up the water slower.

Making predictions helps the children concentrate on the outcome of their experiment. When making conclusions at the end of the experiment, what the children have learned will be clearer as they can compare their understanding to this point in the experiment. 

These were our results: 1
Card – 14.03
Tissue paper – 35.28
Paper Towel – 5.19
Toilet roll – 5.44

Results are the most important part of the investigation. The children learn the skill of recording data, how to interpret it and what that means to the investigation. This is where the relationship between maths and science is exemplified as the children are see the real life applications of the data analysis skills that they learn in maths class, using tables and graphs to display their results.

We found that the thickness of the material did not make the difference, as tissue paper is thin and did not absorb well. The important factor was the surface of the materials, as those which had indentations absorbed better. This is because when flattened out, the surface area would be greater, therefore the material could soak up more water.

Conclusions are where you see what the children have learned. In the case of the above experiment, we learned how absorbent materials such as kitchen roll and toilet paper work – due to the indentations, not the thickness of the material.

The planning sheets we used during this input were incredibly helpful in planning the experiment. They would be excellent to use in a classroom to keep the children on track and to give them a framework for investigation planning, which could be slowly removed to allow for independent work.

Do you wanna count the snowmen?

 

When looking at nursery rhymes to promote counting, especially with early years children, there were many that came to mind. I remember singing songs such as “Ten in the Bed” and “5 Little Speckled Frogs” when I was young, however, when researching one for this module, I found the rhyme above particularly useful.

Firstly, as in many of these rhymes, the songs use the number name sequence going from “5 little snowmen…” down to “1 little snowman”. This gets the children practicing the numeral names and can learn about counting backwards, as in school we tend to focus on counting forwards.

Secondly, the song counts the snowmen on the screen. This reinforces the numeral names and their sequence from 1 to 5. It also has the children counting forwards, which means they can practice both in this rhyme.

The third thing I particularly like about this rhyme is that they include a noise for every missing snowman. For example, when you get down to 2 snowmen, there are 3 “shh” noises after it. This leads the children into addition and counting on, as they are learning that there are 2 snowmen there and 3 missing to make the total of 5.

I think this rhyme is particularly good to be used in the early years classroom to promote counting, and could easily be extended beyond 5 when the children improve in their maths ability. The subject could be changed depending on season or even topic, making it a highly versatile resource.

X marks the spot

So now we have come to the end of our maths journey, and I can honestly say that I have88477-mathematics-of-life enjoyed this module very much. It makes you think of maths and everyday life in a different way. I think everyone would agree that maths plays a huge role in life, however, through this module we have seen just the extent of maths in places you would not imagine, and in many extraordinary ways. I have seen the whole class at points in this module confused, astounded and most of all in awe and wonder of the maths we are being shown.

The main text through this module has been Liping Ma’s (2010) book ‘Knowing and Teaching Elementary Mathematics’, which describes 4 main principles in having a Profound Understanding of Fundamental Mathematics: “Basic Ideas, Connectedness, Multiple Perspectives and Longitudinal Coherence” (p122). At the beginning of this module, these principles meant nothing to me, however, now I feel I have a good understanding behind them, and can identify them in real life through the inputs we have had.

Basic Ideas is where even the most complex maths has some simple mathematical principles at the heart of it. For example, the ability to add negative numbers has the basic principle of adding, however, the even simpler principle of a number line and knowing that negative numbers come before 0. While adding negative numbers is a higher order skill coming later in the maths curriculum, the basics of number lines are taught even before a child starts school.

Connectedness is where maths ideas are connected together. For example, being able to multiply, contains the ability to add as multiplying is just repeated adding. Knowing this connection between the two allows children to grasp the underlying principles behind what they are doing which, Ma argues, allows them to have a more solid understanding.

Multiple Perspectives is the ability to see how to solve a problem from different angles. For example, when solving 7+9+13 you could complete the sum in that order, or you could add 7 and 13 first, making the sum easier. Being able to comprehend that problems can be solved different ways allows you to choose the best one, making problems easier.

Longitudinal coherence is looking at the development of skills, described by Ma using the progression of the curriculum. When looking at measuring, children start by learning weights or lengths and what they look/feel like. They can then move on to learning about comparing objects and then converting units. This progression is linear, therefore describing longitudinal coherence.

As a result of this module, I find myself thinking more mathematically about life. At work, eating lunch, even putting up Christmas decorations I find myself considering the mathematical concepts involved. While I would not say that I understand every element of complex mathematics that I have been taught, I would say that the module has taught me things about maths that I had never thought about before, and has made me see life in a new way. A mathematical way.

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary edn). Routledge. Oxon.

Music and maths

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface.”                                                                                                                                          – Du Sautoy 2011

There has been some distinction in school subjects between those creative subjects such as music and art, and subjects which are considered more academic, such as maths and science. However, when we look at the relationship between music and mathematics, there are a substantial amount of links between the two.

Counting plays a huge role in music, especially if playing along with a backing track or other musicians in an ensemble. I personally joined the school orchestra in my sixth year of school asrest a percussionist, and found out these difficulties quickly. However, I believe that this is a prime example of Liping Ma’s “multiple perspectives”. There are large sections of the piece where certain instruments would not play, often written in sheet music as shorthand, such as in the picture right. This would indicate that 2-time-signaturethere are 15 bars rest. If a piece of music has 4 beats in the bar (as indicated by the time signature, see picture left, where the number of beats is the top number), then this would indicate 15×4 beats rest, or 60 beats. A musician has a few option in how to approach this mathematically. They can work out that they are waiting for 60 beats and count these out, however, this becomes difficult if you lose count. The other option is to keep the numbers in their simplest form. I found it easier to count using your fingers, a skill which is often discouraged past early primary mathematics. Counting four beats and then denoting this with one finger, then counting another four beats and denoting this with a second finger was my strategy, which seemed to work well.

Looking back on this with the mathematically thinking I have acquired through this module, I can see many other mathematical qualities in this other than simply counting. The number of beats in the bar denote a base system, as I have discussed in a previous post. As I was counting in fours and then denoting this with a symbol (in this case a finger), I had effectively used a base 4 system in working out the timings, just as farmers denoted a particular amount of sheep with a stone in their pocket or a mark on a post.

There is also an element of pattern and symmetry in music that is often overlooked. There are often repeated patterns or phrases in music, especially in minimalist music, which is made up of repeated phrases built upon one another. An example of this is shown below in the clapping music, where one phrase is repeated with slightly altered timing to create a minimalist piece:

I believe that this would be a good tool to use in a classroom with pupils in order to to reinforce their maths learning. This, I believe, can link with Ma’s principle of “Longitudinal Coherence”, which looks into how ideas and topics are developed. In using music to teach children about pattern and sequence, you show them how these skills can be applied, therefore giving the topic a relevance, which is extremely important for young children. This would be an interesting lesson in to try in future.

References

Du Sautoy, M. (2011). ‘Listen by numbers: music and mathsGuardian. Available at: https://www.theguardian.com/music/2011/jun/27/music-mathematics-fibonacci (Accessed: 25 November 2015)

12 is now 10

confused

Image from https://www.dietdoctor.com/why-calorie-counters-are-confused

From the title, it would be understandable for you to think I had gone mad. In fact, quite the opposite. I had a wonderful lesson today exploring the joys of number systems and place value.  Although at first it was not as clear, it was exciting watching the numbers evolve and make sense in front of my very eyes.

The first thing that struck me about the lesson was looking at a counting system used by shepherds when counting their sheep in medieval times:

This system uses a base 20 system, where when the shepherd counted 20 sheep, they would img_20161017_221632put a stone in their pocket to signify 20. They would then start again until they again reached 20 (40 total) and another stone in the pocket, and so on.

You can see a degree of repetition in this system with 11 (Yan-a-dik) literally standing for one and ten. However, what perplexes me is why they have tags for numbers 6 through 9, as in their system they do not seem to be used again. They have no need to have numbers beyond twenty, as after this they begin again, so why not make 6 “Yan-a-pimp”? This seems, to me, a flaw in their system, which otherwise seems to be a sensible system for them.

As I had previously read about this system before the lesson, seeing it come up automatically hooked me. This I can relate back to the classroom, as if children, like I did, recognise what they are being taught, they will associate with it much better, and I believe will be more likely to take the information on board. I think this links to Liping Ma’s idea of ‘interconnectedness’ (p122) (Ma 2010) as relating new learning to what the children already know is likely to engage them and make them eager to learn.

mz2gtsdhMy excitement grew when we were then told that “Yan Tan Tethera” was the name of a Scottish Country Dance and the crib (instructions) was put on the screen, almost like a foreign language to everyone else, but looked so familiar to me. It gave me a sense of homely warmth, that I can only imagine children feel when they recognise what is on the screen in front of them. This again links back to the idea that children are more likely to be engaged in the learning if they can relate to it. For example, talking about farming to children in the inner city will not resonate with them. I am hoping to try this dance out in my dancing group and will update my blog with it soon.

 

To us using base 10, or decimal, the idea of any other base system seems alien to us. The most file0002120440786common base system to us, apart from base 10, is binary. Binary is a base 2 system used by computers consisting of only two digits – either a 0 or a 1. Having done Standard Grade Computing, I am fairly familiar with how binary works and how you can make any number using this system. The way I know how to use binary is using a place value system, doubling the numbers each time. This is because in base 10 system you have place values of ones, tens, hundreds etc, where the columns are 10x as much. Because it is only a base two system, the numbers only double each time. There are some examples of binary below:

16+4 = 20binary

32+16+4+2+1 = 55

64+4+1 = 69

By adding up all of the numbers with a one in that column, you can work out what number the binary represents.

chars_img

Image from http://gorpub.freeshell.org/dozenal/newdigs.html

With this idea in mind, it makes looking at other base systems much easier. For example, we then looked at base 12 systems, which is thought by many to be a more appropriate base system than base 10. Base 12 includes 2 extra single digits to replace what we know as ten and eleven (respectively shown in the picture left). These extra numerals are needed as the numeral “10” uses two columns. In the base 12 system there is a “12” column rather than a “10” column.  The video below explains this very well, however, instead of these digits above, she is using T and E to represent ten and eleven.

dozenal

As you can see above, decimal columns are multiplied by 10 each time, and binary numbers are multiplied by 2. This then translates to dozenal numbers  being multiplied by 12 each time, as you can see here.

There are some who have suggested that a base 12 system would make more sense, especially in terms of looking at fractions like 1/3 and 1/4, which are not as neat in decimal. This moves on to the fact that 12 is divisible by more numbers than 10 (1,2,3,4,6,12 rather than 1,2,5,10). 12 is a fairly common number in terms of maths, looking at time especially.

pitman80

Image from http://dozenal.ae-web.ca/clock/diurnal_2

Note: these clocks are commercially available.

In conclusion, this is a confusing topic to get your head around, which is exactly what some children may feel when faced with what is difficult to them. It is important that we give children the chance to play with and explore the numbers, as we were given the chance to do, which really helped me understand the topic. Children should, in my opinion, be supported, but should be encouraged to be explorers in order for them to feel the sheer joy of what maths truly is.

 

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary edn). Routledge. Oxon.

What even is 6?!

Years ago, there were no numerals. No names to define amounts. This is because it simply wasn’t necessary until people began forming villages and such where numbers and numerals were needed as a means of comparison for trading. This in itself is difficult for us to imagine, growing up counting in an Arabic (sometimes known as Hindu Arabic or European) number system, with numerals 1, 2, 3, 4 etc. I should point out that there is a distinct difference between numerals and numbers.

Numerals – symbols we use to denote an amount i.e. when we use “6” , that is a numeral

Numbers – a quantity or measure of amount

Breaking this down further, there are digits. Digits are like the letters of maths – the single digits that make up a numeral. Maths is Fun shows this perfectly (link at bottom of blog):

capture

Numerals are what we use to talk or write about amounts, whereas numbers are the idea that exists in our heads about quantity.

Our Arabic number system developed in India, as the video below shows:

Most languages today use these numerals, however, this was not always the case. The first number system was the Babylonian system in Mesopotamia, using not a base 10 system, but a base 60 system (however, there are elements of base 10 as the system uses the symbols in a tens and units format). Many early numerals are more like symbols to us, just as our numerals would be to the Babylonians – it is simply a case of what you know and what you are familiar with.

Even Roman Numerals, which we are more familiar with, are letter/symbol based. There are two theories about the origins of Roman Numerals (link at bottom). The first is based on hand gestures, just as children count on their fingers now (10 fingers = our base 10 system).

For example, 5 = V. The hand gesture is this (similar to a V): win_20161003_16_07_23_pro

win_20161003_16_07_28_pro

 

10 = X. The hand gesture is this (a cross with the thumbs or hands):

The second theory is based on tally marks on tally sticks – a system used long before the Romans, especially by shepherds counting their sheep.numbers1

This same site also alludes to earlier number systems such as the Egyptian system. This is similar in ways, with a single line representing “one” however, they used lines for all digits up to “nine”, and pictures beyond these. An example of larger numbers is shown below (both pictures from Discovering Egypt website).

 

numexam21

It is clear that there are many other number systems other than our own that have been used throughout history, and even today in Chinese and Japanese languages. I personally have found these fascinating to 14585279_1215438281830924_533875691_nlook at and I believe children would find this interesting too, looking at the unknown and how it relates to the obvious that we see and use every day. This study into different number systems all looks towards Liping Ma’s relational understanding. I would not teach these systems while children are still learning their first numerals (1, 2, 3 etc) but it would be an interesting activity with older children, showing them why we have the numerals we do, and where they came from. The activity we did this morning, creating our own number system (see my attempt on the right) was a thought provoking one. You grow up only knowing the Arabic numerals, that creating foreign ones is strange and alien. I think children would learn a lot from this type of activity, not just about number systems, but about how numbers are formed, written and constructed. Like I say, this is not an activity for early years children beginning their maths journey, but for children who are comfortable with the numbers they know and can be stretched further.

References:

Pierce, R.  (2015) ‘Numbers, Numerals and Digits‘. Math Is Fun. Available at: http://www.mathsisfun.com/numbers/numbers-numerals-digits.html (Accessed 3/10/16)

Roman Numerals and Roman Numbers (no date) Available at: http://www.knowtheromans.co.uk/Categories/SubCatagories/RomanNumerals/#VIII (Accessed 3/10/16)