I’ve recently spent a lot of time thinking about maths.  A lot.  Not so much the maths itself but about how I teach maths and how my children learn maths. I’m currently undertaking an e-course through Stamford University Online called How To Learn Math, which has opened my eyes to so many possibilities and helped me to address many of the poor lessons I absorbed as a maths learner myself.

I’ll try to come back to this topic a bit more when I’ve finished the course and I’ve developed some of these ideas but basically there are some fundamental principles that I’ve been getting wrong.  Messages that I received that I’ve been passing on to my children, with a negative impact on both them and me.

See I’ve always hated maths, I loathed it.  I felt stupid in maths class and even as an adult, taking courses as part of my post graduate when studying teaching, I was in tears in a room full of strangers.  It was crazy nonsense to me and I couldn’t make sense of any of it.  Now this may make me sound like the worst possible person to teach a child maths but here are my thoughts on that:

1) I am INCREDIBLY motivated to make sure my children don’t have the same experience I did;

2) I can respond to their specific needs and pace, I don’t need to be an expert to do that and;

3) Many actual maths teachers are terrible at teaching maths.

There, I said it.  The way maths is taught in schools is largely bad.  And do you know how I know that?  Because the nice lady on the Stamford e-course told me so.  There is a whole section at the beginning about how many of us are scarred by our experiences in the classroom and how things need to change in order to help everyone be as successful as they can be in maths.

{Number Pegs activity from Playful Learning the book                                                        The fractions activity is from the post Playful Learning – Learning With Circles }

 

So here are some of the key things I’ve taken away from the course so far, they may seem small but to me they have been profound concepts that are already altering the way I teach.

1 – Maths is not about natural ability, most of us are capable of being good at maths.  I found this idea shocking as, like many people, I always saw maths as something of a gift.  You either have it or you don’t.  This is what is known as a fixed mindset and is the kind of mindset that prohibits learning.  If you believe you are rubbish at maths and can never improve you won’t.  In order to grow you require a growth mindset, allowing you to accept change and develop; but in order for that to happen you must…

2 – See mistakes as positive.  What?!  But mistakes are bad aren’t they?  That’s why we call them mistakes!  I mean we all say that ‘we learn from our mistakes’ but really we know that is tosh and that being good at stuff is what counts (and if you can be good with no effort so much the better).  But in fact our brains benefit from making mistakes, our synapses fire much more when we make and subsequently correct mistakes, more even than when we get it right.  That’s right, we learn more by getting it wrong.

And finally (for now)

3 – Speed does not equal success.  This may seem like a small detail but in fact is central to our perception of what makes us successful in maths.  Speed in class, speed in tests, getting the answer first.  I don’t think I’m the only person who associates being quick and being good at something.  But this is the enemy to understanding, the rushing through things without strong understanding.  I was rushed and I rush in turn, leaving behind the hope of really getting it for the short term satisfaction of the right answer.  This is a mindset I’m hoping to abandon in favour of allowing my boys to really understand in their own time. If that means sitting on the floor for 40 minutes working with manipulatives to do 5 subtraction questions (like we did yesterday) then that is what we do.  And we’ll do it everyday from now on.

{Santa Geometry Activity from Ed Emberley’s website, December activities.                       The wonderfully inspirational Picture Pie book by Ed Emberley.}

The course is taught by Jo Boaler and she uses a great quote by Fields Medal winner Laurent Schwartz.  The Fields Medal is like the nobel prize except harder to win, so I’m going to assume he’s a pretty clever chap.  Yet he talks about how he was often the slowest in his class and how he always worked slowly throughout his career.

“What is important is to deeply understand things and their relations to each other.  This is where intelligence lies.  The fact of being quick or slow isn’t really relevant.  Naturally, it’s helpful to be quick, like it is to have a good memory.  But it’s neither necessary nor sufficient for intellectual success.” Laurent Schwartz

This idea that being quick wasn’t important was like a boulder being lifted off my spirit.  I had never realized what an ingrained idea this is until I challenged it.  Why is it good to be quick? Why can’t we explore things deeply and with real understanding?  Well we know why of course.  In a classroom understanding is not the main goal, it can’t be; proving that the ‘standards’ have been met and that the school is doing it’s job is always the first priority.  Not because teachers or parents or even politicians want it this way but because when we judge one another by a ‘norm’ instead of by looking at individuals in a way that respects them as distinct, we lose the opportunity to really connect.

So the idea of speed being king has also gone out of the window.  It’s a relief all round I can tell you.  I’m taking on board what Jo Boaler says about learning, that we should always be at the edge of our understanding and therefore making mistakes and growing from them.

Another idea that is being reinforced by this course is that maths is not arithmetic.  Arithmetic is a part of maths but maths is so much more and that we have to work at strengthening the whole maths brain not just the memorization part of it.  This is something Stephen and I have been talking about for a while and we’ve begin drawing in other elements.  We’ve incorporated games to introduce strategic thinking, apps that allow for more fun, stories to touch on maths concepts, songs and rhythmic movement to reinforce learning  and generally tried to approach things with a more varied perspective.

With that in mind I’m making sure that our maths hour includes not just our textbook work but work that works on skills and on building what I’m starting to call the ‘maths brain’.  The part of the brain that works on logic, spacial recognition, reasoning and strategic thinking.  This goes beyond simply working on arithmetic and begins to incorporate other elements, especially those of creativity and movement, in order to solidify learning.

One of my go-to resources when exploring any topic is Playful Learning.  I’ve been a fan of Mariah Bruel who runs and orchestrates that website for years, and my admiration has not diminished since I had the chance to make small contributions to her blog over the last year or so.  Her charm and warmth shine through all of her work and she has a wonderful knack from bringing together ideas in ways that creates clarity and inspires action.

I’ve owned her book (also called Playful Learning) since it came out and regularly use her resources page as well as the wonderful contributions on her blog to give me some ideas for inputting more creativity into my teaching.  Today’s maths lesson with the boys came almost exclusively from Playful Learning related sources so I thought I’d share them for anyone else seeking a bit of inspiration.  I’ve popped a link beneath each photo so that you can find these resources easily yourself.

{Freeform geometry creativity from Neirin at the top followed by his pattern work based on the Learning With Circles post.  This was the making patterns activity. }

Today when I was talking to Huwyl about a correction he needed to make (in a different subject) we talked about how the word ‘mistake’ has such negative connotations, I said I wished I had another word I could use instead that expressed our new understanding of the value of mistakes.  He thought for a minute and then said “You could just point at the mistake and say ‘Your brain needs to grow here’, then I’ll know I need to look at it again. ” That moment alone, from a child who has been horrified by mistakes, smiling up at me over a spelling correction felt like a huge shift.  I feel like we are finally finding our way to where we want, and need, to be.