Inquiry 2018 Summary

Inquiry Focus
This year I have been inquiry has been based around developing the mathematical dialogic discourse ability of my children. In particular my focus has been on developing their ability to explain and justify their mathematical thinking as this was an area of weakness for my children.

Target Children
My Target group were made up of 3 boys and 3 girls of varying mathematical ability. They were selected because they all struggled to express and justify their mathematical thinking.

What happened for my children?
 - More confidence to share
Every child became more confident to share their thinking in class. Anecdotally this is what I was seeing in class as the year progressed. Children who once shied away from sharing were now sharing and children were becoming more confident to speak up when they didn't understand something and question it. This Anecdotal information was verified with the data collected from a student voice survey.

 - Increase in ability to explain and justify their thinking
My target kids had a small increase in their ability to explain and justify their mathematical thinking. As mentioned in previous posts this has been an area of frustration for me as I have not been seeing the gains I thought I was going to see.  Below shows the data of my target children taken from the measuring tool I designed to capture their ability to explain and justify. It needs to be pointed out that this data was taken when children were working independently on their maths problem these responses were unsolicited. This was not a teacher facilitated discussion.


 - April

  - June

  - August

 - November

The greatest improvement has been in the children's use of the word 'because'. In the last few months we have really been focussing on using 'because' to justify our explanations. My kids would often explain what they did but would not justify it. This data matches with what I'm seeing with the rest of my class too. It has been slow going and we have a way to go but we're getting there. 

Anecdotally the children are talking more and developing the ability to discuss and justify their thinking. Children who were once not engaged are now showing engagement and children who once would not participate in discussions are which is encouraging.

Has this had an impact on their maths achievement?

The jury is still out on this. The Maths PAT data below shows minimal increase in their achievement however these results have been effected by our schools' teachers and children learning and adjusting to DMIC maths. 5/6 of the target children made progress. Their progress average was 4.3 scale points. According to NZCER the national progress average for year 7-8 is 5.4 scale points. The average for the whole class that made progress was 5.1.

 - PAT data

What did I do to make this happen?

 - Waka paddle prompts
There was deliberate teaching on the type of things one would say if they were effectively explaining and justifying their mathematical thinking. These phrases and words were made into little waka paddles. The children would hold a bundle in their hand and the key was to use them in a maths session. Once you had used a prompt you would discard it. the idea was to get rid of all the waka paddles from your hand. This was used as a way of introducing the phrases and vocabulary into to the children and reminding them to use it.



 - Insisting on a response
In our maths sessions opting out was not an option. If I child was called upon they had to give some sort of response. "I don't know" was not an option. If they didn't have a response they had to say "Can you ask someone else please?". At that point I would ask someone else but then come back to them.

 - No hands up
Hands up was banned in our maths sessions. The children soon learnt that anyone could be called on to share their thinking which encouraged them to participate in the problem solving. They couldn't really on the usual eager beavers. At times the eager beavers found this frustrating as they really wanted to be the one to share but as time went on they adapted to the new system and no no hands up is the norm.

 - Discussion based games and activities
I used games to help get the children used to using the discussion vocabulary. For example to help ingrain the word 'because' in the children justifications they had to each say the following.

"I'm going to a dessert island and I'm taking _____________ BECAUSE _____________."

The focus of this was on the because. Starting a maths session with this simple game helped the children explain and justify more effectively when it came to their maths.

Next steps
As mentioned before this inquiry has been pretty slow going and I haven't seen the maths achievement I had hoped to see. I'm interested to see if next year the maths achievement will come now that the children have had a year learning how to effectively engage in dialogic discourse. My hope is that with this embedded in the children they will be able to focus mainly on maths in their maths sessions not on developing their dialogic discourse ability.

Using 'because'

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.
WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

As mentioned in a prior post I'm not seeing the progress I was expecting to see at this stage of the year.  Discussing my frustrations with Dr Aaron Wilson he assured me that inquiries which involve a culture and behavioural change are often slow going and can take a long time to see change. So that was reassuring.

The main frustration I have is that my kids struggle to use vocabulary that effectively explains and justifies their thinking. They will to some degree explain and justify their thinking using their own vocabulary however, the person trying to understand their thinking is often having to infer meaning and join the dots.

Among other unused vocabulary and phrases the most common unused word in helping to explain and justify is the word 'because'. Despite having introduced it earlier this year as part of the waka paddle prompts and insisting the children use it while explaining their maths problems the word 'because' is not yet common place in the classroom.

To combat this I'm going to introduce some activities/games where the kids have to use the word 'because' in order to successfully participate/complete the activity. My hope is that by using the word more frequently and highlighting it in a fun way prior to a maths session the children will transfer the use of 'because' to their mathematical explanations and justifications. I'll keep you updated.

Waka paddle prompts

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

The data I collected confirmed my suspicions that my kids struggled to explain and justify their reasoning in maths. My hunch is that the kids don't know how to do this effectively. To help them learn I have made prompts of the kind of things they should be saying when explaining and justifying their thinking.

The idea is that each kid holds a few prompts in their hands and their goal is to meaningfully use the prompt in their maths session. Once they have used it they can discard the prompt. My hope is that over time using these prompts will become second nature and they will no longer need them. I used the symbol of the waka paddle as we often talk about how we are one whanau and we are all in one waka. We need to all paddle in the same direction if we are to get anywhere. 

Venturing into DMIC maths

I have taken the plunge and have introduced DMIC maths in my class. DMIC maths sees the students actively engaging in problem solving and taking more responsibility by actively listening, justifying their thinking and inquiring into others thinking to help them with their own understanding.

DMIC maths has every one as participating equally as part of the community or whanau.  Every one shares their thoughts, every one asks questions and everyone is in charge of developing their own mathematical understanding.

Venturing into DMIC maths has been a challenge for both myself and the kids. The kids have been used to the teacher telling them how to do things, which strategy to use and when to use it, so to turn that upside down, having the kids being active participants rather than a passive sponge, is foreign to them. They have been reluctant to talk, share their thoughts or challenge other's thinking but the good news is we are seeing progress.

Equally I'm used to teaching specific strategies for specific problems. I'm used to telling them the information I think they need to know. So to take a back seat and actually listen to what the children can work out together without jumping in with my way of doing things is a struggle.

We're into our 3rd week of using DMIC pedagogy and the kids are slowly getting use to it (as am I). Discussions are being had and mathematical thinking is starting to be challenged. I have seen glimpses of what it could look like once our mathematical community/whanau is alive and thriving.