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.
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