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.

Patience Young Grasshopper

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?

I recently presented my inquiry to a group of people at the Manaiakalani hui. While presenting I was asked what have I learnt about myself throughout this process. My response was that I didn't have as much patience as I thought. It is taking much longer than I would like to see a change in my kids which is really frustrating. At times I see glimpses of significant shift in their ability to explain their mathematical thinking then at other it times it's like it's week one, term one all over again.  I'm assuming that this is par of the course however it's still frustrating. I long for the day when those glimpses of effectively explaining and justifying are no longer glimpses but the new norm.

So where to from here? My advice form others has been to keep persevering and keep doing what you know works. The latter part is a good reminder as it's easy in the moment when it's not going well, when I'm feeling frustrated/tired etc to put aside the things you know work. For example using the waka paddle discussion prompts or requiring the kids to speak in full sentences and use the word because in their explanations. So,  I'm going to keep implementing that things that work, persevere, keep the long game in mind and get back on the horse.

Data, Reflection & Next Steps

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?

Below is the current data taken from a recoded maths session of my target group.

It's great to see the children explaining their thinking more freely however unfortunately they're not using the word 'because' often enough. They say things like "so you go 20.3 x 2 which is ...." but they don't explain why they multiplied 20.3 by 2 therefore, not justifying their thinking. It is also evident that the children are not asking questions of each other off their own bat.

So what can do or change to further develop their dialogic discourse? Although I've introduced the waka paddle prompts, had the children participate in talking activities and modelled dialogic discourse I'm not seeing the results I thought I'd see. This has me wondering do I just need to be more patient or do I have to try something different? Maybe it's a bit of both.

Recently, on my blog, I was challenged by Dr Jannie van Hees to look at incorporating real world maths into my class, to get my kids out of the class to explore the maths around our local environment. She suggested that using "... relevant, motivating, authentic contexts will generate much talk and figuring out....and when suggestions are shared, and justifications expected, rich maths and maths language dialogue will occur." This makes sense to me I guess the challenge lies in incorporating it in my DMIC lessons but I'm sure it can be overcome.

Going into Term 3 Reflection

As term 3 kicks off I've been reflecting on my inquiry this for this year. In this reflecting I was reminded of the inquiry that I did last year. I found that I have been so focussed on my inquiry this year that I have forgotten about the things I discovered the previous year.

Things like:
- How effective materials are for learning new mathematical concepts and knowledge.
- How hands on follow up activities are effective in concretising new learning.
- How combining create to learn tasks with hands on follow up activities and materials is effective in    consolidating new mathematical concepts.

Problem
How do I keep inquiring into this years inquiry while still applying the things I learnt last year? The simple answer is to 'just do it' however when you're engaging in a whole new maths pedagogy (DMIC) this is easier said than done.

Possible solution
DMIC maths sees myself working with half the class while the other half works on independent activities. My plan is to incorporate my learning from last year into the activities the children are doing when they are not with me. I haven't quite worked out what this will specifically look like however I'm determined to put something into place so that my learning from last year doesn't go to waste.

Quick Inquiry Update

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?

Anecdotally my target group are making progress in their ability to explain and justify their mathematical thinking. They are speaking with greater confidence and are using the word 'because' more frequently. They still often need teacher prompts but I'm finding they don't need as many teacher prompts and are more willing to share their thinking.

The waka prompts have been helpful in giving the kids something to launch from and they they are using them more frequently without me reminding them to use them. Unfortunately the kids still like to play with them and they can be a distraction but they are more useful than not. It has been great to see some of the kids request to not have waka prompts as they are confident they don't need them.

This week I will again be recording and measuring the mathematics discourse of my kids. I just hope the data reflects my anecdotal notes.

First run with the waka paddles

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?

This week I used the waka paddle prompts for the first time. As they were a novelty the kids were eager to use them. At first they weren't using them meaningfully. They viewed it more like a game to get rid of their waka paddles. After some more discussion around the purpose of the paddles and how the prompts needed to be used appropriately and meaningfully the paddles started to be used more effectively. One annoyance is that some kids were more focussed on playing with the paddles than the maths task however, I'm hoping that once the novelty wears off this won't be much of an issue.

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. 

Some Baseline Data

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?

This week I recorded my target kids collectively solving a problem. My goal was to capture and measure their ability to explain their thinking and inquire about other's. I noted done each time each child used any of the phrases, or similar phrases below. The kids worked on the problem for 15 minutes and this is their results.It's worth noting that two of the target group were not there that day. Their row has been marked with a -. 

It's interesting to see that the children did try to express what they are thinking however it often wasn't backed up with a reason. The word 'because' was seldom used and the others were left to infer the mathematica thinking and process from what was said e.g "You add 20 to 100 and then you....". Equally interesting is that only one child asked for further information/explanation from others as they expressed their thinking.

This married up with what I have been seeing anecdotally so it's nice to have some actual data. We clearly have a long way to go in developing a community where kids can confidently express their thinking and inquire of others. My next steps involve explicitly teaching the kids how to express and justify their mathematical thinking. My kids need to view each other as both a learner and teacher. They need to connect with the idea that they can learn from their peers and that what their peers have to say is valuable.

Inquiry update: Let the recording begin!

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?

While I had every intention last term of recording my students in order to measure their mathematical dialogic discourse ability, due to the business of school life and external factors (a baby being born 5 weeks earlier than expected) this did not happen. 

However it's now week one of term two and I will be recording this week! It's going to be great to have some baseline data on my kids, a reference point to build from. I only wish I had done this earlier as anecdoatally I have already seen my target kids become more confident in their ability to engage in mathematical dialogic discourse. 

Measuring my kid's dialogic discourse ability

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,  to measure the dialogic discourse of the ability of my kids I will be recording my target group during their maths lesson and I'll be noting down each time a child uses specific justifying and explaining language and each time they inquire about others people thinking. Below is a list of questions and statements I will be listening out for. If you think I have left something out I'd be keen to hear from you.

Measuring and Tracking Progress

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?

One issue I had was working out how to measure the mathematical dialogic discourse ability of my kids. Anecdotally I could see that they struggle to explain and justify their thinking but how was I going to get quantifiable data. I discussed my problem with Dr Rebecca Jesson and we came up with (well she came up with) this solution.

I will record my target group during a maths lesson then I'll listen back and note down every time a child uses specific (which is yet to be decided) justifying and explaining language and each time they refer to the context of the maths problem when explaining their thinking.  I will also be noting down how often they need teacher prompts to draw out an explanation. By doing this regularly I should be able track and measure the kids mathematical dialogic discourse ability.

Target group PAT data

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 my previous post my target group is made up of 3 boys and 3 girls. Below is a table of their Term 1 PAT maths data. While my focus is to develop the dialogic discourse ability of my children I hypothesise that if this happens then their mathematical knowledge and ability will also increase making them more proficient mathematicians.

The target group were selected because they struggle to vocalise what they are thinking. It's interesting to see that the struggle to explain and justify your thinking and engage in dialogic discourse is evident across the varying academic levels.

Student feedback

Recently I gave my class whole class a survey to complete around speaking in class. I wanted to hear from them their thoughts about sharing their thinking and speaking in class, how difficult they find and what makes it difficult etc.

Below are some of the interesting trends collected from my target group survey responses. My target groups responses to all questions can be found here.

- Every target child noted 'I'm afraid of what others will think of me' as a reason for what stops them from sharing their opinion in class.

- 4/6 noted 'They don't want to get a wrong answer' as a reason for what stops them from sharing their opinion in class.

- 4/6 said their equally happy sharing their thinking in front of either gender. 2/4 noted it would be easier sharing the thinking in groups f the same sex as them.

- Overall they are not interested in listening to others thinking


It's evident from these responses that I we have a lot of work to do in creating a supportive mathematical community where kids feel safe to share their thinking and one where they value the thinking of their peers.

My target group

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?

My target group is made up of 3 boys and 3 girls. They were selected because they struggle to vocalise what they are thinking but more importantly they are kids who work well when given a task and would be up for a challenge. Three of the children are naturally quieter than some which may be a contributing factor to them struggling to share their thinking.

My next steps involve hearing from the children themselves. I want to find how they feel about  sharing their own opinions and thinking, how easy they find it and if they find it a challenge what are the contributing factors that make it a challenge. Watch this space.

Back to the drawing board - My new wondering

As mentioned earlier my Manaikalani COL inquiry wondering was "How can I use Developing Mathematics Inquiry Communities (DMIC) pedagogy to develop the vocabulary of my kids? The focus was on developing my kids general vocabulary using DMIC maths.

Having done some research into vocabulary development I have since decided that trying to develop general vocabulary requires different pedagogy to that of  DMIC maths. I was also challenged by Dr Rebecca Jesson to think more about the problem I'm trying to solve before I think about how I'm going to go about solving it e.g vocabulary development pedagogy or DMIC maths. This was great advice and I have now identified the problem I wish to inquire in to.

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

In fact the struggle to do this in other areas too however it is particularly poor in maths (my hunch is if it improves in maths it will also improve in other areas). This lead me to a new wondering. 

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

This year I will be endeavouring to find a solution to this problem. Any thoughts/ideas you have on the matter would be greatly appreciated.

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.

Manaiakalani COL Inquiry 2018

“Recognising and spreading sophisticated pedagogical practice across our community so that students learn in better and more powerful ways...”

The Manaiakalani Community of Learning is working together on this task using the expertise existing in of our community of learning.

Like last year I have selected the following CoL achievement challenge for 2018.

#6. Lift the achievement in maths for all students years 1-13.

More specifically my focus question is : How can I use Developing Mathematics Inquiry Communities (DMIC) pedagogy to develop the vocabulary of my kids?

The teaching as inquiry framework I will be using in 2017 has been specifically co-constructed for Manaiakalani schools using our familiar Learn Create Share structure.
The elements in this framework share close similarities with other models New Zealand teachers use.

I will be labelling my posts as I update my inquiry throughout the year to make the content easy to access.

Labels:

LEvidence, LScan, LTrend, LHypothesise, LResearch, LReflect,

 CPlan, CTry, CInnovate, CImplement, CReflect,

SPublish, SCoteach, SModel, SGuide, SFback, SReflect

Label Key:

LEvidence	Learn - Gather Evidence	CPlan	Create - Make a plan	SPublish	Share - Publish
LScan	Learn - Scan	CTry	Create - Try new things	SCoteach	Share - Co-teach
LTrend	Learn - Identify Trends	CInnovate	Create - Innovate	SModel	Share - Model
LHypothesise	Learn - Hypothesise	CImplement	Create - Implement	SGuide	Share - Guide
LResearch	Learn - Research	CReflect	Create - Reflect	SFback	Share - Feedback
LReflect	Learn - Reflect			SReflect	Share - Reflect

Dr Jannie Van Hees and Dr Bobbie Hunter PD

Today Dr Jannie Van Hees talked to the COL teachers about how to better develop the language acquisition of our children. She had a lot of great things to say but what really stood out for me was closely it aligned with Dr Bobbie Hunters PD on Developing Mathematical Inquiry Communities DMIC. DMIC see's the children doing the speaking, explaining and justifying their thinking.

Both Dr Jannie and Bobbie had these goals as part of the social norms of the classroom:

 - Every contribution is valuable
 - No hands up
 - Everyone's effort is honoured (by teacher and children)
 - Children valuing/taking seriously/actively engaging with other children's thinking.

This Year I will be endeavouring to make these social norms part of my classroom as I explore DMIC maths with the lens of language acquisition.