Friday, 31 October 2014

Mathematically rich language: Shape space and measure.

Basic language:
"Which number is bigger?"

3 7
Whats the answer? Do you have enough information? Does it make sense?

'Bigger?' Bigger than what?
Do I mean larger or greater, or do I mean of more value? 

We ask questions like this every day, using language which makes sense to use because we can infer meaning from context. Adults also make links between certain words as we understand they have similar meaning e.g. longer, bigger, fuller.  But to children, especially those with EAL and those who are just beginning to learn mathematical language, it can be confusing.

Lets try another example:

Take this as a beaker of water in the water provision. (I know what you're thinking, you're wasted, you should be an artist!)

"its full" says the teacher. I suppose in a way it is. Just like a cup is full of tea or coffee or a shop bought bottle of water is full.

Of course, its not actually full. Full would be when a container is filled to capacity. 

The problem lies in the language we use in every day scenarios and how we relate these to our practice in the classroom.

In mathematics we need to be conscious of the language we are using when we are introducing new concepts. Settings should plan for the specific vocabulary to introduce to children in this situations:

Example 1:

We are working with children in the construction area. One little boy brings a cylindrical brick to me and I tell him "big." He brings another cylindrical brick which is smaller than the first and I tell him "small." Finally he brings me a longer cuboid brick. This brick is longer but thinner than the largest of the two cylindrical bricks so I say, "longer."

Firstly the term big and small are subjective and depend on comparatives in order to be true.
Instead I could have said "round" or simply, "brick."
The second brick is where I could begin to introduce comparative language such as "bigger" "smaller" "longer" "shorter" because I could use the initial brick to compare against.

Secondly by comparing the cylindrical bricks and the 3 brick I was having to focus on the length because it was thinner. I also couldn't use 'bigger' because bigger refers to volume (3d) where as longer and thinner refer to area (2d). Volume in this case would have been too complex. 

Example 2:

Whilst working in the sand tray outside a little girl brings me a big bucket she has found. "Empty" I say to her. She gets a space and empties a space load of sand into the bucket. "Empty" she says.  "Not empty," I say. 

I could say 1/10th full - but in the Early Years that means nothing to a child since complex fractions are not part of their world yet.  Instead I said 'not empty' because the term empty refers to when the bucket is devoid of mass which it not isn't. 

Examples of subjective and finite terms - they cannot usually be more or less of any of these terms (think superlative)

Empty, Full, biggest, longest, shortest, smallest, heaviest, lightest, furthest away, closest, nearest etc.

e.g. if a box is the biggest, it remains the biggest until another, bigger one, is found. The second box does not become the "more biggest." 

Comparative terms: - terms used to compare one object to another.

longer, shorter, bigger, smaller, half full, half empty, quarter full, three quarters full, heavier, lighter, closer, further away/more distant, more, less. etc.

Extending basic language:

As adults we make links between terms, understanding them to 'mean' the same thing as another, e.g. bigger and of most value, longest and tallest.  We shouldn't necessarily use this language but it shows that we understand that they show commonality and we can usually understand each other.  We sometimes use language such as 'bigger' synonymously with other size related language.
Once children have a firm understanding of basic language you can begin to get them to think about how these terms relate to one another. This gives them a better understanding of this language, understanding of questioning but also the value of the word. 

We develop this understanding by repeating examples of correct vocabulary in play and encouraging children to use these themselves. In other areas of provision adults should model the correct language but draw in links with similar experiences:

Example 1:

Little girl L is playing in the sand area. She built a castle. "Big," she said. "It is big, its tall," I said. Little girl L repeats, "tall".  Later L is playing in the construction area and she makes a road. "Big," she said. "Yes L it is big, its long," I said back.

Whilst F had an understanding of the word big, she needed further examples of vocabulary to use. These examples are more accurate but we both understood when she used 'big.'

Below are examples of words which are generally synonymous with one another:

Children begin to understand that these terms link in terms of understanding about shape space and measure. 

Language should be displayed prominently within your setting for both children and adults.  When labelling items in areas (especially maths) considering using some of this synonymous language to develop understanding of other terms.

Here in our maths area we have 3 different buzz light years. We used 'big, medium and small.'  We chose this because big and small were absolute (there were no other buzz light years in the setting and we were comparing them only). Around these terms we placed other vocabulary related to these terms. Equally we placed 'in between' and 'middle' around medium.

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