Looking at learning through the eyes of a child

I have been on this journey into play for three years now.  Each year goes from strength to strength and my 'approach' to teaching continues to improve...why, what is it that keeps it going and getting stronger? 

There's no hugely mystical reason, basically I have chosen to channel each and everything I do through the eyes of the child.  Because I have never really grown up, I find this quite easy 😊.  The other thing that makes it incredibly easy is that I know my children, I spend a lot of time talking to them, play-based learning makes that possible.  No longer am I rushing from reading group to reading group, madly trying to rush them through a timetable that they have no ownership over.  Now I can sit down at a table and talk to them about their interests, pose questions and wonderings and listen to the conversation take a direction that I never expected.

My current concern is that so many classrooms are governed by the eyes of an adult.  Environments are designed beautifully, but they are beautiful from an adults perspective.

Topics of learning are selected by adults, in some circumstances, adults that are not even present in that classroom, just making decisions based purely on their 'coverage' requirements.  In other situations, topics that go right across the whole school, because that is 'what we are doing this year.'

How learning is delivered is decided on by adults, with very little thought given to the children.

Play-based learning and Number Agents have given me an absolute gift.  A gift I have been very privileged to pass on to many teachers now.  This gift, is the ability to stop, to listen, to discover and be able to see learning through the eyes of the children in my class.  Have I perfected this lens, absolutely not, but I am working on it.

This child lens has allowed me to make changes to everything I do, from reading, to writing and of course in maths...but much, much more.  It has changed me as a teacher and also as a principal. 

Through this child lens I have learned to stop and just go with the sense of wonder that children have about the world around them...this has led to a much more dynamic and authentic framework for learning.  In fact, we cover so much more of the curriculum than ever before, in much more authentic ways. 

I worry that too many in our profession still place so much emphasis on pre-planning...spending hours on end detailing achievement objectives and learning outcomes, but not giving a thought to what the children might like to do.   Or they give a cursory thought to the children by asking them what 'topics' they would like to cover.  Yes this might get to the interests they have, but hey, just like us, they don't know, what they don't know...until they are curious enough to want to find out.

I worry when people talk about spending hours each night on planning, in my opinion this is wasted time.  My mind is busy during the day, when I am working with my children, but I would only spend half an hour planning each week....if that. 

It worries that in many schools plans have been used years on end.   I can't even imagine regurgitating a plan more than once, and I can not at all see the usefulness of delivering the plan another teacher has created for their class.  Don't get me wrong, I plan, I know some basic endpoints that I would like to get to, a lot of these are based on dispositions, rather than knowledge, and I draw on Te Whariki much more than ever before when thinking about my teaching.  Most of my planning is on the spot and in the moment, and a lot of it, even though they don't know it, is done by the children.  It is seamless and evolving, most of all it is engaging and very real. 

I also worry that many in our profession gravitate to programmes, because they want to get it 'just right' for their kids.  Many of these programmes are delivered from books, or presented in worksheet form...now in my opinion in these cases we are not using our child lens at all, but once again our 'coverage' and 'we have to do it this way' lens.  If these programmes are used for ideas, or starting points, but then shaped by your understanding of the children in front of you and innovated upon accordingly, then that is a different story.  That's why I love Number Agents so much, it is a philosophy, an approach...but it will never every prescribe how to teach or what materials you may use.  In fact many people have read my book now, but all have made the approach fit them and delivered it in their own way, for their own children.  It should inspire and ignite ideas, not prescribe the way you do things.

It also worries me that when asked, teachers talk about how much new entrants and juniors in general love routine, they love timetables, they love to know what to expect...don't get me wrong, my classroom is not anarchy (although at some points in time it can seem like organised chaos) it is absolutely based on rituals and structures that they understand.  I think even the youngest of children, while they like to feel secure, safe and to belong, also like to be able to explore learning, interests and urges outside of the rigidness of a timetable that is governed by an adult, to feel like they are in control, just like us. 
I would actually say that most children are people pleasers and sit well within a routine and timetable because it pleases us and this makes them happy. 
There is a difference between setting rigid routines and having expectations.  We have high expectations (developmentally appropriate) that are based around kindness and respect, our play-based environment allows us to actively model and coach dispositions that reflect these expectations.  It worries me that the advise we give to many new teachers is to be 'tough' in those first few weeks of the year, when in essence what they really need to be doing is taking time to form attachments with 'their children' it is these relationships that will make management easier later on. 

Now don't get me wrong, I know that some children need to work within more structure than others because of behavioural needs and developmental needs, however I do believe that by working on relationships and slowly releasing the structure over time, these children too will be able to follow their own interests and urges in their own good time.

When I talk of children in this post, I don't mean just juniors, I mean all children, even those at intermediate and high school...if we are to look at what and how we are teaching through their eyes, we will then be able to engage in practice that best suits them. 

I have yet to meet a child of any age that wants to do science from a work book or copy mathematical rules from a whiteboard.

Food For Thought - Why are we so worried about what children are NOT doing?

I continue to come across thinking around school entry and learning readiness that worries me.  There is so much information out that about how the brain develops and the time that this may take, yet it seems to be largely ignored.  I am not going to go back through this research as I have posted about this before.

Firstly let me get it out there again...I hate the word acceleration.  I don't believe we need this word in order to understand that some children just need extra support.  All learners should have the benefit of being known on an individual level, not just those targeted for acceleration.  As teachers I feel it is our responsibility to know each and every child for who they are as an individual and do our absolute best to support them wherever they are up to.  This may be children technically thought of as struggling, those at an 'expected' level and those children working above expected level.  In fact my view of acceleration is that in order to best support children we actually have to slow down, not force more learning down their throat.    If we were to apply the thinking of Te Whariki, we would no longer apply deficit thinking, but it would be obvious how far they actually had come.  Just because children enter primary school this doesn't mean they should move from the wonderfully open curriculum of Te Whåriki into a narrowly focused learning environment academic acquisition.  I love this paragraph from Te Whåriki on an inclusive curriculum

"Te Whåriki holds the promise that al children will be empowered to learn with and alongside others by engaging in experiences that have meaning for them.  This requires kaiako to actively respond to the strengths, interests, abilities, and needs of each child and, at times, provide for them with additional support in relation to learning, behaviour, development or communication."

What a fabulous statement for all levels of education!

How do we do this?  Well it starts with actually knowing how learners develop, how the brain develops and how we can tune into this development to best assist children. Nathan Wallis speaks about this in terms of building a house...you wouldn't put the roof on before laying foundations and building the walls necessary to support the roof would you?

So why is it that the minute children enter school we leap into learning the alphabet and maths, why do we foist them into an emergent reading group (where for those that are not ready, will sit for months and become more and more frustrated by learning to read.)  Why do we treat children like they are produce coming into the factory and being put on the conveyor belt of learning that travels at the same speed for each and everyone?

Why an earth are we still applying deficit thinking for the poor little individuals that walk into our room?  How does this serve their learning journey, for us to think of them as not being up to par the moment they walk into our classrooms. 

What if we were to flip this thinking on the head, to look at these children through a different lens.  What is it that they do know, where are they up to developmentally and what will we do next to help them on their learning journey.

Something I have found out is that we are doing a great disservice to all children by not looking at them as individuals and considering developmental needs.  Not only those that shock horror, don't know any letters or recognise numbers, but actually also to those that do.  We have children that walk into our room with a huge amount of knowledge...and it is just that, knowledge, not understanding.  If we were to think of them academically, many of these children would be reading and writing straight away...what I have actually discovered is that many of these children lack gross and fine motor skills along with emotional and social understanding.   They need these skills, because obviously in their house the roof is already being installed....only to come crumbling down when their foundations are not strong enough to hold it up any longer. 

Thinking of children as play experts and allowing them time to build these foundations does not hold them back.  In time they build the foundations, in turn their house is strong, robust and able to weather any learning storm it may face.  I have not got any 'data' on this yet, but our learners who have been allowed time to work through this approach are more resilient, flexible, enthusiastic and interested, able to challenge themselves...they have not been held back, in fact completely to the contrary, many of them are doing far better academically now than their peers who would have gone through a more academic based approach.  They are also so much more advance socially and emotionally.

Please pause, think about the research, think about the why of what you are doing and consider each child as a competent individual.  We have the power to make a difference for these children and to also make this teaching gig a lot more rewarding, how fantastic is that!


My diagram about learning readiness based on what I am learning about brain development


My goals based on what I am learning about the learning process.

This is a journey...

I feel very privileged to be in a position to readily embark fully on this play-based journey and now into our third year I am beginning to feel like I'm really starting to 'get it.'

I can confidently stand behind the decisions I have made regarding our learning approach in the juniors and feel backed by research.  I know my why and feel absolutely confident within that. 

But just like everyone, or school is not perfect, our children are just that, children.  We have worked incredibly hard on our culture, it has been and continues to be a journey.  I walk with pride around our school, watching the creative play with all year levels working together, I listen to the hammers creating yet another hut modification and I brim with pride when parents speak about how happy their children are....but don't be deceived it is not all roses at our place either.  Our children do  make mistakes, we as teachers make mistakes, we have bad days occasionally,  just like everyone else. 

Things do not always go the way I would like them to go, I still doubt myself (although the old voice in my head that believed in academics all the way, is becoming faint.)  Even Number Agents, as fabulous as I believe it is, doesn't always hit its mark the way I wanted.  My agents are not always angels ...😁

What I am trying to convey here is that for those thinking I have it all together, please remember that we are all human and like everything we have our ups and downs. 

But should this prevent us from trying...no, it should make us even more determined to do better.  I hate to hear comments that relate to child and teacher competency as a reason for not embarking on this exciting adventure of play and creativity.  I hate to hear "but my children couldn't do that." 

If there is one thing this journey has taught me is that all children are competent , competency looks different from individual to individual.  What they are all very good at, is making us feel incompetent at times.  It is these moments that have taught me the most, when I have had a difficult time of it, when I can't unravel the mystery that is the child in front of me, when I can't find the switch, when I feel quite incompetent, it is in that moment that I can choose to find a way back, it is in these moments that I learn the most about myself and the children that I work with.  It is in these moments, that if I allow myself some time, I have my great lightbulb moments.  In fact in all honesty Number Agents was born out of a feeling of incompetence.  I hated my maths programme, felt like I was failing to meet the needs of my learners, and boom, had a moment of inspiration that has changed my  maths teaching forever.  What was the key?  I had to admit, I didn't know what to do next.

So if you are feeling a little incompetent, if you are feeling a little lost, swamped or maybe more like overwhelmed...please take a little reassurance from me...we all feel like that sometimes, go for a walk, embrace that feeling of 'not knowing' and see what lightbulb moments you have...I know this is one of the ways I work out where to next. 

This is the place I go...where I do most of my thinking at least twice a week...I walk and think and forgive myself for my mistakes....this is the place my ideas are born and where most of these blog posts are written in my mind.

What I really want to get across, is even those that we view as 'most competent' have our moments...we question ourselves, but the difference is, we use these as learning experiences.  Please know that you are competent, and that frequent feeling of incompetence?  Well it is normal and should be embraced...don't let it defeat you.

An example of this for me within our play-based class can be found within this story:

We have a small group of children that would go to the same play, with the same materials each day.  There seemed to be a construction and trajectory urge going on...basically they would build something and then just throw cars at it.   From what I have learned from Sarah and Longworth Education I knew to just let them go with it...I took faith in knowing that although it looked the same to me, they would be doing different things within this play.  Over time a few of these children moved on, but I had one who was stuck, this was all he wanted to do.  I will admit, I started to doubt myself and this process.  I began to feel quite incompetent...perhaps the old me needed to take over and just tell him what to do?

I will admit I walked on this one...I walked and thought about it...what could I do, should I do something, or nothing at all.

And then it occurred to me that within this activity was a version of construction.  Our children had shown an interest in building barricades as part of their 'war' games.  They had also shown an interest in other types of structures, thanks to the other children and their huts.  I took a punt and set up a few provocations around castles, just a few pictures and books, and a lovely castle made out of a tv box (not my creation, but my lovely team.)
Now whether this sparked something within this group or not I will never know.  But my patience in just allowing the play to take its course was rewarded with this...

A stadium

A football ground

The play changed, the construction urge became more interesting and the whole group once again came back together with a different task in mind.  No more throwing cars, they started creating various structures.  Hey, they didn't go the castle way...but they did take up the tiny little hint about structures.

So for all those out there with children that do the same thing, day after day, just let it run...eventually it will morph and change, it must just be what they need to do for now.

What is my Why? Brain Gain, Brain Gain Buddies, Adding Tension and Less is More!

A bit of a combination post today.  I'm not sure about you, but Number Agents is the highlight of our day.  I love it, the children love it and their mathematical understandings continue to blow me away.  Plus by this time of year there is a wonderful storyline unfolding and it is so exciting!

What is my why?

Firstly, what is my why, I think you really need to think about this before embarking on any new approach or change to how you are teaching.  What is your why?  Why are you changing, what is your desired outcome?  Are you doing it because others are, or is this something you really want to do?

My why is pretty simple, I want children to love learning.  Particularly in terms of Number Agents, I want children to love maths, to have deep number sense, to learn through a playful mode and to believe in their abilities to develop new strategies.  Ultimately my major why, and this is much broader, I would like to play my part, in not only eliminating math anxiety for my children, but for all children.  I want to give all children the absolute gift of seeing maths as a connected, beautiful area of learning that can be found all around them!

When breaking down my why each term, I like to look at it in terms of number sense...what is it that my agents need to know in order to develop confidence and have success?  I also know that in order to do this, I need to develop my understandings about maths, I am constantly learning.

This is my what my thinking looks like:

https://drive.google.com/file/d/1NhO-z9F433Wl7rGDnpcWw0oXShGCFjyl/view?usp=sharing


Number Agents is like a storybook, I like to think of it like a story, each session of agents is a new chapter, we of course are the heroes and the villains are obvious.  It is playful and I play an integral role in this, I have to be part of the play.  Just like any good story, we add tension and crazy storylines that add excitement, the agents play a huge role in constructing these storylines.  No two sessions are the same and they are always memorable.  Intrigue plays a key role, and if you have read my blog post on intrigue, you will know why that is so important in the learning process. Here it is if you have not seen it.

Brain Gain and Adding Tension

One thing that keeps this approach fresh is the teachers ability to add details to the storyline that perhaps the agents didn't see coming...just like a good movie, there is always a good twist in the tail...or many twists.  Agency is based on Mantle of the Expert and a key part of this dramatic approach is tension.

Head Villain is the way we generally add tension.  Currently we have two storylines going...the first is the suggestion that the villains may be hatching a plan to kidnap agent 81...that has been bubbling away in the background of agency, suggested at by Head Agent and recently by Head Villain himself.  The suggestion of this plot running in the background keeps the agents on high alert and encourages them to add to the storyline.  Yes I will be kidnapped soon...but don't worry, like every good superhero story, the agents will save me and we will again foil Head Villain.

We laid down another tension today...the concept of brain gain was something last years agents were hot on...they had a little pot that they came up with that contained the brain gain.  This years agents have not hinted at it, but today I decided to drop the idea.  One because it allows me to link it to the work we do on growth mindset and talk clearly about how by working together we are contributing to our brain gain (which this year is stored in an invisible container stored in the portal) ssshhh don't tell the villains, they are looking for it.  We increase brain gain by working together and solving problems, we need brain gain to defeat the villains.

Two, because this concept allows me to lay down another tension.  Today we found out that an agency in Rotorua had their brain gain siphoned overnight...the villains are always on the lookout for brain gain because they use it to make themselves smarter.  Caught on their surveillance cameras was an image of Head Villain.

Three because it allowed me to bring in a 'real' context for exploring the concept of fractions, the agency had three quarters of their brain gain siphoned and only have one quarter left.

We must now stay alert...the last thing we want is a villain 'stealing' our brain gain.  Who would help our clients then?

Brain Gain Buddies

I had a huge aha moment today.  Like any new entrant room we are a real mixture...we have children that have been at school for a year and others that have been at school for six weeks.  This does get difficult at times (I won't lie) and sometimes the concepts professor delivers are a bit puzzling for our new agents.  

After our playful discussion about brain gain I suddenly had the idea of brain gain buddies.  This is simply giving an experienced agent a less experienced buddy ...but by applying brain gain to the idea of having a buddy, the agents lapped it up...happy to work together in the venture of growing their brains they worked away beautifully.  This also meant that when it came to solving the problem, three pairs would combine into a group and I knew at least 2 of the agents were more experienced and able to share their understandings with their less experienced colleagues.  

Brain gain buddies exploring tally marks.

Less Is More

I know I have said this before, but within this world less is more.  The drama within the world is so important and it is vital that time is spent talking about tensions and building characters.  Without this, it is just a normal math session.  I always aim to follow this flow once checked into agency:

1- Song

2 - Game or professor knowledge session or dot talk or visual image

3 - Problem

4 - Talk moves

5 - another song if time, usually by popular request

Sometimes we can fit in a dot talk and a game, but I aim for short segments.  Quality over quantity is vital and it is really important concepts are revisited over and over again.

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I have been so happy to read about all of the success Number Agents is having around the country....it is still so new, but I thank all of you brave souls for making the leap, and for recommending it to others.  

This is not my job, it is my hobby.  I am a teaching principal, but will always find time for those who have read my book about this approach and want to have a go.   If I can help, I certainly will!

Steps into play in a senior room

I am frequently asked what play looks like in our senior rooms.   In our school from year 4-6 we use mantle of the expert.  (Junior rooms may or may not use it also but focus on drama for learning)  Mantle is playful and as you will read in the second excerpt below, very dynamic, often fluid and seriously amazing.  Certainly something I would have loved when I was at school.

The way our school is set up, all children get access to free self-directed play in a very student centred environment.  Middle and senior rooms have been experimenting with other types of play and the first except demonstrates a first step into this.  

In our school we very much see development being a 3-4 year process when introducing new ideas...1st year is around having a go, dipping toes, 2nd year is around doing more, developing programmes based on the research, 3rd year is around consolidation and 4th year is around sharing with others.

In terms of our school environment and culture, that has and still continues to be a journey.  We've worked incredibly hard to get to where we are and continue to work on creating a culture and environment that our children can thrive in.  We are about 12 years down the track with this, it is not a quick process, but it certainly is worth it.

The words below are not my own, they are taken from the blog of a Year 5/6 teacher, our teacher inquiry is very broad, but is around the topic of engagement and motivation.  I wanted to share them with you, because the first one shows how the first step may be taken and the second one shows the brilliance of Mantle of the Expert.

An Invitation Into Play Through Art - Year 5 and 6

Today, for the first time ever, I created "an invitation to play" with a "provocation" set up on a table.

So after researching Leslee's comments about setting up invitations to play, and thinking about how such things could be used in a senior class, I decided that since I was devoting our day to calendar art, I would set up an invitation to play for early finishers if they so desired.

I chose art because that's what we were all doing anyway. I printed off a picture of Paul Klee, with birth and death date underneath, which I stuck in a frame. I printed off facts about him, and pictures of some of his artworks, including Once Emerged from the Grey of Night (1918). I placed a jar of water, sketch wash pencils, vivid markers, HB pencils, rulers, watercolours, brushes and several different types of paper, as well as textured wallpaper, on the table. I took a photo.

And as an afterthought, added a tin of watercolour crayons as well.
Isla finished her calendar art and asked what the table was set up for. I bit my tongue. I said she could play with whatever she liked there, if she wanted to. After quite some time she started to paint pictures of pineapples (her favourite, she always put pineapples in her artwork when she can!) and other fruit. She then painted a background inspired by In the Style of Kairouan which actually looked pretty cool on the wallpaper sample. She cut out her fruit pictures and glued them on, then moved on to another piece inspired by Once Emerged from the Grey of Night. Meanwhile, a group of three boys joined her at the table. They were keen to paint too. I was interested to see what they would choose to do.

They each took a sheet of cartridge, and proceeded to draw, then paint in watercolour, not something inspired by a Paul Klee piece, but the image on the tin of watercolour crayons! They didn't even open the tin.
So there you go, they did play! Just not how I expected they would.
I will do this again, next time I will add more variety and choice of media, and maybe several artists but choose 1 theme. I'll have a think. It was pretty easy to set up and they were totally engaged in what they were doing which was nice. But then it is probably just this group of kids, they enjoy and are interested in everything!

Mantle Off Track but Terribly Fun

Mantle has kind of morphed into a huge problem solving almost escape room type thing which the children are loving and I'm having heaps of fun putting together.
My initial plan has gone way off track but that's ok because the learning that's happening is amazing, everyone is fully engaged, and the other curriculum areas are being implemented as well.
While trying to figure out how I could bring in a few pre planned "tensions" I had a moment that went like this...
I was intending to give the "company" a cloze reading activity using a newspaper article about sneakers made from ocean plastic, but it just didn't fit with who they (the company) are, why on earth would they be doing cloze reading activities? The phone went ring ring (that was me saying "ring ring, ring ring") I picked up the phone (which is just two pieces of pvc pipe stuck together) and had a conversation with ... Great Aunt Myrtle! I made it up as I went along and the children were all so excited, like it was real, and Great Aunt Myrtle has evolved into a crazy but helpful old dear who has a liking for puzzles and mysteries.
It turned out she had spilt her cup of tea on the article, so the company had to figure out the words from a code and put them in the right places. The clues started off simple enough, but whenever anyone looked like they were almost there, I found I could draw it out a little further by adding in extra problems to solve along the way. The class loved it so much, they wanted to do more of the same the next day. So I invented Polly Ethylene, the evil, devious owner of a plastic bag manufacturing factory. We had to hack her "acebook" account and shut her down as she had a large group of followers who were opposed to not having the option of plastic shopping bags at the supermarket (for various ridiculous reasons, some of them real) but it turns out she also has an evil plot to do more environmental damage, and unethical plans for the future, so our company have been working through a whole bunch of clues and riddles to discover the evidence that will lead to her arrest.  The clues have involved so much awesome maths and literacy, and the children are so into it! They managed to find the box with the plan, which had a combination lock on it. They succeeded in opening the lock, only to find the evidence in a jar with another lock! The evidence once they crack that lock is in code too, and the clue for the code was in the box but they can't figure out what that clue is for... yet! It's been so much fun, and they've discovered morse code, braille, binary and semaphore, worked with fractions, time and measurement problems, grids and coordinates, place value, plus had to solve lots of riddles. And I'm having so much fun watching them problem solve and work together!
It's funny, Murgatroyd, the original pretend person we were dealing with who started us off with our first commission, has kind of faded into oblivion. I had to send a pretend email from him to the company the other day just to remind them of his existence and that he does actually have expectations that we have agreed to meet! But there is nothing like an evil villain to make things more exciting!

Challenging our thinking about maths

Mathematics, the teaching of it, and the acquisition of vital knowledge and understanding for children are something I feel quite passionately about now.

If you had asked me 20 years ago I probably would have told you it would be the first thing lost from our programme if we ran out of time.

 Of course just a quick glance over my blog posts shows you that I have many areas of interest, including literacy development.  Over the years I have come to view learning and development as something that we do a disservice to by seeing it as 'curriculum' areas...however for the point of this post I would like to talk about mathematics as just that, an area of curriculum.

There is always a lot of debate around maths, the current discussion  at the moment seems to be around 'streaming' or 'mixed ability groups.'  I find that people are more prone with maths teaching, much more than any other teaching area to stand vehemently behind their opinion, and often refuse to listen to the ideas of others.  Sadly on social media this often means indirectly putting others down, by so obviously belittling their point of view.  In all honesty we need to realise we have a lot to learn from each other.

Along with these often inflammatory and downright insulting arguments,  there are always various 'one stop shop' programmes being held up as the next big thing.  Either using workbooks, apps, computer programmes designed in my opinion to prop up what is essentially lacking in teacher knowledge and understanding of what mathematics actually is.  Often I think we hide behind these programmes, not because we steadfastly believe in them, but because we feel a real lack of understanding ourselves.  When used well as part of a balanced approach I am absolutely sure they are worthwhile in some way, however it would be my contention that this is not always the case.

I know many will be saying that very thing right  now "hey it is about balance, everything has its place." 
Yes this may be true, but what I want to really know is this,  why is it that we need these things, why are we not coming out of training college with a deep conceptual understanding of maths and how to teach it so that we ensure children have a depth of understanding that is needed to use it in the real world.  Why do we need these programmes and some seem to rely so heavily on them for direction. 

Right about now there will be many saying that it is because these programmes are engaging and motivating for students...hey this may be the case, but I believe that there are ways we can make this beautiful area of learning engaging and motivating without tying ourselves down to a programme.

Now, I know it sounds like I am now doing exactly what I accuse others are doing, but let me put it out there, I believe that if we are doing something based on sound understanding that withstands rigorous teacher inquiry and is backed by research, and it works for our children, allowing them to see the openness of maths and appreciate that it is all about patterns.  If we are using approaches that allow children to see the connectedness of maths, that it is all around us and allows us to pose and solve interesting real life problems.  If we are using approaches that involve talk, sharing of strategies and what we notice and if we understand maths anxiety and work actively to make this something of the past for our children.  If the children and their learning in maths are our why, then we are doing the thing that is right for us and right for them.

I have no intention at all to put specific programmes or methods of teaching down, but I do want to provoke thought about what we do in the teaching of maths and why we do it.  I want all of us to be deeply reflective and honest in order to stand behind what we do for the absolutely right reasons...and one of those reasons is not allowed to be "because we have always done it this way."

Do I believe there is one programme to rule them all...no I don't and that is why I call Number Agents an approach, because at any time I can modify how I do something if needed, believe me, Number Agents has changed A LOT since I started it.   Within this approach I am free to use bits and pieces of what I have found works, but not prescribe to one set programme.

My opinion has been formed from 20 years of teaching and the last ten years of deeply inquiring into teaching.  I do believe that our approach to teaching maths needs to be based on what our children need in that moment, what we've noticed, not what the work book tells us to do next, or what we have so diligently planned for the next two week block, no matter how well it may be based on what works.

Hey I know that is on the nose to say that I believe teacher understanding of maths and the teaching of maths is lacking, but I believe it to, in many cases, to be true.  I believe we are not being trained well enough in the teaching of maths and I think we are ourselves effected by how we experienced maths and either directly or indirectly take this into how we approach the teaching of maths.

Many teachers in my opinion have lost sight, or never ever have had the benefit of knowing what maths is , what it is children need to understand and actually how they develop understandings.  Programmes that offer a step by step process to teaching and learning maths depend on this lack of understanding and knowledge in my opinion.

Why do I feel the need or right to even say all of this...because I have been on both sides.  I was quite scared of teaching maths when I first started, I felt ill equiped to teach it.  I modelled myself on what I saw.  My children had task boards that kept them busy and required very little initiative or thinking on their part.  I taught in ability groups, diligently planning out what I needed to do based on the curriculum.  I had little understanding of why I was teaching what I was teaching, or how to focus in on the need and respond in that moment.  I planned my maths in two weekly blocks based on different parts of number and strand and diligently stuck to that planning regardless of what I saw in front of me.  I used modelling books as I developed in my career, but still planned to do two or three week blocks of learning.  I saw strand as very seperate from number and genuinely didn't see the connected or open nature of everything.  I did pre and post tests and relied on various 'speed' tests or 'instant' knowledge to show me how well a child was doing.  I remember in some teaching situations we shared plans, one of us would write a certain plan for number, another would write a certain plan for strand etc...enough for the whole term, and then we would share these and teach to each others plan.  This seems so foreign to me now, why would we have taught from each others plans when the children in front of us were not the same...they may have been a similar level, but their needs and abilities were not the same.  I was never challenged on my mathematical understandings when it came to teaching, never challenged to think about why I was doing what I was doing, and that is just as well because I don't think I would have been able to answer the hard question of ....why?

As I moved through my career I slowly came to understand more, for me the teaching of the Numeracy Project, however flawed it may be, showed me the whys and hows.  It filled in gaps that I had in my own learning as a child.  Lightbulbs went on for myself personally.  I slowly improved my teaching of maths, but I still stuck to the book, still taught in blocks and still valued speed.  I still saw maths as sequential, I still planned in blocks and set out directions for learning, before I knew where my children would take it. 

In my current school we went through maths PLD in 2015.  This really challenged our thinking, I think it may have been the first time that I felt really challenged, having already put in place Number Agents, I was in a good place to be challenged. 

I don't know if you noticed, but I used the word 'we'...that is because I am lucky enough to be in a team that are prepared to challenge their own thinking, we challenge ourselves and each other, to the benefit of our collective practice and the good of 'our' children.

Prior to this time we had been streaming our classes, with excellent results.  We felt our mathematical teaching was really humming along, most children spoke openly about loving maths, so we had no real reason to change, for many it was their most loved area of the curriculum.  Luckily enough we had a culture of embracing challenge and faced with research and very deep reflective thinking we found our way to problem solving, talk moves and a huge variety of techniques that enhanced maths in our school.  For those that refer to the work of Joe Boaler as a passing 'fad' I am not sure if they have really read what she has to say.  But we did, and we liked it. 

Ultimately streaming ended in our school for good in 2016 and teachers now teach mixed ability.  Having experienced both ways of doing things we feel well placed to voice our thoughts.  While we were successful before, now we feel we are really developing mathematical understandings, rather than creating learners that see maths as something that has one right answer and where speed is rewarded. 

Our children still do very well in this area of learning, but not only this, their mindsets towards mathematics are developing beautifully.  Those that tell you children that are 'gifted' in maths can not be extended in this environment are wrong.  Actually embracing mixed ability problem solving, more open problems and talk moves has changed our whole view of what a 'gifted' mathematician may be. 
Mixed level grouping does not hold our 'high' children back.  A teacher with a good understanding of the teaching of maths can work well within this approach.  In fact, you may find your definition of 'high' mathematical achievers totally changes when you start a problem solving approach, mine certainly did.  When faced with more open problems, which require a great deal more thought, or could have various answers, your slow, careful thinkers shine.  Our 'high' achievers are often challenged by having to share their strategies, or even think about another way to solve a problem.  Try it, you might be surprised.

What I really think it all comes down to is us understanding maths.  Understanding how we develop understandings and what it is children need to know.  While I plan for a week now, I actually plan day to day and moment to moment.  From professors task it may be noticed that their is a common lack of understanding around a concept, in the event of this, professor will modify what he is teaching and refocus on what needs to be focused on.  I will then reflect on this at the end and maybe tweak the next days planning.

I don't feel like I 'know it all'  I am constantly learning.  I think by putting one programme in place, we take this state of learning away from ourselves, we need to be open to learning more, to listening to the ideas of others, without rebuffing them before we reflect.  We need to be reading research, applying it if needed.  We have to be open to changing and tweaking what we do, for the good of our learners.  We also need to be learning more about this at teachers college, so that we are ready to implement best practice when we eventually have our own classroom.

Most of all, we need to be open to challenge, and able to stand behind what we do, able to answer the whys and be prepared to do so if needed.

Maths is beautiful, I only wish I knew that when I was at school.  What a gift we can give to our learners.

These are excellent starting points for understanding how we can embed deep foundations for children in mathematics, and to see maths as what it is ...all about patterns!

https://nrich.maths.org/10737 - early number sense

https://nrich.maths.org/10738 - the tenness of ten

https://nrich.maths.org/2479 - a sense of ten

If you have not visited nrich, or youcubed, these are musts....there is so much information on these sites that can genuinely 'enrich' your understanding of mathematics, because if you are to teach children, you need to have a deep understanding yourself, and I think that often that is lacking.  In my opinion this is why people reach for the next new thing...deeply aware that they need to fill in their own understandings as a teacher.

Yes we are teaching within the 'mathematical' curriculum, but what are we really wanting to achieve.  Well I would hasten we would like to help develop problem solvers that can approach problems creatively and have a wide range of strategies to do so. 

When was the last time you went out and 'did' maths...well probably often, but I bet you didn't think of it in that narrow way, because what you were doing was connected.  That is how mathematics needs to be presented to our children.