Patterns: The building blocks for mathematical thinking

Recent early childhood research has found that the ability to make and understand patterns is a critical skill for future mathematical understandings. Studies have found that an understanding of patterning can lead to the development of analogical reasoning and the ability to identify, extend, and generalise patterns is important to inductive reasoning. The studies have found that a child can learn these skills at a very young age.

Papic and Mulligan (2007) found that teaching the "unit of repeat" is the key concept. The unit of repeat is the element that constantly reoccurs. For example, in a pattern that goes: Blue, Yellow, Blue, Yellow, Blue Yellow. The unit of repeat is "Blue, Yellow". If the pattern was changed to : Blue, Yellow, Red, Blue, Yellow, Red. The unit of repeat would be blue, yellow, red. It can also be any other representation e.g. square, circle; rectangle, circle, triangle.

Joanne Mulligan when she lectured us about the findings was so particular about the finding to the point that if the unit of repeat was not completed e.g. red, blue, red, blue, red. We should not label it a pattern at all as it doesn't demonstrate a understanding of the unit of repeat. However, the child can be scaffolded and asked "what needs to be done to finish the pattern?" and if they are able to suggest the addition of "blue" then they are on the way to understanding mathematical patterning. A sound understanding of the "unit of repeat" concept was the key to future mathematical development.

Those of you who are familiar with mathematics will see that this "unit of repeat" concept is identical to the algebra concepts. E.g. a+cd. This is why the study also recommended a focus on the 'structural features' of the pattern rather than the colours - as a focus on the colours of led to a over simplification of the pattern that was occurring.

Overall, the study has opened a new direction in mathematical practices and understanding in the early years. So when you next look at a child's building or construction ask yourself:

•  Is there are unit of repeat happening here?
• How can I draw attention to it?
• What scaffolding do I need to provide to build on this child's understanding?
• How can I discuss the concept but in a different way? e.g. drawing it, building it etc
• How can I model (or demonstrate) the unit of repeat in everyday practice? For example, setting the table has a unit of repeat, everyone has a pair of shoes and so on.

What are your thoughts??

Maths Links: Early mathematical thinking

Thank you for all your feedback and positive comments about yesterday's post. Hopefully I can live up to everyone's expectations now :)

I think off the top of my head the winner was documentation as a place to start which I will try and do a post about over the next few days. If you are keen to look at template/ ideas Carly over at Early Childhood Resources did a post today about observations, the format she recommended is similar to one of the tools I use (probably the influence of the same uni at very similar times).

But as today is Monday it's time for Joyful Learner's maths links... Head over and check it out for some great maths ideas www.joyfullearner.blogspot.com

The main thing I wanted to share with you was some quick places that will quickly get you up to speed on the latest maths research if you haven't studied recently.

One of the best places to start is the Australian Association of Mathematics Teachers position statement on early childhood maths which you can find here: http://www.aamt.edu.au/content/download/721/19509/file/earlymaths_a3.pdf

A article about common misconceptions about maths education in the early years: http://www.earlychildhoodaustralia.org.au/australian_journal_of_early_childhood/ajec_index_abstracts/early_childhood_teachers_misconceptions_about_mathematics_education_for_young_children_in_the_united_states.html

Dr Jenni Way highly recommends the following book for excellent practical and up to date advice on applying maths in the early years:
Dr Kate Tucker,2010, Mathematics Through Play in the Early years (2nd ed.) Sage books. This is the book depository link for you: http://www.bookdepository.co.uk/book/9781848608849/Mathematics-Through-Play-in-the-Early-Years.
To paraphrase Jenni "I have been waiting for years to find one I could recommend and this one is it". It's only $33 and free worldwide delivery! And tax deductible if you work in the industry. Have just ordered it myself.

So there's some reading to whet your appetite... Next Monday I will write about the vital importance of developing patterning skills in the early years.


Posted by Wendy

"we are the change we have been waiting for" - Barack Obama

A post about upcoming posts

Yesterday, I had the privilege of attending a Sydney University conference about the Early Years Learning Framework and the National Quality standards.

As a result, I have lots of excellent material that I plan on sharing with you over the next few weeks/months.

A broad summary of what I intend to write about for you...
- documentation within the context of the eylf so portfolios, observations, assessment and daily diaries
- ensuring that families are integrated into your practice
- language and literacy in the early years
- using popular characters e.g. Superheroes, barbie and Thomas in your practice - what the research is saying
- maths in the early years. This particular presentation was so fantastic I have enough for the whole year
- working together as a team to achieve the eylf outcomes
- how to use the reflect respect relate document
- how to demonstrate continuous quality improvement ( for this, I will also draw on my previous experience in hr)
- more about advocacy

Posted by Wendy

"we are the change we have been waiting for" - Barack Obama

Maths Links: Integrating the concept of time into the curriculum

This is part of Joyful Learner's Math Links... come over and check it out at http://www.joyfullearner.blogspot.com/

A critical maths skill that all children need to learn is the ability to read a clock and both types of clocks, not just a digital clock.

Many people argue that telling the time is too complicated a skill for young children but I know many 2 year olds (and even some babies) who are able to understand the basics. The main skill is an understanding of the numbers and the idea that they represent a concept (time). Most children have been exposed to time as a concept from a very young age - for example, being asked to wait for something.

Like many complicated concepts, such as reading and writing, it is all about modelling and demonstrating how the skill is used in every day life.

For example, for many children I like to introduce the concept of  time (and a clock) when they are arguing over a toy. For example, Joe can have the toy til the big hand gets on the 2. For a very popular toy this can even involve the making of a waiting list then writing the numbers and drawing what the hands will look like.

It is also useful for when morning tea, lunch and afternoon tea are coming as well as when their families will be here. It can also be used in a pictorial communication system to enable children to plan their day.


I also like to supplement this with clock puzzles that show times etc. At the expense of coming across as a Melissa and Doug Sales repersentative (I promise I'm not) this clock is incredible and suitable for all ages.

What do you do to help your children understand the concept of time?

Maths links- the joy of an abacus

This is part of Joyful Learner's Maths Links come over and have a look www.joyfulllearner.blogspot.com

I have recently had the good fortune to acquire a beautiful Melissa and Doug wooden abacus.

When I studied maths at university there was a lot of talk about buying hundreds boards for the children - which seem to be ridiculously expensive for what they are - and subsequently it was on my wish list of things for my new centre.


But having watched the children play with this abacus, I think a quality beautiful abacus achieves the same ten by ten purpose but in a much more open ended beautiful way.

I have observed all of the ages in my centre from two year olds to just under six relish the counting and maths play that this abacus provides - ranging from simple moving of the pieces to counting all the way to 100 while moving the pieces (one to one correspondence at it's best)

If you don't have a abacus... I personally recommend one very highly and if you don't want to buy one you can simply make one via threading ten sets of ten... Even more maths plus fine motor!

Lemonade Making

One of the most exciting play moments that has happened to me this year has been the making of lemonade with the children.

We made the lemonade because we were all outside playing in the sandpit making pretend drinks (including lemonade) and I suggested why don't we make it for real!  Starting a month long love affair with lemonade (that is still continuing for some of the children).

I found a no cook lemonade recipe online (from american profile) brought in the ingredients and went from there.

First, we wrote the recipe out on the white board. I started and then the children wrote a line each (these were mostly the older children) 

We then all worked together. First, the children were given a lemon and we talked about how we were going to get the juice out - lots of suggestions!

Then I cut the lemons up and gave each child a half. I asked them to not taste the lemon until they had juiced their half (some couldnt resist so luckily we had spares).

The children juiced their half each and added it to the large measuring jug.

Then when that was done we moved onto the sugar. Each child added a spoon each.

Then we all had a turn stirring (counting to ten as we went). Then we added the water and then we drunk it!!

It was very exciting and surprisingly delicious.

The children and I proceeded to make lemonade over and over with same and different children over the next few weeks. At one stage we even added limes to the recipe (I had some at home which were looking a bit worse for wear).

I supported this learning experience by a poster talking and showing about the process including the recipe which you can see below and pictures of each step. I placed lemons, the juicer and the measuring cups on this seat (didnt have a spare table). Here the children are pretending they are at a lemonade stand.

I also provided opportunity for further exploration through dramatic play.--providing the materials with wooden fruit. Below this child is making lemonade.

And he is sharing it with his friend. You can just see in the blue cup is just wooden lemon

Here is a different day and different children also exploring making the lemonade in dramatic play.

The children got so good at making the lemonade I didn't even have to tell them what to do - just give them the materials!!

Come over and play at the Childhood 101 "We Play" link-up.