The format of this reflection is wholly and unashamedly inspired by this post from @TAnnalet.

As the end of the year is fast approaching, and I’m leaving my current school after 5 years, it seems like a good time to reflect on my practice. I feel I’ve come a long way in the past couple of years to create an inquiry based approach to maths in my Grade 4 classroom. I’ve also tried to instill in my students a positive approach to learning maths. I feel like it is working! But what about from the students’ point of view?

We started out by brainstorming the things we had done in maths this year. I then sent the students a survey to complete – they could choose to reply anonymously or not. I knew what I wanted to hear but was that what the students had to say?

Here are some of the responses – the good, the bad and the ugly.

**What do you think it means to be ‘good at maths’?**

- Maybe to solve the question correct, not fast and think deep to know the answer.
- I think being good at math means to be able to answer questions and to feel good about some questions and to be able to explain your thinking and to understand the question
- To know how to do the things like + – and all the others.
- Doing the questions slowly and carefully. Also to observe clearly as you do the questions.
- Could really quickly respond to a question and try to investigate in math.
- To get good grades and have a want to do math.
- I think being good at math is you can always get 100%.
- It means to understand the question and solve and explain the question in a very clear way.
- It means that you know the answers and you can do it and you think its easy and everyone else thinks its hard.
- It means that you are good at imagining numbers and having good confidence.
- I think being good at maths means that you can calculate fast, know what does the question mean and you have to enjoy math.
- Having good strategy.
- It means that you are good at addition, subtraction, multiplication and division.

**Are you good at maths? How do you know?**

- Yes – because I am good at times and other math problems.
- Yes – because my teacher gives me feedback and helps me so I get better and know that I am good at maths.
- Yes – because I’m in the HighFour competition team and also, when I solve the questions, it is usually correct.
- Yes – I am in high four competition team and get good grades
- Yes – I am good at math because I am improving a lot. And I tried hard.
- Yes – I’m good at maths because I practise my maths at home for extra home learning because I don’t want to be bad at it.
- Yes – because when I do sorts of challenges, I have confidence and I always think that I can do it.
- Yes – I know that I’m good at math because I’m good at calculating and I enjoy math, but I’m not that good at literacy math to understand the math question.
- Yes – everybody is good at math. For example: I am good at multiplication, addition and subtraction. And some body else might be good at division.

**Do other people know if you are good at maths or not? How do they know?**

- Yes – When I solve the math questions, at least 80 percent is correct. Never below 80 and I tell people.
- Yes – they just saw me always thinking about math question and can solve these question in a very little amount of time.
- No – because they are not the people who are doing the tests and they don’t know if you really thought clearly or just rushed over the test.
- Yes – they see me solve questions in a really little amount of time and see me solve hard questions
- Yes – they see how I work, they could decide I am bad or I am good.
- Yes – they just look how you are working and what level you are.
- No – they don’t know because I usually cover my work and don’t tell them the answers even if I’m right

**What happens in maths lessons that makes you feel like you can do it?**

- I use my brain and try to solve the question and want to make my parents proud.
- My heart is not moving and I know can do it
- A motivation in my head comes up and I love good challenges so it makes it easier and when some one says I can’t do it it makes me want to do more.
- I don’t know I just feel like a can do it. I love math and learning new things about math. It is the best thing in the world. I just think that it help if I feel like I can do it, by saying to myself I can do it.
- When I finish a test or something.
- If I know the answer I just quickly write it down and it makes me happy

**What happens in maths lessons that makes you feel that you can’t do it?**

- When people say I can’t do it
- Sometimes if I’m not paying attention, And not working hard enough, I feel that I can’t do it
- Some time it is very hard, so I didn’t think about that
- Sometimes multiplication makes me feel like I can’t do it because sometimes I get really stuck and miss out a whole load of it.
- Then sometimes I can’t do anything about math. Because if I fail then I think they will think my math level is getting lower.
- When the questions is beyond what I know
- All of the questions are all the same types and the questions is really boring that you have to do it really fast and you have to all get them right.
- I am nervous sometimes.
- When I don’t understand and I don’t know what to do.
- When I get stressed and start not believing and say I’m bad at maths.
- When most people all understand it and I am the only one that can’t (even though it’s easy question).

**What do you enjoy about maths lessons?**

- Tests.
- Challenging things that could burn your heart out.
- I enjoy that sometime I can be able to feel good about something and that nearly always work in a group.
- I really enjoy the math challenges and problems we do in maths class.
- They stretch my brain and gets me to learn more so I grow up to be smart.
- I enjoy maths when my teacher gives me some hard and challenging question that really makes me use my brain.
- I enjoy fun games that also help me learn and also make me have fun.
- Yes and of course because math lessons have a lot of games and I enjoy them. Some times when there is a challenge then I feel great about it.
- It can challenge yourself and I like challenging stuff.
- Being creative and using your imagination.
- I enjoy to work with partners because you can talk about what your thinking is.
- I enjoy learning about numbers and that means good and challenging maths.
- You learn new things and you can do it while having fun.
- All of the questions is really fun and they are all not about getting the right answer and not about doing it fast.

I went away and looked at the responses….

Some were encouraging. 20 out of 21 students believed they were good at maths and most mentioned the challenge being the enjoyable part of maths. It looks like the growth mindset messages are sinking in.

Some not so much. *They don’t know if I’m good or bad at maths because I usually cover my work and don’t tell them the answers even if I’m right. *

Some completely threw me. *I think being good at math is you can always get 100% *and* When I solve the math questions, at least 80 percent is correct. Never below 80 and I tell people. *I have never given the students a score or percentage in maths – where is this coming from?

I needed to find out more so I wrote some wonderings to share with the students:

- I wonder why so many of you talked about tests, grades and speed.
- I wonder what you think I think being good at maths means.
- I wonder if you can connect what we have done in maths this year with how you feel about yourself as a mathematician.

We revisited the list of things we have done in maths this year and opened up a discussion about my wonderings.

- at my last school there were 2 rules to maths – be fast and be right
- my old teacher made us do lots of calculations
- my parents want me to be good at adding, subtracting, multiplying and division
- what we learn now is about our future and getting the grades for university
- when I do maths with my tutor they give me a score
- but we don’t do tests and get grades – we do assessments so we can see where we have got better and what we don’t understand yet
- maths is about finding patterns
- it’s about the world around you
- it’s about understanding, being creative and using your imagination
- it’s about having the confidence to try
- you ask us to slow down, not speed up
- we do all the thinking
- we ask the questions and find the answers
- you don’t mind if we get things wrong – you help us explain our thinking to see where we went wrong
- you can be slow but still really good
- I like that we do all the hard work
- you give us a picture or an idea and we then have to work out what we want to do with it
- we find things out together
- other teachers give you a word problem to solve – the person who wrote the question did all the thinking – kids just need to take the numbers and do something with them. That’s not good.
- it’s better when the students do the thinking, not the teacher – I like that you make us think so hard in lessons

So, it seems that something is working. I love that the students recognize and appreciate that they drive their own learning and they are ones expected to do the thinking. I love that they recognize that I don’t value right and wrong. I love that I have a class of confident and determined mathematicians.

I am still left wondering about their initial responses and the importance they place on grades and tests. No matter what we value as teachers, the students are sadly right – grades do still matter and you will be judged by your score in a test and you will have a clock ticking away with a time limit to complete your assessment and your answer will be checked right or wrong. Just not yet kids!

Your post and Lana’s bring home for me how many mathematics-related experiences children have outside of our classes, whether it be with family, tutors, other classes or whatever. I guess we can’t expect that our own vision of maths immediately becomes our students’. There are lots of competing voices that are about speed, tests, scores, competition. They’re all around.

It’s a measure of your success that you’re getting lots of statements like “you don’t mind if we get things wrong – you help us explain our thinking to see where we went wrong.”

I guess it emphasises the need for outreach of some kind, to share our practice with parents too.

I would be interested to ask my colleagues similar questions:

What does it mean to be good at maths?

Are you good at maths and how do you know?

Are your students good at maths and how do you know?

What do you enjoy about maths lessons?

What do you do in your maths classroom that reflects your answers to these questions?

It would be worthwhile as well, perhaps afterwards, to look at something like “How are mathematics practices changing?” in the scope and sequence document. We all have skeletons of poor or no-longer-relevant maths teaching ideas in the background. They deserve to have a good burial!

(I put the ‘How are mathematics practices changing?’ list in this blog post http://followinglearning.blogspot.fr/2015/12/the-students-active-attitude-towards.html )