'I want to do really hard work - in a book!' shouted Jane.

The truth was Jane and her partner had just discovered Venn Diagrams for themselves - at seven.  

In a relaxed and productive Maths session she and John had worked, chatting away - we call it Work Chat and you are allowed as much of it as you need - while sorting through some number cards from 0 to 100.  

The Maths session got off to a great start when I produced the equipment for each pair:

• 2 hoola hoops (borrowed from the gym)
• number cards 1 -100
• work cards ( you can view mine here.)

The work cards aimed to consolidate the children's number sense and to provide challenges for those ready to move on. 

Easy tasks included sorting the cards into odd and even numbers. One child was in charge of one hoop - for the odd numbers, the other for the hoop - for the  even numbers, so each had a designated task.   I chatted with the pairs at work and together we wondered who would have the most cards and how many each might have.  When the task was completed the children were asked to find any number patterns - which they duly did.  When they finished I sent them to look at the large 100 Square hanging on the classroom wall and to see how they could relate what they had just done to a different visual format.

Success!

Many curriculum objectives had been fulfilled including:

• Estimation
• Number
• Pattern
• Sorting and Categorising

John and Jane - both  bright children - worked happily on sorting the cards into those greater than 20 and those less than 20.  We discussed who would have the most cards, they wondered where 20 would go as it was neither more or less than itself.  They told me the only way to work it out was to get on with the task.

Minutes later and with every card but one laid out in the hoops  before them they puzzled over 20 which Jane held in her hand.  I hovered, waiting to scaffold an answer is necessary.

More or less together they decided in a Eureka! moment to lay it between the two hoops.  

But in the physical act of doing so, it occurred to Jane to do this instead:

Another curriculum objective ticked:  

• Higher Order Thinking

Jane and John were utterly thrilled to discover this and their enthusiasm and example inspired all the others working at similar tasks.  Soon the floor was littered with Venn Diagrams!   Jane declared she had seen it before somewhere.  They went on last week to discover the relationships between counting in 5s and 10s and consolidating their grasp of   

• times tables

This week they will look at patterns while counting in 3s and 6s, then 6s and 9s.  I would like them to come up with this while looking at counting in 3s: (each column adds to 3, 6 or 9)

 3              6           9

12            15         18

21            24         27

30            33         36

More complicated in one sense, yet easier as it is entirely visual is the pattern which can emerge while counting in 6s: 

 0          6          12          18         24

30        36         42          48         54

                                                      60        66

While counting in 9s is simplicity itself - each number in the pattern adds to 9!

But I'm waiting to see.  Maybe they will have other ideas, perhaps I will have to scaffold a bit or we can share ideas.  I know both John and Jane and many others in the class are capable of grasping it.  But you see they a little stuck on this notion that hard work comes in a book.  

Parents, educators, society in general has long subscribed to the notion that children, sitting at a desk in communal silence, scratching away on a book with a well chewed pencil while a deep frown takes root on their little faces is a sign of hard work.  And only with that type of hard work will success come. 

Nah!  It comes with hoola hoops!

Annette Black

                 

Seven Year Olds, Maths and Higher Order Thinking - Mutually Exclusive?

Of course, the answer is 'No!'

But with a proviso - or two.

At seven, John or Jane has school comfortably sussed, knows what is expected of him or her and with indulgent encouragement from teachers and parents dishes it up in various measures.  

When it comes to Maths, there can be hiccoughs along the way, a groan or two when the Maths' books are called for - but  hey, there are only four things you really need to know how to do - add, subtract, multiply and divide.  You can even make that two, once you see the relationship between adding and subtraction, multiplication and division.  

So how hard can Maths be?

And then comes higher order thinking.

It begins with word problems.  Unsuspecting seven year olds can easily polish off the first few:

Seven birds were perched in a tree.  Three more came along.  How many were there altogether in the tree?

You can scaffold the process - colourful, interactive flipcharts, sticky dickie birds for everyone's little fingers and amusing role plays.

Gradually though, a little more oiling of Poirot's little grey cells is called for:

?     ?     ?     ?     ?

John  is eight.  Jane is seven years older.  How old is Jane? 

You use the word detective strategy.  What are the key words?  Which key words prompt you to add or subtract?

Some instinctively get it. Some Johns and Janes get it with a little help.  For others - a sizeable portion - it will be blood, sweat and tears throughout the most important and formative period of their life.  

And they still won't get it. 

?   =    :-(  

Wise and experienced teachers scratch their heads.  Staff room discussions are many. New ideas are pounced upon, quickly and expertly acted upon but soon after everyone is scratching heads again. 

Just like me.

Truly objectively looking at the problem while wearing my mathematicians hat, examining all the data carefully and using my own higher order thinking skills this answer was formulating itself:

Higher order thinking cannot be taught.  It is an innate skill.  You have it or you don't.

Gradually, though this paradox unwound and I realised:

Higher order thinking cannot be taught.  It must be discovered.  By everyone, for themselves. 

For two years now in my classroom Maths has been a voyage of discovery.  A busy, noisy, action packed time of the day in which old fashioned counters, technology and text books are used in equal measure and  to which everyone looks forward.

And I'd like to share it, so that it can be further tried and tested.

And changed.

Next Week's Post: 

Jane seeks a lifebuoy!

Jane Grapples with Self Reliance and Discovery

'I want to do really hard work,' shouted Jane,  'in a book'.