Mathematics in songs and rhymes
Singing with very young children is a wonderful opportunity to enjoy repetitive and harmonious sounds which immerse us in a story. Adding actions and gestures can enhance children's listening skills, and deepen their understanding of the music and lyrics.
Singing songs and rhymes can also be a unique opportunity to provide a connection between the mathematical language and concepts that are sometimes embedded in such texts. The basis of songs and rhymes for young children is repetition of words, lines and stanzas, opportunities to enjoy repeating patterns. Further still, are opportunities for us to put on our mathematical lenses and look more deeply at these cultural texts. Let's start by enjoying the well known nursery rhyme, Five Little Ducks.
Enjoy listening to
Five Little Ducks
sung by Amber
Playschool
Australian Broadcast Commission (ABC)
Can you see and hear the mathematics?
We love the way Amber sings this popular nursery rhyme. She is having fun, connecting with us, and demonstrating the story as she sings. If we put our mathematical lenses on and watch the video again, we also notice the alignment Amber makes with some very important mathematical concepts of patterns, position, and length, and the principles of counting. Immersed in all of these are the precursor concepts of attributes, comparison, change and pattern. The age of the children you sing this with and to may suggest emphasis on the precursor concepts rather than the more formal ones.
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Amber inducts us into the song by telling us she is on a farm, and asking, "Have you ever been on a farm? Maybe you have seen 5 little ducks". This kind of field building orientates the children to the context, promoting connections with their everyday experiences .
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Amber introduces us to the ducks - all on one hand, each as one of her fingers and begins the song:
Five Little Ducks went out one day, Over the hills and far away, Mother duck said Quack Quack Quack Quack, but only four little ducks came back...
This kind of representation - showing 5 fingers and saying it is 5 - connects with childrens' natural ability to subitise, or immediately recognise a quantity without counting.
As the song proceeds and the number of ducks decreases by one each time, Amber aligns this decrease with 1 less finger (or duck!). This 1-less pattern (5, 4, 3, 2, 1, 0) continues until there are no ducks left to come home. This decreasing pattern sets up an interesting opportunity to ask children, "how many do you think will come back this time?". It also demonstrates the important counting principle of stable order which says counting numbers have one correct order. We can attend to this order by counting forwards - 0, 1, 2, 3, 4, 5 - or by counting backwards like Amber has in the song - 5, 4, 3, 2, 1, 0.
What isn't made very obvious but could be with an addition to Amber's approach, is the counting principle of one-to-one correspondence where we pair off each object with a different numbered word, making sure the count and the quantity align. In this situation this could be counting the ducks (your fingers) from the first 5 - "let's count these ducks: 1, 2, 3, 4, 5" then perhaps doing the same when there are only 4 - just to check! Doing this would also invite children into the principle of cardinality where the last counting word said is the number in the group - we counted up to 5 so there are five ducks.
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When Amber gets to 3 ducks, she wonders "where are those other two ducks?". In this moment she is introducing the concept of parts that make up a whole. For example, 5 is made up of 3 and 2 because 3 ducks came back and the other 2 are still over the hill and far away. Amber continues this wondering (and worrying) when only 2 ducks come back: "where are those other 3 ducks?", connecting the next part-whole relationship for 5, i.e 2 and 3 make 5.
One of our observant pre-service teachers thought that Amber also demonstrated the principle of conservation/order irrelevance​, where the number in the group is the same despite its formation​, when she brings back 2 ducks but they are not the same ones as the ducks that left - she has changed fingers but is still representing 2!
This could be an interesting talking point at some stage. ​​
Positional Language and gesture
Five Little Ducks went out one day, Over the hills and far away,
The oportunity to align the positional language of "over the hill" and the extra concept of distance (length) is also taken in this version of the song. The suggestion here is that something "far away" is a long way away as the ducks can no longer be seen.
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Amber deliberately uses the green hill prop to demonstrate the concept of "over" as she sings the line and moves her hand up and then down on the other side. ​
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Intentional Singing
Five Little Ducks may seem obvious in its connection with mathematics - there are five ducks! We may choose this song because it tells a lovely story and is fun to sing. Choosing it also provides us with the opportunity to be intentional in drawing out many mathematical concepts and principles. Like Amber, we can do this by using simple resources and making the most of embodied learning (gesture and movement) to assist in this. Making sure that we are aiming for precision is also important here - we need to make sure that the mathematics we draw attention to is correctly supported by our gestures and prompts. What comes to mind in particular here is the singing of Twinkle Twinkle Little Star where we gesture a shape with our fingers when we sing the line: Like a diamond in the sky. The shape people often make is a kite or a rhombus - this is the correct name for the shape, not a diamond - this is not a name of a mathematical shape. Be careful about that one! Funnily enough the Like a diamond in the sky is about the twinkling they do in the previous line, not about their shape. Sing it and see!
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Overall we think it is fascinating to look closely at songs and rhymes with a mathematical lens and invite children into this world while they sing along.
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