Setting up the Conditions for Effective Teaching and Learning in Numeracy

Transcript

NARISSA LEUNG:  Hi, everyone.  Welcome to the Numeracy Webinar Series.  Lovely to see you all.  I've been looking at everyone saying hello on the padlet. It’s so lovely to see some familiar names there.  Very pleased with the effort from Malmsbury.  I believe the teachers are coming to us from their sick beds, so terrific work there. 

Welcome to the Numeracy Webinar Series.  Welcome back if you visited us in the Literacy Webinar Series and thank you for coming back.  Hopefully you'll find tonight's session as useful as the Literacy Series. 

So before we begin, I would like to acknowledge the traditional owners of the lands on which we all come to this meeting tonight and pay my respects to Elders past, present and future.  Tonight I am coming to you from the land of the Wurundjeri, but a special hello to the Dja Dja Wurrung people.  That's where I used to work, so hello to all the people in that area. 

Alright. So my name is Narissa Leung.  I'm an education consultant in Victoria.  I'm also a former primary school principal.  I work on a few of the projects here at Bastow and you can see my contact details on the screen.  So I'm @rissL on Twitter and I've recently set up this Oz Lit Teacher page on Instagram and Facebook.  That's because people were asking about texts, mentor texts, for teaching, reading and writing. And as soon as Kim Kirkpatrick sends me her maths list, I'll be able to start sharing some maths books on there as well.  So that's me and a big welcome.

Alright.  So if you are new to the webinar series, this is how it works.  Fortunately for all of us, I do not stand up here and waffle on for the whole entire time.  I break it into chunks and I know ‑ and a lot of the research says ‑ that it's through conversation that we get our deepest meaning out of things, and you can see I've put a quote up there from the book ‘Academic Conversations’. 

So we do have a back channel happening tonight.  It's on padlet and the lovely Laura ‑ hello to Laura's parents too ‑ sent out a link to the padlet tonight.  So if you would like to join the conversation on the padlet, it does really help to get feedback as we're going along and for you to contribute your ideas, your resources.  That's what helps to build our system and make it a stronger system.  So if you have resources that you currently use in your school for the things that we're talking about tonight or if you've trialled some practices or there's some links or things like that, it would be fantastic if you could share those in the back channel in the padlet.

The good news about the padlet is that you can access it after tonight.  We do have a lot of people joining us tonight, so sometimes the padlet goes really quickly and you think, “Oh, my goodness, I can't keep up with that”, but that's okay because you can call the website up again tomorrow and then you can start to go through and find some of those gems that people are sharing.

The other thing I just want to mention tonight is that if you are familiar with the webinar series from last year, we have listened to your feedback and we've reduced the time to one and a half hours.  So we will be finishing up at 5.30 tonight.  So that's good news for all of us getting home.

I understand that some people are attending in groups, which is fantastic.  Some people are attending by themselves, and that's great too.  That's why we have that padlet, so that you can chat to other people and not feel like you're alone in this.

So the agenda for tonight ‑ tonight is really about setting up the conditions.  So before we can have all of this amazing maths work happening in our classrooms, what are the conditions that we need to ‑ what are the foundations that we need to make sure that we've got happening in our classrooms to then build on really strong maths practice in our classrooms? 

So we're going to look at building a growth mindset for numeracy; we will be looking at understanding our students as mathematicians and sort of talking about student engagement in maths and what that might mean for our teaching; and we're also going to look at the Birth-Level 10 Numeracy Guide, which is the new resource that's recently been put up by the Department of Education.  So we're going to have a look at that at the end.  That might be brand‑new for some of you, some of you might have already had a look at it, so we're going to have a look at that at the end.

Our Understanding Goals for the session are ‑ the first one, you'll strengthen your knowledge of the importance of fostering growth mindsets and specifically related to mathematics teaching.  So we looked a little bit at growth mindsets in one of the literacy webinar series, but tonight we're looking at it through the mathematics lens.  You'll understand the importance of, and strategies for, gathering evidence about student learning and engagement, skills and knowledge in mathematics.  And, finally, you'll deepen your knowledge of the range of supporting resources.  So this is our success criteria.  We're going to come back to the success criteria at the end of the night, as all good lessons do.  I need to practise what I preach.

Before we launch into talking about growth mindset, I just want you to have a reflection about your own experience learning mathematics in school.  So you can see I've put a little cartoon up here: 

Help me figure out this homework problem.  What's 3 + 8? 

OK.  Assign the answer a value of 'X'.  'X' always means multiply.  So take the numerator (that's Latin for 'number eighter') and put that on the other side of the equation.  That leaves you with three on this side, so what times three equals eight?  The answer, of course, is six. 

Gosh, I must have done all the others wrong.  These problems seem awfully advanced for first grade if you ask me.

Okay.  So thinking about that, I am going to ‑ this is our first reflection, and if you have the resource pack next to you, it would be great if you could jot your thinking in the resource pack that Laura emailed out to everyone.  It's Activity 1 in the resource pack, just thinking about what do you remember about your experience learning numeracy in school, how have these earlier experiences influenced or impacted the way that you teach numeracy now, and the third one, what are your strengths and areas for improvement in teaching numeracy?  So we want to have a reflection on these things before we launch into our new learning.  And I would love you to share some of your thinking in the chat around this: what are your early experiences, how has that impacted you now? 

So I'm going to give you three minutes to engage in this reflection and I’ve got a little timer there, so I'm going to start that now and I'll come back to you in three minutes.

(Activity 1)

NARISSA LEUNG:  Okay. Thank you, everyone, for sharing your thinking in the chat there.  It's really interesting to see the range of responses that we've received and I think it's really important for us to think about what are the implications or how has my earlier experience of numeracy now impacted how I teach numeracy?  I think that's really critical to reflect on that and maybe to discuss that with other staff members.  So thanks so much for sharing your ideas in the chat.  It's very interesting.

So let's have a look at attitudes to mathematics in adults.  I found this fascinating because when I started to tell people, "Oh, I'm going to run a webinar series on numeracy", it was as if I was sort of carrying a confessional box around with me and everyone just started confessing all of their - how much they hated maths or how much anxiety they had around maths.  Lots of people said, "Oh, I'm so glad that's you and not me", that type of thing, and I was really fascinated by that.  So I thought it was something that we need to talk about tonight because this is very commonplace across not just our system but much wider than that.

So just having a look at some of the research around this, see this one here from Haylock:  "Findings indicate that many adults, in relation to mathematical tasks, admit to feelings of anxiety, helplessness, fear, dislike and even guilt.  The feeling of guilt is particularly marked amongst those with higher academic qualifications, who feel that they ought to be more confident in their understanding of this subject."  I find that so interesting because when we talked about literacy, I didn't have anyone saying to me, "Oh, I'm so glad that you're doing that and not me", but for maths it's really different.  Those ideas or those feelings of anxiety, helplessness, fear and dislike seem to permeate across the society.

I found the second part of that quote fascinating because, as a teacher, if you go out for dinner with people, at the end people always turn and say, "Oh, you're the teacher, so you can work out how much everyone has to pay" if we're splitting the bill and that's kind of when the dread sets in. You think, “Oh, my goodness, everyone is watching me, I'm supposed to know how to do this just off the top of my head”.  Maybe that's just me, I don't know. You can share your thinking in the chat whether that's happened to you too, but just that you think that because you have reached a certain academic qualification, then you should know how to do this.

In terms of our maybe parent knowledge, "Of course I'll punish him, but not until I figure out if he's on to something."  I really like that.

So then thinking about attitudes for our students when it comes to mathematics: "Mathematics, more than any other subject, has the power to crush students' spirits, and many adults do not move on from mathematics experiences in school if they are negative", which I'm very pleased to see that for a lot of you, even though you may have had a negative experience in your school, you've been able to turn it around through some way or another and I think really digging into how did you do that.  If you had that negative experience when you were going through schools - and I see someone referred to Shut Up and Be Quiet work sheets - how did you then change your view about mathematics because that's the knowledge that we're going to need when we're working with our own students. 

So "When students get the idea they cannot do math, they often maintain a negative relationship with mathematics throughout the rest of their lives."  I'm sure that you can think of the students that this applies to in your own setting.

This quote comes from Jo Boaler's book. She has a book called "Mathematic Mindsets" and she does a lot of work on growth mindset in mathematics. And she says that many people have been ‘traumatised’ by maths, which I think is a really strong word, but she said most of the trauma is fuelled by incorrect beliefs about mathematics and intelligence.  So if you can do this certain type of mathematics, and usually it's to do with recall, fast recall, that means that you're intelligent, and if you can't do it, then that means that you're not intelligent. 

Unfortunately, these beliefs do permeate our society and are often reinforced in different things.  For example, in Jo Boaler's work, she talks about the first time that the Barbie doll could speak, some of the words that she said were, "Maths is hard", or t-shirts that you can buy for children that say "I'm too pretty to do maths". So just these constant reinforcements about the difficulty of maths and how hard it is and kind of turning us off wanting to do it.

So talking about maths anxiety, it's a real thing and it manifests itself as an unpleasant emotional response to maths or the prospect of doing maths and is more common in women than in men, which I find really interesting.  There's a lot of research to back that up.  When worries and self-doubt occur, thinking and reasoning can be compromised.  And the research suggests that that whole idea of having the maths anxiety, not only do maths-anxious people avoid participating in maths, but they often perform more poorly than what they're capable of doing.  Part of that is because of the fight or flight response in the brain, that when the anxiety builds up and they start to tell themselves "I can't do this", even though they actually are completely capable of carrying out the task, that stops them from being able to perform to show that they are able to achieve that task.  And maths anxiety has been recognised as an impediment to maths achievement. 

So I think that's really important for us to recognise as teachers and to be constantly asking ourselves: if this is the case, what are the implications for us as teachers?  What does this mean for us when we're working with students who may come to us with maths anxiety?  Or with our parent community, who might have these anxieties around mathematics, how can we work with them to role-model to our students the attitudes and the beliefs that we want them to have around mathematics?

So just in addition to - this is another study that I thought I'd draw your attention to just adding on to that idea that the research suggests that females have more maths anxiety ‑ it's more prevalent in females than in males.  This was a study on year 1 and 2 students and the anxiety of the teachers who were teaching them.  It was an American study.  The teachers were female teachers.  The study wasn't conducted because the teachers were females.  It was conducted with year 1 and 2 students and all of their teachers happened to be females. 

What they found in the study was that at the start of the year, there was no relationship between the amount of maths anxiety the teacher experienced and the student beliefs around mathematics.  But by the end of the year, as the teacher anxiety increased, the students started ‑ by the end of the year they'd formed the belief that boys were good at maths and girls were good at reading.  So the level of anxiety of the teacher impacted the student beliefs around mathematics and it also impacted their achievement in mathematics.  So I think the implication for this is that we have to be aware of what are our own anxieties around mathematics and how might that be impacting on our students, their beliefs and their achievements in mathematics.

 

Well, I've painted a really grim picture at the start.  Welcome!  So what can we do about it?  That's the question that we're all wondering.  So you can see here that Haylock and Boaler and lots of other educators and mathematicians and researchers suggest that we need to change how we approach maths teaching with our students.  So we need to shift perceptions of teaching mathematics away from the notion of teaching recipes and more towards the development of understanding.  And I see a few of you in the chat before said that when mathematics was taught in a real - or made links to real‑world learning, that's when it made sense for you.  So that's what we're talking about, moving away from recipes and really moving towards numeracy in the real world.

I really like this quote from Jo Boaler.  She says: "Teachers need to offer mathematics as a learning subject, not a performance subject."  I think there are some real implications for us as teachers to be constantly reflecting on what is the mathematics ‑ what's the beliefs and attitudes that are coming out of the way that I'm currently teaching mathematics?  Am I promoting it as a learning subject or am I promoting it as a performance subject? 

In her research there, she said that students thought maths was more about answers than it was about learning, so that probably gives us something to reflect on, to think about, intentionally or not, what are the messages that we're sending our students around mathematics and numeracy?

So we're just going to watch a short video on Jo Boaler explaining the growth mindset and mathematics.  While this video is on, I would love to see what your thinking is in the chat, how you're connecting to what Jo Boaler says, or if you've got resources or how have you worked with this in your school, pop your thinking in the chat.  Let's have a look. 

(Video played):

Hello.  So I'm here to tell you that what you have believed about your own potential has changed what you have learned and continues to do that, continues to change your learning and your experiences.  So how many people here ‑ let's get a show of hands ‑ have ever been given the idea that they're not a math person or that they can't go on to the next level of math, they haven't got the brains for it?  Let's see a show of hands.  So quite a few of us. 

I'm here to tell you that that idea is completely wrong. It is disproven by the brain science, but it is fuelled by a single myth that's out there in our society that's very strong and very dangerous and the myth is that there's such a thing as a math brain, that you're born with one or you're not.  We don't believe this about other subjects.  We don't think we're born with a history brain or a physics brain.  We think you have to learn those.  But with math, people - students believe it, teachers believe it, parents believe it.  And until we change that single myth, we will continue to have widespread underachievement in this country.

Carol Dweck's research on mindset has shown us that if you believe in your unlimited potential, you will achieve at higher levels ‑ in maths and in life ‑ and an incredible study on mistakes showed this very strongly.  So Jason Moser and his colleagues actually found from MRI scans that your brain grows when you make a mistake in maths ‑ fantastic.  When you make a mistake, synapses fire in the brain and, in fact, in the MRI scans, they found that when people made a mistake, synapses fired.  When they got work correct, less synapses fired. 

So making mistakes is really good and we want students to know this, but they found something else that was pretty incredible.  This image shows you voltage maps of people's brains, and what you can see here is that people with a growth mindset who believe that they had unlimited potential, they could learn anything, when they made a mistake, their brains grew more than the people who didn't believe that they could learn anything.

So this shows us something that brain scientists have known for a long time, that our cognition and what we learn is linked to our beliefs and to our feelings, and this is important for all of us, not just kids in math classrooms.  If you go into a difficult situation or a challenging situation and you think to yourself, "I can do this, I'm going to do it" and you mess up or fail, your brain will grow more and react differently than if you go into that situation thinking "I don't think I can do this".

So it's really important that we change the messages kids get in classrooms.  We know that anybody can grow their brain and brains are so plastic to learn any level of maths.  We have to get this out to kids.  They have to know that mistakes are really good. 

But maths classrooms have to change in a lot of ways.  It's not just about changing messages for kids.  We have to fundamentally change what happens in classrooms and we want kids to have a growth mindset, to believe that they can grow and learn anything.  But it's very difficult to have a growth mindset in maths if you're constantly given short, closed questions that you get right or wrong.  Those questions themselves transmit fixed messages about math, that you can do it or you can't.  So we have to open up maths questions so that there's space inside them for learning.

NARISSA LEUNG:  Wow, so many messages in there I wish that I had learnt so many years ago.  It just makes a lot of sense to me and I think - just reading some of your responses in the chat, I think a lot of what Jo Boaler just talked about then made a lot of sense to you as well. 

My thinking around this is that we need to share this message with our parent community as well so we can work in schools to build a growth mindset, but if our students go home and a fixed mindset is being reinforced, then it's probably not very productive to building that culture of a growth mindset that we're trying to build with our students. 

So thank you to ‑ I see Lauren has shared a name of a book that might be useful for us to think about our growth mindset in mathematics.  So thanks to people for sharing in the padlet.  Just a reminder, if you do share in the padlet, it's a great idea to change your name from anonymous because then we can respond to you and say thank you for your contributions.

So let's have a look at fixed mindset, what does fixed mindset mean, and then we're going to look at what does growth mindset mean, particularly for students in mathematics classrooms.  So students with a fixed mindset, they thrive when things are safely within their grasp and we know these students in our classes who will have a go at things, but as soon as they think they're going to fail, they'll cross their arms and say, "I'm not doing that" and often won't even have a go at doing whatever it is that we've asked them to do.  Anything where they might come across as failing or they see that they might flop or fail in front of other people, they often will steer really clear of, and for me in my experience, nd particularly this has been boys, it has been a strong experience with boys, and sometimes boys with ADHD or something like that where they just don't want to fail.  So "Yes, I'll do things that I know that I can easily accomplish, but anything in that grey area, I'm not even going to have a go at doing that".  So if things get too challenging, when they're not feeling smart or talented, they lose interest and find other ways to not engage in the task.  And asked when they feel smart, it's "When I don't make mistakes, when I finish something fast and it's perfect", and I saw a few people in the chat when we asked about your experiences of learning numeracy in school, a lot of references to fast, especially multiplication tables or when we used to have races, we used to play maths footy, so we had to race against other people to say the answer to the multiplication that the teacher had said, plus I was forced to play for Collingwood and I just don't agree with that!  "When something is easy for me, but other people can't do it", so judging themselves and judging their own skills based on what other people can or can't do. 

So really for the fixed mindset, it's all about the now and perfection now.  So being smart is a quantity that you are or you aren't, and “Luckily for me I am, so that's great, until I get into the next year level and I start to get challenged and then I really struggle because I haven't ever had to be challenged before and I'm not really sure how to deal with it.”  So they often see challenges as something that's quite confronting and not something that they should really embrace and say, "Oh, this is going to make me a better learner."

So flipping over now to the growth mindset, so people with a growth mindset believe that their basic qualities are things that we can build on and it's usually attached to the amount of effort that we put into something and our perseverance and our grit really.  So they believe a person's true potential is unknown because it all depends on how much effort we put in, how much work we do, those types of things.  So there's no cap on our potential.

Success for these people is about stretching themselves and really embracing challenge and moving forward and seeing that as a really important part of learning and growing as a person.  So we're focused on becoming smarter, but it's not an end point, it's a constant journey, and these students or these people thrive on challenge.  The bigger the challenge, the more they stretch.

So another bit of growth mindset research ‑ this is one of the many research articles around growth mindset and student achievement, but in our current climate, especially in Victoria, where we sort of talk about every student, every postcode, and the Minister is really passionate about ensuring that all of the students in our state have access to high‑quality education and they all have great opportunities to succeed, I think this study is really important for us to keep in mind. 

So this was a study of a nation‑wide sample of high school students from across Chile, so it was quite a large sample, and they wanted to investigate the effects of growth mindset on academic achievement.  So in this study they confirmed the thing that I guess is no news to anyone, that socioeconomic status does have an impact on academic achievement, but - there's a but; let's go to the next slide ‑ I've just pulled out two really important quotes from this study ‑ they also found that a growth mindset is a comparably strong predictor of achievement, and I think that is pretty huge.  That has some huge implications for us as teachers, particularly if we're working with students from a low socioeconomic background.  We can't just say, "Oh, well, they're from this background, so therefore that's why they're achieving how they are."  So growth mindset is a comparably strong predictor of achievement.

They also found in their study that students from lower income families were less likely to hold a growth mindset than their wealthier peers, but those who did hold a growth mindset were appreciably buffered against the deleterious effects of poverty on achievement.  So that really blew my mind when I read that because I think that has a whole lot of implications and it's really exciting for our kids that this research has found that for us. 

So I'm wondering what are your thoughts around this research, is this something that you have witnessed in your own classrooms or is it something that you're now going to take back and think, “Right, what does this mean for us and our work around growth mindset in the mathematics classroom?”.  Pretty amazing I think.  So I'm going to leave that – I’ll look forward to your thoughts in the chat on that one. 

Okay, so what are the teaching implications for us?  So we know all of the research. We know that our anxiety around maths might contribute to student achievements. We know that growth mindset does have a positive relationship with student achievement.  What does it mean for us and what are the implications for us as teachers? 

So, first and foremost, one of the most important influences on learning is the teacher's belief that all children can learn mathematics, and I think this is something that we need to reflect on to say, "Do I really believe that all of the students in my class can learn mathematics?  Is that something that I believe and what are the actions that I'm taking in class to demonstrate this belief to students?".  So I think that's something that is probably a good discussion to have in the classroom. 

The other thing I would add is that I think we need to have a belief that we ourselves can continue to develop our numeracy skills and knowledge and that that is a constant ‑ as it is with literacy, that's a constant journey that we're taking and that we should be excited about ourselves.

So it is critical that, as we are role models, we ourselves model growth mindset in mathematics and that's in the things that we say, it's in the choices that we make around ‑ even the choices that we make around time.  So on our timetable, I definitely cut out time for literacy, but when someone says, "Oh, there's an extra PE lesson; who wants it?" and it's maths, I think, “Oh, actually, yeah, we'll go out for PE instead.”  So it's all those messages that we're sending to students about mathematics, all the tiny little things that we're doing that are sending out beliefs.

The other part about this is that if the adults around the children need to role model growth mindset and believe that everyone is capable of achieving in maths, how do we bring our parents on board for that?  So I would love your thinking in the chat around how do you bring parents on board with modelling and supporting a growth mindset in mathematics because I think that's a really huge part that we probably haven't got right across the State just yet, although ‑ a little taster for later on ‑ in the numeracy guide, we're going to have a look at some of the resources that might help us for that.

So researchers and academics suggest that one of the things that we can do as teachers is to reflect on the elements of a growth and a fixed mindset in our own teaching and to work out what might be some of the triggers for us that put us into a fixed mindset style of teaching.  So you heard Jo Boaler refer to before - she said that if we are only giving sort of short‑answer questions in mathematics, then we are reinforcing that fixed mindset.  So what are the triggers for us where we find ourselves accidentally slipping into a style of teaching that reinforces a fixed mindset? 

So I've put an example here.  This is from Sun's research.  I've put an example here ‑ so the situation is that when we encounter students making mistakes or encountering struggle, our fixed mindset trigger for this is that we might not want our students to feel embarrassed, so what do we do?  We avoid bringing attention to them and we tell them it's important and then we quickly call on another student so that we can reduce the time that that student is sitting with that uncomfortable feeling of not having the right answer. 

A growth mindset reframe for that, suggested by Sun here, is that we use that opportunity to help the students to see that that mistake, as Jo Boaler talked about before with all the synapses firing, is a really exciting part of learning and we can move forward in our maths knowledge if we acknowledge it and we talk about it and we work out how you came to have that, how you came to have that answer, so rather than kind of just skipping over it and moving on to the next person until we get the answer that's in our heads so we can move our content forward, holding it there and sort of pausing in the challenge and discussing that.

The thing is that's all good and well, but we have to have a culture where that's okay and where that's not embarrassing and where we all have this common understanding that mistakes are good and it's good to talk about them.  So here, "Before children can become interested in maths, they have to be comfortable with it.  They must perceive their environment as physically and psychologically safe before learning can occur."  There are a lot of implications from that. 

So share in the chat how are you doing this in your numeracy classroom, how are you creating that culture where we can share, "Oh, I got this wrong; this was my mistake; can anyone help me with this?", because that doesn't just happen by itself, and if we don't invest in building that culture, then we're not going to get to the point where we can openly talk about the mistakes that our students are making.

Here we go: "I know it's wrong; I'm just waiting for the autocorrect."  Wouldn't that be nice just to have a carry‑on autocorrect?

So supporting growth mindset, what are the other things that we can do in our maths classroom to support a growth mindset?  We can focus on growth mindset language, and I saw someone in the chat before talked about that key word of ‘yet’.  So when we have our students saying, "Oh, I'm terrible at multiplication; I can't do that", then adding just that one word on the end, ‘yet’, just to constantly reinforce that we might not be there at the moment but we can get there with effort, persistence, drive, grit, all of those types of things.

We can provide feedback based on effort rather than sort of the praise feedback of, "You're a really smart student" or "It's so great that you already knew that", those types of things, so just directing our feedback towards the effort that people have put into things; place more emphasis on sense-making and less on procedures; and this one, the task predicts performance, so anyone that has been in Leading Literacy will know exactly what I'm going on about here.  This is Richard Elmore's work, ‘the task predicts the performance’.  So this is as teachers that we need to reflect on, “What did I ask the students to do in maths today or in numeracy today, and if the students completed that activity exactly as I asked them to, what skills, knowledge, attitudes and beliefs would they have developed as a result of that?”.  So if I asked them to engage in this task where they had to talk to other students and justify how they got their answers, what skills and knowledge and beliefs and attitudes would they have developed as a result of that, and really looking deeply to see: are we creating tasks in our class that are developing the skills and attitudes that we want our students to be demonstrating?

And then finally I've said: model how we make mistakes ourselves. Very important and it's even better when we realise that we've made a mistake and then we can use that as an example.  So we need to provide our students with the rich, deep and engaging instructional tasks that cause them to really think and grapple with challenge so that we can have that excitement about overcoming the challenge. 

Some schools talk about the learning pit.  That's James Nottingham, his work. He calls it ‘the learning pit’.  I'm not suggesting that everyone has to go and adopt the learning pit, but I am suggesting that having a common language around growth mindset in your school is a benefit for the teachers and for the students and for the whole community.  This is one approach, so referring to the challenge of learning as being in the learning pit.  And I know in the work that I've done in lots of schools, it's really interesting to hear ‑ even at PD, teachers will say to each other - they'll turn and say "Oh, I'm in the learning pit here", but it's seen as something that's good, to be in the learning pit, because it means that they acknowledge the struggle, but they know they're going to go back up the other side.

So I'm just going to play this short video.  It gives an outline of what the learning pit is.  But it's just so that you can be thinking about what's our frame of reference?  When we're talking to our kids about challenge, what's the common vocabulary we're using across our school so that students accept that challenge is a really exciting part of learning.  Let's have a look.

(Video played):

Michael Jordan is a very famous and successful basketball player; in fact, the most successful North American athlete of all time.  He holds the NBA record for the highest regular season scoring average and highest playoff scoring average.  He came from humble beginnings, and to get where he did, he needed to be focused and to work hard. But to do this and above all else, he needed to be resilient.  To be resilient means to be able to withstand or recover quickly from difficult conditions.  He once famously said, "I've missed more than 9,000 shots in my career.  I've lost almost 300 games.  26 times I've been trusted to take the game‑winning shot and missed.  I've failed over and over again in my life and that is why I succeed." 

He recognises that failure is a necessary part of success.  Without failing, you can't learn because it's when we're confused, when things go wrong, when we hit a problem and don't know how to fix it, the real, deep and powerful learning begins. 

To help illustrate this idea, it's useful to think of this as a visual metaphor called the learning pit.  First we're faced with a problem, given a task or introduced to a new idea.  We may feel apprehensive or worried that we may not be able to do it.  It's at this point that we have to leap into the pit.  The only way to resolve the problem is to move forward, jump in and have a go.  Sometimes this can take guts and determination. 

When we first face obstacles in a task and we find ourselves at a dead end, we're at the bottom of the pit.  You may feel that you don't want to speak out in class for fear of getting the answer wrong or are so confused you don't know how to start.  It is at this point that we must move through this sense of fear and begin to try.

Once you start applying different approaches or techniques, you begin to learn.  You'll make mistakes, but once you have, you'll be able to think about what went wrong and how to fix it.  This way you will develop a much deeper understanding of what you're learning. 

The learning pit is about learning to know what to do when you don't know what to do.  When you're finally out of the pit and see what you've achieved, you'll feel an overwhelming sense of achievement and satisfaction, but even more important than this, you will have developed resilience, which will continue to help you long after you've left school.  The next time you face a learning problem, go on, jump in.

NARISSA LEUNG:  I think that does a really good job of just explaining very briefly the idea of the learning pit and it's so fantastic to see people sharing resources in the padlet about the learning pit and also the other resources available from Jo Boaler.  She has a lot of things out there.  She runs a website YouCubed with lots of resources and I think we need to use these resources for ourselves as much as we do with our students.

Speaking of resources, here are some of the ones that I recommend.  A couple of people have referred to Carol Dweck's work on mindset.  That's the growth mindset book that started all of this thinking really.  Then Jo Boaler's work ‘Mathematical Mindsets’ and the one on the far right, ‘The Elephant in the Classroom:  Helping Children Learn and Love Maths’, both worthy reads.  And if you want more information about the learning pit, that's James Nottingham's book ‘Challenging Learning’.  So there's some of the resources.

The other thing I was going to say ‑ I forgot to put it on the slide ‑ is when we're thinking about our own anxiety around mathematics, we have to work out how we can address that and how we ourselves can start to see the beauty in mathematics.  So ‘Woo's Wonderful World of Maths’ is a good place to start to build our own understanding around the ‑ yeah, it really is the beauty of maths out there in the world.  He talks a lot about the things out in the natural world. 

I was very lucky to have some really passionate maths teachers, especially in primary school, so I was exposed to the beauty of maths and how it helps us to make sense of the world early on.  So if you're thinking about “How am I going to build my own knowledge around that?”, that's one place that you could start.  Otherwise, the numeracy guide that we're going to talk about later is another place.

So I'm going to give you three minutes now just to reflect.  We've had a lot of information over the last 40 minutes, so let's stop and reflect to say what have I learnt, what's confirmed for me, what's new, and to share some of your growth mindset‑related resources in the chat.  So I've set the timer and I'll be back in two minutes 40 seconds.

(Activity 2)

NARISSA LEUNG:  Alrighty.  Thank you, everyone, for again posting your thoughts in the chat.  It certainly helps me, otherwise I don't really know what's happening out there.  Interesting, I liked what Helen shared about how she shared her struggle with her own mistakes and how the students said that she'd become a better maths teacher from last year. Very funny. I had a little laugh at that.

So now we're going to look at student engagement and learning about our students as mathematicians.  So we’ve got here, "You know, for something that sounds like two killer robots, this is really disappointing.” Very funny.  It's a maths joke, everyone!  Come on.

I love this quote.  I'm going to read this out to you because it resonated with me in terms of when we're leading a change in our school, this quote really comes to mind: "A tale describes an old man digging frantically in the night, the ground around him illuminated by a lantern on the wall in front of his house.  'What are you looking for?', inquired a friend.  'The gold coin that I lost', replied the old man.  'How did you lose it?', asked his friend.  'I lost it while working behind my house', he said.  'Then why are you looking for it in the front?', wondered the man.  'Because there's enough light to dig here', answered the man.

This for me, I just think, wow, this is how we have approached change in our schools for a long time because we're so busy in schools.  We've got our meetings and our curriculum maps and our proficiency scales and our moderation and our this and our that and we don't have the time to look and find out where should I actually be digging because that takes time to work that out.  So we feel pressured to sort of implement quick fixes in our schools because we're always trying to work out - to improve what we're doing for our students.

So this whole next section that we're going to talk about now is really about working out where do we need to start digging.  So if you're coming tonight thinking, “Yeah, I want to change what I'm doing in maths”, or “My students aren't achieving the growth I want them to achieve in maths”, we're going to talk about that now to say: “Let's work on the areas that are going to make the difference for your students.”

So enter the FISO improvement cycle.  I'm hoping this isn't brand new to you, but if it is, that's okay. Welcome.  So we're talking about the FISO improvement cycle which has four phases and tonight we're going to look at the first one.  Basically, this improvement cycle encourages us to take an inquiry approach to whatever it is that we're doing in our schools. 

So we are going to start with the evaluate and diagnose phase and this is where we really need to force ourselves to stay in this phase and actually this is a really good time of the year to be doing this because we've all just ‑ maybe all of us, if you do six‑month reporting, you will be right across what's happening with your students because you've just been knee-deep in reports and really working out what has happened over the last six months.

So we need to ask ourselves, and sometimes this is a hard question to think about: are we digging in the right spot?  So are we spending our time and our resources on the areas that actually need attention?  So when we say to ourselves, "Oh, I've got to change my maths instruction; it's just not working", or if you're a school leader and you're saying, "Right, our maths data isn't improving" or "our growth is not as strong as we want", are we spending our time working out what is it that has led to our data looking like that?  If we don't – otherwise, we're going to be digging in the wrong spot.  So we need to be working out: are we digging in the right spot? Are we putting our shovel in where it's going to make the most difference?

So for the evaluate and diagnose phase, I am instructing you all: put down your shovels.  Put them down. Lock them away. No digging for this.  We are just finding out what's happening in our school.  So we need to slow down to speed up, and that has to be our motto here: slow down to speed up.  Work out where it is that we actually need to start digging and take the time to work that out before we go, "Right, let's adopt that school's program because it worked for them."

So I'm going to encourage you here to put your shovel down and pick up a magnifying glass - this is your new tool - and start to work out what's happening for your students.  So who are our students?  Who are they mathematically? What's working for them? What are their attitudes and beliefs around mathematics, now that we know that that's actually a really important part of the equation – oh, that's a bit of a maths joke I think there.  Pretty impressed with my own maths work!

So in order to evaluate, we need to have a clear idea in our mind of the end point.  So if you think about in the Literacy Webinars we talked about students need to know where they are now, where they want to be and then work out how to close the gap, this is exactly the same.  So, as teachers, as school leaders, we need to work out ‑ sort of backwards planning. So what do we want our students to be able to do, know and be by the end of the year, or if you're talking in terms of school leadership, when our students graduate from our school, what do we want them to do, know and be in terms of mathematics and numeracy?  It's a big question.  It's really big and it needs a lot of discussion.  But we have to be clear on that end point so that we can sort of work our way backwards to say: okay, well, if that's where we want them to be at the end of year, we want them to be believing that maths is a really exciting subject and that it's very applicable out in the real world and all of those types of things, we now need to work out what's the current situation? What do our students currently believe about mathematics?  Do they believe that mathematics is all about answering things quickly or finishing work sheets or having races?  So work on getting that end point in mind first and then we're going to start talking about: how am I going to gather evidence of that? 

So if you open up your resource pack, Activity 3 in there is asking you to think about what do you want your students to be able to do, know and be?  So for be, it's like the attitudes and beliefs in terms of numeracy ‑ if you're doing it as a classroom teacher, then maybe you'll think: “When they leave me at the end of the year, what skills, knowledge and dispositions do I want them to have?”.  If you're doing it as a whole school, be thinking when they leave our school what do we want them to do, know and be, and I would love you to share some of your thinking in the chat. 

So I'm going to put the timer on for three minutes.  This obviously is a discussion that needs to go for a lot longer than three minutes, but tonight we're just going to have a little taster of it.  So I look forward to seeing your do, know and be in the chat.

(Activity 3)

NARISSA LEUNG:  Okay. Wow. so interesting to read everyone's do, know and be in the chat.  I really loved ‑ Sandra commented that she's sitting there by herself ‑ welcome, Sandra ‑ and so she said that she'd be confident to answer her do, know and be but she's really keen to go and ask the team what their do, know and be is.  That's a really great point, Sandra, because we have to have a consistent message across our school for all students to benefit.  It's not okay for every teacher to have individual do, know and be for this.  So we have got to be all on the same page for this so we're sending out the same message to our students.

Now that you've done the heavy lifting in terms of thinking about the end goal, “What do I want my students to achieve or do, know and be by the end of however long?”, we have to go about starting to collect some evidence to say, “Okay, well, if that's what I want my students to do, know and be in six months' time or by the end of their primary school or high school years, what's the current situation?”, and that's what the evaluate and diagnose phase of the FISO improvement cycle is, saying what is the current situation and how do I know, and we need to know because we need to measure ‑ when we go about and make some changes, we need some data and evidence at the start so that when we do make some changes, we can pull that same data and evidence out and compare it to the new data and evidence at the end of the cycle.

So what do we know about our students as mathematicians? What do we know about the ‘be’ part?  How do we know what their beliefs and attitudes are and have we had discussions with our students about this before?  So let's have a look at some of the ideas around this.  First and foremost, we need to realise and acknowledge that data isn't always numbers - or data aren't always numbers, I should say.  So: "Evidence isn't just a number.  Evidence of learning is much more than just student test scores.  It includes what a student can write, make, do and say, as well as what they can't.  Teachers can collect this evidence in many different ways.  They can do so formally through standardised assessments, traditional teacher‑set tests and performance assessments ... or they can do so informally through interactions with students and by observing their behaviour in class, for example.  Different types of evidence are necessary to build a complete picture of each student's learning."  And that's what we really want to be talking about now.  We want a complete picture of the student learning.  So, hopefully, if you're on the six‑month reporting cycle, you'll have a pretty good picture of the student learning, but you might find that you need to add in the student attitudes and beliefs part to that data set that you've got about the students.

So what can we do about it? How can we go about collecting this data and evidence?  I've put some examples up here, many of these that I've used with my own students in the past.  So one is a student survey.  I'm going to give you some examples.  And people who know me from Leading Literacy or from working in the schools will know I always love a good student survey because you can never underestimate or overestimate what the students are going to tell you.  They are the experts on themselves and their learning.  They have a lot to say and they are very honest generally when they respond to these student surveys.

Student interviews is another really great source of data.  It doesn't mean that you have to go and interview every student in your school.  So when I was principal, we pulled a couple of students out of each class and conducted a really brief interview around numeracy, and the information that we gained from that was eye opening.  So one of the questions that we asked our students was to bring along a ‘something’ that represented maths for them. And at that stage ‑ we were at the very start of our maths journey at that stage ‑ we had quite a number of students bring a work sheet.  We had a few bring a calculator, a couple bring dice and say that they brought it because they play maths games. But the number of students who brought a work sheet was a real eye opener for us and then we asked a follow‑up question around "Why did you choose this?". 

Maths biography is another idea, particularly for secondary students, and I'll show you an example of one of those in a minute.  Classroom observations ‑ we seem to devalue or we don't place enough value on classroom observations.  We are professionals.  We've been trained in the role that we have.  We need to value our own observation.  So it's probably a bit late to have this discussion. We should have had this before our report‑writing cycle because I find that people always want some type of test that spits out a number that says, “This student is working at level 4.5.”  We need to take into consideration our professional observation of that student's skills and attitudes and beliefs. 

Feedback analysis ‑ so feedback analysis is looking at ‑ sometimes it's just flipping back through the maths book or even recording your own feedback, verbal feedback, and saying, “Well, what was I focused on in the feedback?  So was I giving the feedback that would have built growth mindset or was the feedback that I was giving reinforcing a fixed mindset?”.

Task analysis ‑ we're going to have a look at that one in a minute.  And then the ones on the far right, they're more sort of if you're thinking about whole‑school change, so observations, student and teacher observations. So a student observation is ‑ at our school we had three people come into the classroom.  We each watched a student, so one of us watched a high student, a medium student and a low student, and we just watched to see what happened for them in the numeracy lesson. So what did they do, what didn't they do, how did they engage with the task?  And we just wrote down exactly what they did.  And that was really interesting and really helped us to critically look at ‑ at that stage, our growth data wasn't terrific, especially for our high‑achieving students.  When we did that student observation, we looked at the tasks that our students were engaging in.  So I was following the high student.  We could really see that we weren't pushing these students.  So we got some really great data out of that.

Photos is another one.  From my Leading Literacy, you will know I always talk about photos, but photos of what does a lesson across the school ‑ what does the start of a lesson look like, what does the middle of a lesson look like and what does the end of a lesson look like, and sort of laying that out to say what's the numeracy journey for our students through our school.  So are we really heavily focused on using manipulatives in the juniors and then we get to the seniors and we just fall off the cliff and go straight to only using abstract?  In our year 7s, do we have manipulatives? And then by the time we get to year 9, we don't see any of those.  So what's the journey for our students through our whole school, what's the experience for them?

Classroom environment ‑ what do the walls say about how much we value numeracy in our school, what does the corridor say about it, what does the newsletter say about it?  Do we even value it?  Do we mention it at our assemblies, do we mention it in our newsletters, all of those types of things.  And then at a leadership level, what's the teacher talk around numeracy?  And I saw some people in the chat were talking about ‑ you know, lots of people say, "Oh, I hate maths" and hopefully after we talk about this idea of the growth mindset and the teacher anxiety impact on students, we might be able to change some of those conversations.  So these are all different examples of evidence and data that we can gather to say: what's the current picture in our school?

I think this is really important because this helps to guide us to work out where we need to be digging.  We might start saying ‑ if we don't really go deep in the evaluate and diagnose, we might start working on teaching a specific type of maths that isn't even addressing the problem.  So through the student survey and the interviews or the maths biography, we might realise our problem is actually an engagement problem, and that's where we need to be spending our time first before we go and work on this other problem.

So let's have a look at a couple of them.  Student survey ‑ these are some of the questions that you might ask.  What do good mathematicians do? That's a very important question because it tells you the messages, whether intended or not, that students are receiving about mathematics and mathematicians in their room.  So for us, when we were at the very start of our maths journey, our students were saying they finished things quickly, they finished the work sheet, they don't get anything wrong, like lots of those types of responses.  Of course, we never intended for our students to be having those thoughts around mathematicians, but it really gave us great data to reflect on to say, “Okay, this is what our students are telling us, and even though we didn't mean to send that message across to them, what can we do in our teaching to help students? We want them to believe this about numeracy, so what can we do to shift our student thinking from this over to our intended end goal?”.

“Do you like maths?  Why? Why not?”.  I forgot to add I always ask, “Are you good at maths and how do you know?” or “Are you good at numeracy and how do you know?” because I think that gives you data on the type of feedback and where do students go to get that feedback.  So if they're saying, "I'm good at it because last year I got a B on my report", then we know that ‑ well, firstly, that's a long time ago to find out. You're relying on data from six months ago. But we also want our students to know that they're good at numeracy because they know what being good at numeracy looks like and they can judge themselves against that, rather than sort of waiting for someone else to kind of dob them on the head and say, "You're good at it", "You're good at it", "You're good at it".  So we want to develop that student agency so they can decide themselves, "Well, I know that I'm good at it because I problem-solve, I stick with the challenge", all of these things.

“What is something that you're good at, something that you're not so good at?  How often do you get feedback?  When do you think you'll use maths or numeracy in your life?”. That will be an interesting one.  And I always ask, “What would you like to change about your maths lessons? “. You get some really fascinating answers for that and it's always really good data for teachers to reflect on.

So that's just some sample questions.  You would do this as a pre-survey from primary school right through to secondary and you could also do this as a post-survey because if you are working on building a growth mindset across your school, I would expect to see consistency in language in the responses students are giving in 12 months' time, if that's something that we're working on.  So that's one suggestion.

A maths biography, particularly relevant for secondary students, is just getting students to write down their history ‑ yes, writing in maths ‑ write down their history as a maths learner. So what's been their experience?  So you can see here, primary school, "I don't mind maths.  I had a really good teacher in year 2.  He loved maths and always wanted to try and show us how exciting maths was.  We used to do maths all the time with him.  I remember using the tens bundles all the time.  In grade 6 I had another teacher who really loved maths.  He had lots of bad maths jokes he used to use too.  I liked doing maths with him because he made it different all the time.  I remember learning about credit card interest with him", right through to down the bottom “Something I'm good at, something I'm not so good at and something that worries me”.  Wouldn't this be great data at the start of working with some students to find out what's been their history up until now and how can I use that in my teaching? How can this information help me to reach these students in a better way or in a more effective way?

And, finally, the task analysis.  We've looked at student attitudes and beliefs, so now let's look at the work that they're doing and what can we learn about the students' knowledge and skills through their actual work that they're doing?  So we're going to look at more of this in the other webinars. 

This is just an example.  I pulled these from NAPLAN practice questions, so they're probably seared into everyone's minds already.  So if we look at these questions – so the first one is a year 3 NAPLAN practice question, where might our students go wrong with working out the answers to these questions?  And this is the discussion that we can have with the other people in our team before we give these questions to the students.  So where do we predict our students might go wrong with these? 

So for the first one, a movie ticket for one adult costs this; a movie ticket for one child is three‑quarters of that. What are the things that might trip a student up in this?  It might be our students haven't been exposed to three‑quarters written in words like that before because all of our work has been writing with a 3 over a 4.  So that might be one of the things that trips it up.  So having that discussion first and then we give the task to the students and then we talk to them about how they came to have that answer.  What can we learn about our students and their maths knowledge and skills through doing a task analysis?  So rather than sort of dishing out the whole entire test, then we're just going to focus on a couple of key questions. 

This would be great to do now when you know what your topic is for next term.  So, I don't know, “We're studying shape next term. Let's throw out a couple of questions like this now so that we can analyse what do our students already know about shape before we go and teach them a whole bunch of stuff that they already know”, or “What don't they know about shape so that we know we have to address that when we're teaching that topic next term.”  So this would be a great activity to do in a team to work out basically where to dig, where do we need to start digging with this topic.

Scott asked, "Where's the opportunity for us to see their thinking?”. Obviously, that one is a NAPLAN practice question, so I would put underneath there you would ask them to explain their thinking or you’d speak to them about it while they're doing it.

So once we've thought about where we want our students to be, we've gathered our data and our evidence to see what's the current situation, then, and only then, can we start to think about: where do we need to start digging with some more accuracy?  So there we go, we've moved over here.  Now you can start getting out your spade.  So we've really learnt a lot about our students to say, “Right, this is who they are, this is where we want them to be, now how can we work on closing that gap?”. That will stop us from adopting the next school's program because we don't know why that school adopted that specific program.  It could have been to address a whole bunch of other symptoms that our students don't even have or that our school doesn't have.  So we've got to really know what's happening in our own setting to work out which ‑ not medication, but what's our diagnosis in our own setting.

Alrighty.  Wow. That was a lot of information.  I am going to give you ‑ I'm going to shorten it, two minutes, just to do a reflection in your books there and I would like you to share your triangle response in the chat. So what's the most important thing that you've been thinking about as a result of this discussion around evaluating and diagnosing student engagement and student needs?  And I'll come back to you when the timer has got 1 minute left on it.  That will test your ability to watch the clock.

(Reflection activity 2)

NARISSA LEUNG:  Okay.  Well done to all those people who realised there was a minute to go.  Really interesting to read people's responses in the chat.  Thank you again for sharing.  It's been so great tonight how willing you all are to share and to share resources as well.  That is how we develop as a system.  So thank you for that. 

I am very excited to hear that lots of you are thinking about, "Right, I need to go back and think about student voice" because I think for too long, numeracy is over here and student voice is over here.  So let's join those two things together and see what magic happens out of that.  So maybe in our future webinars, I'd love some feedback on how that's gone for you and your students.

And now I have 15 minutes to do a whirlwind tour of the Birth to Level 10 Numeracy Guide.  So here goes.  And I do apologise, this is a lot of me talking.  Just put it in the chat, let me know if you've actually had a look at the Birth to Level 10 Numeracy Guide.  I am calling this an official opening.  I have absolutely no authority to officially open this thing, but I've just done it.  If I had curtains, this is me pulling them back, here it is: Birth to Level 10 Numeracy Guide, with the Numeracy Teaching Toolkit to follow.  So that's a different thing and that's going to come in in around term 3.  So I'm sure we'll be talking about that in a future webinar.

So here it is.  This is what the front page looks like.  The web address is up there, but like all good things on the web, go to Google, type in ‘Birth to Level 10 Numeracy Guide’ and you'll get there.  It's on the numeracy portal as well. 

So the great thing is all the resources of on here align to the Victorian curriculum.  It's heavily based in research and evidence, so we don't need to go digging for that ourselves, and there's also a section specifically for mathematics in the home or numeracy in the home, which is very exciting and might help us to build stronger and more positive partnerships with parents and particularly for things around growth mindset.

So we're just going to watch a short introduction video.  It goes for 90 seconds.  Let's have a look. 

(Video played):

Traditionally, professional learning for teachers is print based or provided after school.  But the world has changed and, along with it, how and when educators access their professional learning.  The Victorian Department of Education and Training's online Birth To Level 10 Numeracy Guide has changed the way we provide you with numeracy and mathematics professional learning. 

The guide places you at the centre of self‑directed learning experiences available online at a time that best suits you.  It presents dynamic approaches to developing learners' numeracy across developmental levels and curriculum areas.  Numeracy topics are broken down so you can learn about and engage with a variety of resources flexibly in bite‑sized chunks that take 20 to 30 minutes.  For example, you can focus on the four proficiencies to build capacity and confidence to teach curriculum content and support planning for numeracy teaching and learning.  Or you can focus on the 10 high‑impact teaching strategies, or HITS. 

The Numeracy Guide was co‑designed with teachers for teachers and families to explore and discover numeracy through six numeracy focus areas.  Critically, the Numeracy Guide has an explicitly curated section for families to support children and young people's numeracy learning at home. 

Explore the Birth To Level 10 Numeracy Guide today and experience immediate benefits as you apply your learning to your own setting to support and improve children and young people's numeracy.

NARISSA LEUNG:  There we go.  So that is the Numeracy Guide in 90 seconds.  I'm going to go into it in a little bit more depth now.  So this is what the home page looks like.  You can see some headings across the top and we're just going to work our way across the headings.  This is so that you know what's there, so that you can know ‑ in the future, if you think, “Oh, actually, I might dig into some of that.”  The great thing, as you saw on the video there, lots of the resources here are designed for teachers to have a look at.  If they've only got 20 minutes, just go in, have a quick look and there's a short activity to engage in. 

So we're just going to start with the proficiencies.  There's a page on the proficiencies in the kit.  So we are going to go into more depth in the proficiencies in the next webinar, and Laura will remind me when the next webinar is and then I'll tell you at the end.  So have a look. You can go in there and do some pre‑reading, if you like, for the next webinar, but it does go into what proficiencies are.  And this is a really important part of our numeracy teaching.  That's why we're going to spend more time on it in the next webinar.

My estimation skills and my time skills are colliding right now and that's why I've skipped over it because I've estimated that I'm going to go over time if I stop and talk about it.  Let's see how we go. 

So, as you saw on the video, the numeracy focus areas - there are six numeracy focus areas:  developing number sense; exploring patterns and relationships; using proportional reasoning; understanding and using geometric properties and spatial reasoning; understanding, estimating and using measurement; and exploring chance and data. 

So let's just dig into one of those a bit deeper.  So we'll click on this one: ‘developing number sense’.  When you do click on that, it goes into some general overview.  So it gives you a bit of an idea about what does it involve, what does it look like in the early years through to the upper levels.  It's birth to level 10.  So it's not just primary; it's not just secondary. It's all of the way across, so what does this area look like across that spectrum, and that's good knowledge for us. 

Then you can scroll down to the bottom of the page and everything has been divided into these developmental stages, so birth to level 2, levels 3 to 8, and levels 9 to 10, and we know if we're teaching year 7, not all of our students are going to be working at level 7.  If we're teaching year 2, not all of our students are going to be working at level 2.  So this definitely helps us with our thinking around: how do I cater for all of the students that are sitting in front of me?

So let's have a look. What does this one look like at levels 3 to 8?  So in here, this is the idea of that kind of 20-minute snippet to build our own teacher content knowledge around this.  So we get a bit of an idea about what it includes, as you can see there, and then some everyday context.  So it's always linked back to the real world outside of the captivity of school; what's going on in the real world for developing number sense.  So you can make some links there.  You could use those links when you're talking to your students.

On the right‑hand side there's a little video there of a student estimating, or doing some estimating.  And this section I love.  They have a section of language related to this focus area.  Language in mathematics is so important and, in fact, it's so important, we're going to talk about it at the next webinar.  So we're going to talk about direct vocabulary instruction in the numeracy classroom.  But I love how there's a language box included in here so that we can be thinking to ourselves: “What is the academic vocabulary our students need access to in order to be successful in this aspect of numeracy?”.

So that was a very quick tour of the numeracy focus areas.  Let's have a look at the HITS areas.  So obviously there are 10.  I've only put six up here.  Well done, 10 take away 6.  It's because I like things to look nice and neat and even.  That's the only reason I don't have all 10 of them on there. 

So if we look at collaborative learning ‑ and I saw some people in the chat said that they want their students to be able to work collaboratively when they're talking about that future vision.  Let's have a look. What does that mean in a numeracy classroom? 

So when you click on that, it goes into the key elements.  Then it talks a bit more about who you can work with and it has information in here. I like this. It says: “working in a shared space is not collaborative group work” and “In the numeracy environment learners have defined responsibilities, they know what is expected of them and their role in the group to achieve the learning outcome.”  Particularly for collaborative learning, we kind of throw out all the knowledge that we have about Gradual Release of Responsibility and sort of make a lot of assumptions that everyone just knows how to work collaboratively.

So again, we can go down to exploring the developmental stage.  So if I'm talking about collaborative learning and I want to say, “What does that mean at birth to level 2?”, here it is.  There's actually a task here, Puddle Fun, and an example of a task that you could implement with your students.  With a video over on the right, you can see Sandy, a kindergarten teacher, describing her children engaged cooperatively in designing a bridge to cross a puddle.  Again, it's only a short snippet, so it's a 20‑minute activity for teachers. 

So you'll see here there's a purple prompt.  These are all of the way through the Numeracy Guide and these are really to get us to think reflectively around: what does this mean for me and my teaching?  So there's a reflective prompt.  The reflective prompts are even on the parent part of it as well.  So they've got some really good questions in there.

Scroll further down on that page and you can get to further resources.  So if I'm interested in collaborative learning in the birth to level 2, what are some other resources that I might want to access?  Here's a link to some other resources. 

And moving across now, we've got a whole tab on resources.  It's quite large.  There are a lot of resources in here, not as many as there are on the internet itself.  I can't remember. There's some ridiculous number of resources for maths.  So the idea behind this is that ‑ I'm going to call them hamsters, there's probably a more positive term to use, but the numeracy people at the Department have sort of curated a bunch of useful resources for us to reduce the amount of resources and so that we don't have to sift through all of the ones that aren't useful.

So on this page you can just type in a search or you can go to the page that looks like this.  You can see there's a filter at the top there, so you can say, “I'm just looking for resources around reasoning” or “I'm just looking for resources birth to level 2”, or you could try your luck at the bottom of the screen and have a look at some of the resources that are down there.  So some of these links link to other websites; some of these link to activities that you could use with students. 

If I filter it by developing number sense, what happens?  I get to an activity, a level 4 to 6 activity, around making cupcakes and it tells you on the right‑hand side where this resource has been drawn from.  So you might be able to go and visit the website or access the resource.

Again, there are reflective prompts for each of the activities, so "How might the practice of selecting specific students to share different strategies and solutions build other students' mathematical understanding?", "How would you use this resource in your context to encourage children and young people's reasoning?", so always asking us to reflect as we're looking at these.

The other part of the resource section is a glossary.  This is terrific.  This helps to build our consistent maths vocab across the school.  So, basically, you can access the glossary via the alphabet at the top and you just need to memorise all of the words in here and then we'll all be amazing.  Or you could just do it one at a time, so you can click on those and then it expands and gives you the definition.  But I think this is really useful because don't forget families have access to this as well.  So it's available to people outside ‑ you don't need to log in with your teacher details to access this.  So it's available to people anywhere on the web really.

Speaking of the home side of things, there's a page here "Numeracy at home" and in here there are some videos for parents.  Let's have a look.  There's a section purely on busting some common mathematical myths, how can I build my child's numeracy, helping with homework.  I can see a lot of use for this section.  I would be pulling these out and putting them in our newsletter or maybe using them at family maths nights, those types of things.

So let's have a look at some of the maths myths that are busted.  So you can see here “Most maths does not make sense to me; maths is a series of rules and procedures to follow; men are better at maths than women; everyone is capable of learning maths.”  So if you click on one of these, then it expands and you get a whole explanation about that myth and why it is a myth.  So I think there's a real place for those in the newsletter and I'd keep putting them out there all of the time.

Again, reflective prompts on the parents' section as well.  So they've just got some information there and “How would you help your child to develop positive attitudes towards mathematics?”, so especially after the discussion that we had earlier tonight, these could be some great resources that you could use and maybe at a family maths night.

And the final section is the evidence base.  This is where I start because I always love to read the research and the evidence.  So on this section, there is information around numeracy in the 21st century, numeracy and the proficiencies, developing a capacity to teach numeracy, numeracy in the early years, and at home with numeracy.  So there's links to research articles, there are links to other websites in here, there are quotes, there's lots of really good information in here and it's not a really heavy section, so you can go and just read one part of it and it is very accessible to all of us.

In that section there is a fantastic video about the difference between mathematics and numeracy and I'm going to hold this over and we're going to watch this at our next webinar, but I think it's very useful to have at a staff level, have that discussion around what is the difference between mathematics and numeracy and maybe even for a parent night.  So let's skip over that.

So that brings us to the end of our introduction to the numeracy ‑ the official, or the unofficial I should say, opening welcome to the Numeracy Guide.  So just have a think about what has piqued your interest about the numeracy guide, what are the things that you think you might be interested at having a looking at or going and digging a bit further into.  It would be interesting to see ‑ Erin has just said that there are so many resources. Very true, Erin.  That's why I just wanted to give a little tasting plate introduction to it so you know where you might want to start.  There are a lot of resources there, though.

So I encourage you to engage in this reflection.  Let's have a look at our success criteria.  So I'd love to get your feedback on this. How do you think you've gone with this over the course of tonight's session? “I can discuss teaching and learning strategies for developing a growth mindset; I can list strategies for gathering information about student engagement, motivation, skills and knowledge; and I can list a range of supporting resources for ongoing learning about maths teaching and learning.”  I'd love to see your thoughts about that.

In your activity pack you'll see a stop, stay and/or start.  I always encourage this to think, ”Okay, if this is what I think about numeracy instruction now, what do we need to stop doing, what do we need to stay doing and what do we need to start doing as a result of our learning? “. I'll leave that as your homework.  Now you've got a whole extra half an hour because we're finishing after one and a half hours, you can engage in that.

And as I just read Laura's love note to me, the next webinar, ‘The Building Blocks for Effective Maths Lessons’, is Wednesday, 28 August.  So I'd love to see you all there, Wednesday, 28 August, and if you haven't signed up already, you can just get on to the Bastow website and sign up for that.  Otherwise we would love your feedback via this survey.  Laura will send a link out to this tomorrow as well and I think she will send a PDF of the PowerPoint slides as well. 

Thank you very much for joining us tonight, everyone.  Looking forward to our numeracy journey together.  This is the first of a series of numeracy webinars, so I look forward to seeing you at future events.  Goodnight.