Monday, 26 March 2018

Practise, Practise.

I had an opportunity to teach a Dmic lesson in front of a peer.  I discussed with my peer how my previous lesson had gone, my reflections and what I wanted to focus on with this lesson.  Using the second group of children, I explained to the children that they were grouped in pairs and they would need to talk to each other and we practised talking and listening.

In launching the problem I introduced the term "equal" and made sure the children understood the problem.  Then it was down to the business of solving the problem in the pairs. 
Discussions went well and solutions suggested. 
One child went and got scissors and cut his "pretend" pie to show his partner that it was the same.
Another child drew a line to make two triangles - were they the same?  During group sharing, discussions sometimes broke down in the children's eagerness to share their solutions.

It was great to be able to share the experience with a colleague and discuss how things went and how could one could keep the focus and momentum going.  My colleague then taught the Dmic lesson she had done earlier in the week to a group of my children.  It was exciting to see what the children knew.  Too often we are busy listening to one or two children who are more vocal and it does not give the quiet children a chance to show what they are capable of.

In the maths warm up the children counted on from various numbers.  Then she launched the problem which she tied into their recent experience of swimming when we would count how many children were going swimming.  The problem was, "If there were 8 boys and 5 girls how many children went swimming altogether?"

The children used different coloured counters to represent the boys and girls helping each other to count.  The children who found counting difficult were supported by the other member of the pair.
Only one pair managed to count out the two groups and combine them so they were able to share what they had found.
Checking each others counting.
One child holding another child's hand to make sure they counted correctly.

My reservations about how were the children going to learn strategies to solve problems when they had limited number knowledge have been proved by the children to be unfounded.  When a child re voices his ideas it is helping him to clarify them.  It is helpful for the children to hear another child use "non technical" language or to hear a solution re voiced in a different way.  They were prepared to help each other and they enjoyed doing so.

The experience was a great way to get feed back on my lesson and to observe another teacher working with children in my class.  I was able to reflect on my own practise and think of ways of helping the children to work, talk and listen more co operatively.  Seeing and hearing the children is all very well but I have yet to solve the problem of how can I record any data to prove that there is progress?  






Saturday, 24 March 2018

Focusing on Dmic Ideas

After seeing how the children engaged in the general discussions in our previous trial Dmic lessons, my focus was to see how I could get the children to use more of the Dmic method of listening and speaking or sharing of ideas at the "pairs" level.

We discussed how to work as a group by listening and looking at the speaker, by thinking about what they had said and then agreeing or asking a further question if they needed to know more information.  The children practised how to phrase questions and what to say when they agreed with what their partner said.  They also practised re voicing.  These are all necessary skills for group work.

Hooking the children into the problem went well.  A child had brought a pie to school the previous week but couldn't eat it all.  We talked about how they enjoyed pies but one pie was too much for them to eat.  How could they fairly share a square pie with a friend?  We unpacked the problem, discussing the terms so that everyone understood what was required of them.   During this discussion we again practised re voicing and listening.

The children needed encouragement to work in a small group without a teacher guiding them.  It is quite a different way of learning for them (and for the teacher!).  They needed reassurance that it was expected that they talk to their partner and that they needed to ask - "What do you think?" , "How do you think we could do this?" to gain information.

Two of the groups were more successful at the pair level talking between themselves and coming to an agreed answer.  The other two groups found it difficult to focus but reminders that they needed to ask their partner kept them working.  Group sharing went well.

On reflection I will need to think carefully about groups, perhaps have a smaller number of groups so that I can hear their thoughts more easily and keep those focused that need reminders.

I had hoped the children might have seen they could use a similar method of folding or cutting their pretend pie to demonstrate the "equal share" that was used in previous solutions to the pizza problems. 

Having a mentor to talk through the lesson and problem solve as issues arose was invaluable and encouraging.

Friday, 23 March 2018

Dmic Challenges




The last lesson I tried using the Dmic method had limited success in engaging a group of children and getting them to discuss their findings.  I noted the difficulty that the children had in notation so I decided to try a session without notation.  We have done iPad work using shapes and also on our maths wall we have shapes.  We discuss their qualities, how to describe them precisely, how we could group them and why.

I put the children into groups of two or three.  The problem was to divide a pizza up between two friends.  We first discussed the terms divide and fairly.  The children came up with the fact that it needed to be cut up so that they each got a piece and fairly meant that the two friends got the same amount of pizza or that it was equal.  I gave each group a picture of a pizza asking them to show me how they would share it fairly between the two friends.

The children first just looked at the picture vaguely saying you need to cut it here with a wave of their hand.  They kept discussing where to cut until one child went and got the scissors and actually cut out the pizza.  He then cut it in half.  This meant there was a scurry to cut the pizza as the others saw what he was doing.

We came together to discuss what he had done - yes he had divided it into two.  Was it fair and how could he show us?  Another child said we could measure it.  Can you show me?  He suggested his finger.
Then I suggested my finger was longer than his finger or another child's.  This raised the question by another child what else could we use.  Another said "That number thing."  Further discussion on what was needed was concluded when a child actually went and got a ruler from my tote tray and showed them how to use it.  He measured across the middle of both pieces saying they both said 9.

I then suggested there was another way they could show that the pieces were exactly the same.  There was much discussion and putting the pieces side by side, together, end on and so on until one girl walked up to the boys and simply put one on top of the other saying - "They are exactly the same.  See!  Nothing is hanging over the edge."

This was a more engaged discussion.  Perhaps the topic of sharing pizza or sharing food was something they had experienced.  I was more conscious of trying not to lead the children's thinking and to let them show me their thinking.  I was very surprised at the suggestion to use a ruler and also the child who came up with the idea to simply put one half on top of the other.

Of course there were still those who found group sharing difficult but they at least  helped cut out the pizza and tried to join in the pairs discussion.  The lack of mathematical notation in the exercise meant that all the children were able to participate in some way using their knowledge of shapes and dividing them up.

Where to from here?  Some groups need refining.  Discussion rules need to gone over particularly reminding them of giving thinking time for others.  A smaller group size instead of whole class maybe easier to get around to hear where thinking is at (although there were only 14 children present).  How do I introduce a problem with notation and still get a high level of engagement?

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?

Sunday, 25 February 2018

Manaiakalani COL Achievement Challenge 2018.

The Manaiakalani  COL Achievement Challenge that I am basing my 2018 Inquiry around is to lift achievement in maths of my Year 1 students.

My inquiry will focus on the role of language in mathematics and how this language can be "normalised" and transferred into other areas of the curriculum and relates to their everyday conversations and usage.

Year 1 students often lack the verbal tools to begin to look at a maths problem or to justify concepts of how they solved a problem so they are less likely to participate in a maths lesson, remaining silent or shrugging their shoulders and therefore do not make as much progress in maths as they are capable of. 

They switch off saying they "can't do maths"  but what they really mean is "I can't find the right words to explain what I am suppose to do and how I did it."

I propose to look at the role of language in mathematics and how I can support my students to acquire this language and thinking that they need to raise their achievement.






Friday, 26 January 2018

Raising Maths Achievement.

2018 Professional Development: Developing Mathematical Inquiry In a Learning Community.

Pt England staff were privileged to begin 2018 with professional development taken by Dr Roberta Hunter.

Dr Hunter gave us the startling fact that "62% of Maori and Pacifica students are failing Maths."

But she also gave us hope that if we radically rethink the teacher's role, and tap into the richness that each child brings to school, these children can raise their achievement levels and be successful at maths.

"Every child is good at maths - it is how they are taught that makes a difference."  (Dr Hunter)

To develop this "culturally tailored approach" of getting to know the children's cultures and how culture impacts on their learning will be a first step.  The need to see the children's culture as a strength and a part of maths which can allow children to connect with each other and see inside each others worlds is an important beginning.  Providing a problem that centres on a particular culture allows a quiet student to open up, show the other children how the problem would be looked at in his culture and be the centre of an explanation.

The children work through culturally based "group worthy" problems.   If the problem can be solved by an individual it is not "group worthy".  These groups are carefully selected and are not based on ability - something we often overlook as we test and group children according to ability in the belief that they learn and work better with similar peers.

After launching and making sure the children understand the problem, they talk, ("friendly argue") discuss, question and reason their way through the culturally based real world problem to come up with a logical answer.  Children are given the tools they need to help solve the problem.  If the problem requires multiplication and they do not know their times tables a sheet may be given.  The teacher does not give a solution but gives the tools needed for the children to discover a solution.

They are all "drivers" not "passengers" with all students expected to participate, contribute and learn.  Inclusion is a key factor.  Getting all children to actively participate and be able to offer explanations, even to think back to how they solved a previous problem and use this knowledge makes maths sound exciting.

This raising of maths achievement takes time - it is a journey that has its ups and downs but if it can engage our children and help the children see that they can reach and achieve higher levels I am excited to be able to take part in such a journey.