Knowing The Full Story

How well do you know the NZ maths curriculum? No, I don't mean just the curriculum for the level(s) that you've taught or teach....I mean the full curriculum...

Some of the best professional development in maths I ever had was when we were tasked with matching measurement problems with the different levels of the maths curriculum from Level 1 to Level 5. It was a much harder task than we all first thought it would be but once we had done it, it gave us such a clear picture of the journey a learner takes through the topic of measurement.

Lately, I have been involved in writing a curriculum for maths....taking one topic at a time and writing outcomes from Level 1 onwards. Doing this has given me such a deeper understanding of the curriculum and the layers of learning within each topic.

I believe every teacher should have this understanding of the full picture before teaching at any level. Sometimes you can get so wrapped up in the level you are teaching that you forget to look at the full picture. You may even be inadvertently setting students up with misconceptions that inhibit their learning at higher levels of the curriculum.

The level of maths you are teaching at is just a chapter of the full story. Doesn't it make sense for teachers to know what the full story is before writing that particular chapter? If you don't, then how will you know exactly what the main character in the story has been through and what you need to write in order to mould that character for what is yet to come in the story?

A Language of Learning

Meta cognition....thinking about thinking. As educators we know how important this concept is in the process of becoming a confident and successful learner. But do we know how to talk with our students about this?

Some schools have chosen to adopt rather complicated terms to describe different elements of meta cognition and then taught these terms to their students so that they can talk about their learning in that same language. It might be just me but something doesn't sit right with me when you hear a 7 year old saying "I'm learning to synthesise"...

There is now a far greater emphasis on the importance of developing problem solving skills and attitudes in our students. In all areas of learning, educators are creating learning experiences that encourage students to solve authentic problems and to be challenged with open-ended tasks. This is a far more palatable way (in my opinion) to give students thinking skills and to encourage them to reflect on their strategies/decisions and thoughts.

I'm interested in the various ways schools and teachers are sharing these problem solving skills with their students. How would a student in your school talk about their learning? How would they talk about approaching a problem in maths ....or in any area of learning. How is a problem defined?

I once asked my class 'what do you do in maths that is the same as when you're reading?' They couldn't tell me one thing. I was shocked. It got me thinking.....they don't realise WHAT they are actually DOING when they are LEARNING or PROBLEM SOLVING.

I developed a series of 'steps' that seemed to me to roughly capture the thinking that we do or we can do when we are faced with a challenge/new question/new information/skill etc

I put these steps into students language and as a class we talked through what each 'step' meant. We discussed how these steps were the same or very similar in maths, art, science, reading, writing and so on. I found it really helped them to see that they were in charge of their learning. It wasn't happening to them, it was happening because of them. They then had a language for learning that we could share and it crossed all learning areas.

What do others do to get their students thinking about their thinking?

If you're interested - my docs are on my Facebook page - Mathematically Speaking

Not Ready To Learn

This morning I'm thinking about those kids in my class and the classes of my colleagues who really struggled with maths and those kids who were always behind in maths. And there is a difference in those two categories....struggling vs behind.

In my experience as a teacher I found that it was rare to have children who genuinely struggled to understand maths. There was maybe 1 in my class, some years there were none. I'm now wondering whether those kids genuinely had dyscalculia. 

But kids who were 'behind' and in my lowest group?....about 3 or 4 every year. These are the kids I'm thinking about this morning. When I think back I wonder how they got to be 'behind'. In some cases they took a bit longer to grasp new concepts, or they didn't have the greatest ability to commit new learning to long term memory so learning facts was slow and hard work. But I also remember that many of those children weren't coming to school ready to learn. 

What some of those kids faced on a daily basis would shock many parents in NZ who are unaware of the level of dysfunction and difficulty in some homes. Some kids were arriving at school stressed, hungry, tired and possibly sick or in pain. Their minds were sometimes on their mothers who were so hungover they didn't get up that morning, their parents who were screaming at each other all night, or maybe the violence they witnessed or suffered. At the less extreme end they may have been up half the night gaming or there was a party that went late or maybe they had to be up late as they accompanied their hard-working parents to their evening cleaning jobs. Or maybe they were arriving for their third day at my school and this was the fourth school they had attended in three years. 

The point is, those kids were over-represented in my lower maths groups and my colleagues' lower maths groups. In some cases we were making great progress with them (along with all the other peripheral support) and then they would suddenly leave. That feeling when you arrive at school to be told they've gone? Empty. Helpless. Frustrated. 

In other cases they just weren't able to focus or learn effectively. They yawned. They hated being behind. They worked hard. They stared out the  window. They cheated to look 'smarter'. They were proud when they learned something new. They doodled on the worksheet. They loved being able to help someone else. They didn't ask for help. They always asked for help. They tried. We tried. 

When we talk about improving maths achievement for that bottom 20% of kids it seems to me that we don't talk about the real issues. Many of those kids don't come to school ready to learn. No amount of teacher education is going to change that fact. 

Learning.....it takes time...

Let's talk Professional Development for a minute...

Why is it that so often when a new concept or teaching skill is introduced to teachers they are often given 1 - 3 hours time to understand it, digest it, question it and internalise it.
A few staff meetings perhaps or a half-day in the holidays and then it's back to business as usual. Sort of. There might be a follow up discussion regarding how things are coming along or a visit to classrooms to see the new concepts in action but other than that, you're on your own.

It takes TIME to implement new strategies in classrooms. It takes TIME to reflect on how those new concepts will affect your teaching style, your teaching programme, your KIDS.

We don't expect kids to all learn new concepts at the same rate but for reason we often do that with adults. We allow children to have a say in what they need to learn next but so often teachers don't get that luxury.

We know that students who have a say in what they learn and how they learn....learn better. We know that they need time to grasp new concepts and furthermore they need time and support when applying new concepts. It's well known that application of a new strategy is harder than just understanding what it is. Do teachers get enough time and support when applying new strategies in their classrooms?

Here's my two- cents worth.....give teachers an opportunity to have some control over what they need to learn next and how they need to learn it. Give them time to understand a new concept/strategy and more importantly give them time and the support to APPLY it.

In my past life as a teacher the 'photocopier talk' went something like this:
'I was so inspired by that PD....I really want to try it out in my class....I just don't have the time to re-design my programme or get my head around it...I wish they would give us time to actually bring this PD to life....'

Possibly some missed opportunities there.

When Harry Met Sally

Okay, a very cheesy title but hopefully it caught your eye?

I recently read a fun quote on the net that said 'Dear Maths, we liked you so much better before you hooked up with the alphabet, sincerely, everyone.' You have to laugh...when Harry met Sally or Numbers met Letters sparks definitely flew for most people.

Ahhh algebra....I have to admit as a formula driven, list driven student, I loved algebra. But in today's more problem-solving driven context I'm not so sure I would have.

But that's not the point of this blog...I want to put something out there a little controversial...to play devil's advocate and I dare a secondary teacher or any teacher to rise to the challenge . I would love that. A little juicy disagreement is what education needs to shake things up and get conversations going.

My daughter (Year 8) suggested recently that she knows everything she needs to know academically unless there is a specific chosen area she needs to specialise in. Granted, I think this was going a tad too far...however, it did make me think. By the end of Year 10 my son will have a good understanding of basic algebra along with all the other maths domains. He can write poetry to some degree, he knows who Shakespeare is, reads material he enjoys and can certainly put together a fine piece of argumentative/persuasive writing when he wants something. So....what now? He's not sure what he'll do when he leaves college and therein lies the problem I guess.

Here's what many people secretly think....they think he doesn't need to know too much more algebra, that he certainly doesn't need to know how to write more creatively and he definitely doesn't need to know that an hours worth of homework a night is only just the beginning for him.

What if he needs algebra later? Or trigonometry? Or decides to become a novelist....well WHEN he's decided that, can't he branch into those areas when he's ready? When he's probably more developmentally ready? Maybe for the next couple of years he should focus on problem solving, being a decent citizen, making good choices, thinking critically and logically. I don't know. I certainly don't have the answers. I hear these kinds of comments from both children and adults all the time.........Maybe, just maybe these same topics that have been compulsory for so many years need questioning. Does a young man passionate about maths and physics need to be put off education because of a compulsory English class that delves deep into thoughts and feelings? Does a budding historian need to be put off due to increasingly more complex maths concepts that will rarely be used in their lifetime?

The Importance of Story-telling

Eureka! Who remembers the story of Archimedes discovering an important mathematical principal whilst enjoying a dip in the bath? The story of Archimedes observing the displacement of the water as he entered the bath and realising that volume could be measured by this displacement is far more memorable than reading the following:

"....the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces."

Stories are a wonderful way to engage students with both maths and science principles and to make them memorable.

Stories are able to bring possibly abstract principles to life and to explain them in unique ways that connect with students at their level of understanding and worldly experience. It's important to note though that not all students do have a similar world experience and therefore culturally responsive stories are essential.

I've both searched the internet and my local library to find titles that will inspire and explain Maths and Science principles for students at varying age levels. It seems to me that there are far more stories available for younger students which is a shame. But even then I admit I have struggled to find a series of books that I could turn to when introducing a new maths concept/principle or to address a maths misconception.

One of my favourite made up 'stories' I used in my own class was the story of 'Anne', the bank teller who didn't understand place value. Poor Anne would hand out the wrong money, give the wrong change, couldn't order numbers properly and much more! Anne had a rather ditzy voice I'm afraid and whenever we were facing place value problems the kids would always want to know 'what would Anne say?!'. So I would miraculously turn into Anne and suddenly know nothing at all about ones, tens and hundreds.....One of the children would have to help tell Anne why she was wrong. They loved it. They could also see the authentic context of place value when it came to money. 

What stories do you use in your classrooms?