Wednesday, 28 February 2018

Our Journey Begins

My 2018 Inquiry about the role of language in mathematics began with using a maths wall and associated discussions to encourage children to acquire language and participate in such sessions.

My hunch is that by using words frequently in a familiar setting the children will begin to view it as "normalised" and transfer this language to their everyday conversations.  For example in maths we are precise in describing shapes.  A shape is not just "that one" with a vague wave of the hand but "the large yellow rectangle".  This language needs to be taught so that they can understand, read and interpret mathematical terms.

I am hoping to make the children "word smart" as well as "number smart" and confident to explore a simple problem that may arise from a real life situation or a structured activity.  They are expected to work in small groups or pairs with everyone contributing in some way.  They can use trial and error or a mathematical method of solving the problem.  They need to encourage others by listening and responding positively even if they feel the answer may not be correct.  In reporting back to the larger group all answers are accepted and discussed to see what might be the best explanation.

I purposely grouped 6 children into 3 pairs for our first try of DMic maths as I thought it would be easier to have a smaller group to see how these groups worked in pairs and to be able to hear all discussions. 

We have used the maths wall since day 2 of this term so the children are already familiar with different forms of numerals (numerals, dot patterns, finger patterns, groups of objects) and how to justify some shapes.  I used the subitized patterns to introduce a simple problem of how many dots do you see and how do you know.

To begin with the children simply counted one to one with each one confirming that there were 8 dots when sharing, although they counted the dots in a different order.  This is the lowest strategy of simple counting.  I referred back to our maths wall discussion when we had 5 dots and someone recognised it was 4 dots on the outside and one in the middle and asked them to look again at the dots.

One child quickly saw a group of three dots and I watched him put a pencil down the line to show his buddy where it was.  At this point, interest by two members of a group waned and they drifted off but the remaining members were keen to try and find groups.  Trying to describe the groups to their partner, visualise what numbers they were using and hold this information proved difficult so I provided different coloured counters to help them map out their numbers as they were talking about.  This made it easier to describe the groups.

Notation was difficult because they didn't understand how to write it down or that they needed to add the groups together.  We came together to discuss what did they think they needed to do to move from the single groups they had found, to finding the answer of how many dots there were altogether on the page.  The word "altogether" suddenly became important and they remembered a problem we had done about adding up our swimmers and non swimmers earlier in the day when "altogether" meant we added the two groups to find out if we had counted everyone.

One group then went away and found that

4 + 3 = 7

and 7 + 1 = 8

The other group found

2 + 2 = 4

take this 4 and add another group  4 + 3 = 7

then take 7 and do 7 + 1 = 8

The two groups looked and said it was the "same end number"
but group one had a "little" way of doing it (ie it had fewer steps in it.)  They had difficulty trying to explain what they meant but they were able to point to their workings and said how many sums they each had.

I plan to give the groups the same pattern next week to see if they can come up with any further ways of recording this pattern.

Points to ponder: difficulty of notation, making sure children are aware of "maths terminology" so that they know what is required of the problem, keeping interest up and making sure children are paired correctly, discussions - too teacher directed?

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