We have been building on our knowledge of multiplication facts by noticing patterns and numbers within other numbers. In this game we choose cards that have numbers represented in dot patterns. We have to justify why that number could be part of another number, by explaining how it can be grouped or multiplied to create the larger number, then we cover that number on the game board. This is helping to build visual representations and to make abstract times tables more concrete. It takes flexibility of thinking and an ability to justify your reasoning. These are both skills mathematicians need.
For example, here we've picked a card that has 5 dots on it. We can justify putting a counter on anything that has multiples of 5. So here we could be saying, this can be part of 30, because 6 groups of 5 is 30, or 6x5=30, or that it can be part of 60, because 12 groups of 5 is 60, or 12x5=60.
'Many mathematicians draw upon Art and many artists draw upon Mathematics'. says Jo Boaler (Maths Professor at Stanford University). We know that there is lots of beauty in Maths.
We have been dialling up the Character Strength of Appreciation of Beauty and Excellence.
VIA, Institute of Character: "Those who express an appreciation of beauty & excellence notice and appreciate beauty, excellence and/or skilled performance in all domains of life, from nature to art to mathematics to science to everyday experience".
Here are some examples of what we have been doing:
We wrote down a group numbers. Using squared paper, we started somewhere in the middle. We took each of the numbers in turn to tell us how long to draw the line and turn a right angle to the left after we drew each line.
Rotational Symmetry Art
The students created a simple drawing on 1/8 of their circle, then they transferred their drawing into all 8 parts of their circle. What a great way to learn about rotational symmetry, fractions and angles.
We have been learning about brain growth and struggle. We know that we need to embrace struggle and accept challenges for our brain to grow.
We know how important mistakes are for our learning. We make mistake dances to celebrate!
Fulop: We focused on making our brains grow. The activity was to emphasise perseverance and to show how the brain learns. We started with a scrap piece of paper. We had to draw a perfect square in the middle, not on the edges. We did it. And that was when The Challenge began. We had cut out the WHOLE square in ONE straight line. Sure, first thought? Impossible. Utterly impossible. Well, no. I started to catch onto the way when Nicola announced that you can fold, and I immediately realised somehow folding had something to do with it. Later, I was still searching for the answer, and every way seemed to sort of change as I nearly accomplished it. In the end, I had to get help, but I kept on trying! For people who passed through “the Square”, there came, “The Oblong”... I tried that, but that was even more mind-boggling! But In the end, I managed square! When you learn something, new, delicate pathways will form, connecting two Neurons. If you keep learning it, and keep getting better at it, it will become a strong pathway, as if the brain paved it. It could also happen that when you learn about something that was an old pathway, it could strengthen. The last possibility is that two pathways you have already connect, forming a stronger pathway. The Brain is very interesting, Isn’t it?
Beatrix: It was really hard and I struggled a lot but I persevered and got it in the end. I tried it two times and it didn’t work but I tried again and I got it.
Charlotte:When you try something for the first time you will make a delicate pathway e.g. I was doing a math problem that was hard. But if you keep on trying and it will make a stronger pathway.
Hadley: It was an interesting feeling. I was annoyed at myself for not getting it but I was also growing my brain. It was quite complex to talk about.
Hunter: New pathways in your brain are delicate and easy to forget and break.but if you repeat and keep learning it the pathway will strengthen and strengthen so that it will be very hard to forget and break. The path ways can also connect with each other and join the learning together. The struggle was annoying and it made feel mad.
Olive: The struggle made me feel a bit panicked but when I calmed down I felt more confident. My brain is growing!
Sabine: I persevered by trying new ways if others didn’t work. I made a few mistakes but that’s ok because mistakes help your brain grow!
Yoichi: My brain grew because now I know what to do and what not to do.The struggle made me really frustrated and I started to think it was impossible. I persevered by not giving up, trying and then I DID IT!
As part of Positive Education learning, we have been inviting students to work through a course led by Dr Jo Boaler (Professor Mathematics Education at Stanford University) and her undergraduate students.
This will help students to develop a Growth Mindset in Maths. This course includes useful information about the brain and the best ways to learn Maths effectively.
Here is some of our learning from Week 2...
Smashing Stereotypes
James: Companies think that girls do not like some things boys like, they use stereotype thinking. More people should have access to different toys, video games, board games and computer programming - they all use maths. People should also let people have more choices of t-shirts colours that aren't just pink for girls.
Inigo: Maths is for everyone! Never get boxed in to anything! Ideas are for everyone to enjoy.
Ajooni: Today, I learned that no one should think in stereotype. For example, pink is not only for girls and blue is not only for boys. The video said that to be good in maths, you should play maths game, board games, build stuff with Lego. It's for everyone not only for boys. No one should tell you that something is not for you.
Mindset in Maths
Darragh: You need to be confident about it and not give up.
Billy: People need to persist and have a growth mindset in order to learn Maths.
Emelie: They need to use perseverance and believe in themselves even when things get hard, and even if they get it wrong they believe that next time they will be able to see the mistakes they did last time and learn from them!
Emily: If you have a growth mindset you think that you can grow your brain if you have a fixed mindset you think that you are smart or not smart.
Sammy: If you want to get better at maths you have to have a growth mindset and just keep trying because if you fail once, you can just try harder the next time and you will get better. You also need to believe in yourself to have a growth mindset.
Messages about Maths and You!
Sophie: When students are praised for being smart they sometimes choose the easy problem. This is because they wanted to get it right again so that people would still think they are smart.
Sabine: Why do you think that when students were praised for being smart they then chose the easy problem? Maybe because if they think they were smart they thought they wouldn’t have to do the hard problem because smart means that you know a lot so they probably thought that if someone said they were smart they wouldn’t have to challenge their brains because they knew that question so they wouldn’t have to get muddled up doing the hard question.
Mae A: I think it is because they really want to know that they are smart. It can be just wanting to think that they are smarter than other people, but it would just make them not as good as the people who choose the hard problem. Even if the people that choose the hard problem get it wrong, their brain still grows and they will get it.I f you set yourself at the easier problems your brain can still grow but not as much as the people who choose the hard problem.
Messages about you
Alex: When people say you are failing it doesn't matter just keep trying.
Coco: The thoughts in your head can really affect your learning. When the students had a test half the class got feedback saying"Im giving you this feedback because I believe in you"and their results were much better at the end of the year.
Hunter J: The negative messages you receive will affect your future in learning unless you shut the negative messages out of your brain and let the positive messages come in instead. you should always try the hard problem because when you struggle it might seem that your bad it but when you struggle it actually helps you to learn so make sure you try the hard problem next time.
Fülöp: The first thing is that the students' achievements are changed by the messages they get. If they get, for example the message, "This is bad. I can't understand what made you think this" then the student will be hurt, and they will think that they can't do that. if they get the message, " I'm giving you this feedback because I want to help you" then the student won't lose much confidence.
As part of Positive Education learning, we have been inviting students to work through a course led by Dr Jo Boaler (Professor Mathematics Education at Stanford University) and her undergraduate students.
This will help students to develop a Growth Mindset in Maths. This course includes useful information about the brain and the best ways to learn Maths effectively.
We asked: What happened when the girl had half of her brain removed?
Charlotte: All the doctors said that it would take along time for the girl to move again but the girl recovered really fast and began to walk and run. All the doctors wore shocked of how fast the girl the recovered.
Ethan: Scientists thought she would be paralysed for a long time because the brain controls your body. Surprising all the doctors, she regained the ability to move quite quickly because her brain grew back and all the cells reconnected. That just showed the power of the brain is more powerful than we ever thought it would be.The brain would be able to grow itself back in a few days. Now that you know that, let's see how you do in your maths test!
Elliot: What happened when the girl had half of her brain removed? The doctors thought that she would be paralyzed for a super long time but her brain connections grew back much faster than they expected so she learned how to walk again real fast.
Summary The video taught us about the brain. Anyone's brain can grow at any time if you challenge yourself. London taxi drivers have to memorise 20,000 streets and 25,000 landmarks. They study for 2-4 year and then take a test called "the knowledge". And their Hippocampus grows tremendously when they retire it shrinks back. There was a study where some scientists got two groups of volunteers, looked at their brains, told them to learn how to juggle, and sent them home. The scientists contacted the first group and gave them tips and encouragement. They didn't contact the second group. After a while they got back together and showed the scientists their juggling skills. Only the first group had learned how to juggle and showed significant brain growth. This kind of evidence proves that the brain is much more plastic than previously thought. Practicing a task for a few minutes every day makes your brain grow. This mean we can learn almost anything.
We asked: How do people feel about Maths?
Yoichi: Lots of people hated maths except for some people. The people who hate math did not think it was useful but the people who liked math thought it was useful in day to day life.
Coco: I think that often people haven't had an enjoyable experience meaning that they don't have many happy memories with the subject.
Cleo: Most people feel a bit bored or frustrated when they do maths. Others use it in work but might not like it quite so much. And some people disliked it as a kid but got better withit growing up.
Georgia: Most people don't like it because there are lots of rules to learn and it can be very frustrating especially when you get things wrong.
We asked our students to summarise the clip:
Anastasiya: Summary of the video "Math Myths and the Brain" There are many math myths that have been for a long time and are actually not true. For example, there is a myth that some people are more talented in math than others. In fact, everyone can succeed in math. But different people can have different experiences. The second important point of the video is that our brain is very flexible and develops with practice. The more we learn the more our brain grows.
Eddie: they were talking about a myth that there are people that are good at maths and that some people aren't. some of the things thy said were "Anyone can succeed in maths", "there is no such thing as a maths person" and "you need to exercise your maths brain".
Hadley: What I took out of this was that you are good at maths you just need to try no one is gifted with maths they have just had a good experience with it and any one can be good at maths.
During the holiday break we ran a workshop on Number Talks. This was attended by 30 teachers and principals from 10 schools as well as Maths advisors from the Wellington region. We wanted to share what we have been doing at Worser Bay because it has a big impact on student engagement and achievement.
What does developing a Mathematical Community of Inquiry mean to us?
Mathematics is a creative and challenging real world activity.
Positive beliefs about mathematical ability are essential.
Maths has to be visual and collaborative; with time and strategies to investigate, discuss, explore concepts and reflect.
At Worser Bay School, we have been inspired by the work of Jo Boaler who is a professor at Stanford University. She provides resources and ideas to help students get excited about Maths.
"You have probably heard people say they are just bad at math, or perhaps you yourself feel like you are not “a math person.” Not so, says Stanford mathematics education professor Jo Boaler, who shares the brain research showing that with the right teaching and messages, we can all be good at math. Not only that, our brains operate differently when we believe in ourselves. Boaler gives hope to the the mathematically fearful or challenged, shows a pathway to success, and brings into question the very basics of how our teachers approach what should be a rewarding experience for all children and adults."
For a Number Talk to be successful, students need to be respectful in discussion. We have co-constructed (with our students) the rights and responsibilities for discussion in a Number Talk.
Our students are learning about the importance of having a Growth Mindset. Research shows that mistakes help the brain to grow. Our students are learning that challenge is a good thing! Here are some things parents can do at home to stamp out Maths anxiety.
Today the Year Four kids made an Array City. Each person made a different building to put on the wall. On the buildings there were time tables to help us remember them.
An array is equal rows and columns. We can make equations from these like 7 X 8 = 56 or 8 X 7 = 56. We can also do repeated addition. Some kids based their building on a real buildings and some just made it up. Now that you know what an array city is you can make one!!
By Marnie and Zoe
We have been learning about arrays because it helps us to visualise Maths in different ways. It also helps us to develop "Number Sense". We have been thinking about multiplication, division, repeated addition, fractions, area and shape! It is great to see how Maths is connected and how we can think about it in different ways.
Research from Jo Boaler says that students in the UK, USA and beyond think that those who work best in Maths work quickly. Actually, those who are best at Maths think deeply and carefully. Speed is the enemy of mistakes and a risk taking culture.
At Worser Bay School we LOVE mistakes. Students need time to work through challenges. Some of our students do a mistake dance when they make a mistake. Our students have designed some posters that we have put up in the classroom.
As part of our Inquiry, "Healthy Body, Healthy Mind?" we have been learning about the brain. We did some learning about Growth Mindset and Maths. We found out how learning happens.
We know that Maths is a creative subject and anyone can learn it!
Today we watched a video about Maths Myths and the Brain by Jo Boaler. We found out that a myth about Maths is that people are not born gifted. Anyone can learn Maths and anyone can do well if they practise, persevere and accept challenges.
When you learn something, synapses fire in the brain. Pathways are formed and the more you return to an idea the stronger the pathways get. When you learn something your brain grows and the learning sticks if you learn it deeply and come back to it often. When you make mistakes synapses fire and the brain grows.
