Tuesday, 21 June 2016

Reflecting on Our Year as Mathematicians

Reflecting, as we know, is the key element to effective learning.

I wanted my students to gain a sense of pride and to be able to glimpse the bigger picture of all the maths enquiries we had explored over the year, so I made a quick slideshow of our main units and added some pics of things we had explored in each.

The children had time to add some reflective thoughts of those they wanted to:

Some comments:

° Since this was the first unit I did in 6A, it helped me realise what maths can be since we did different activities than I had ever done before.

° This unit made me constantly curious, and made me wonder new things.

° I had never seen anything like this! I went home confused and saying, is this history or maths class? But, it all came together. You taught us that knowing isn't the point, UNDERSTANDING, is the point!

° These were the basic understandings I had to know to understand the key to maths so this helped me to open myself to mathematics more and to think about it in ways I had never done before. It made me realise that using numbers isn't scary because they don't even really exist.

° I learnt a lot in this unit and it made me think of things I hadn't before. I used to just accept that numbers were the way they were. But in this unit, we needed to think for our ourselves WHY the numbers are designed in that system. This unit first made me realise what you have been explaining all year- knowing the whys of maths is more important than the hows.

Some comments:

° I already knew what angles were and how to use them, so this unit, I challenged my thinking to see if there were PATTERNS in angles, and prove/disprove my theories.

° This unit was to bring geometry in because experimenting with angles was lots of fun and every mistake is an answer in this unit.

° During this unit, I expanded my thinking a lot more,and helped me a lot with thinking maths is fun because we never did problems on paper, it was always fun, creative activities.

Some comments:

° This helped me realise that maths is everywhere in nature and I think its in other places too.

° Fibonacci numbers didn't REALLY grab my interest, but the activities that we did, made me think about if Fibonacci numbers in nature is a real pattern or just a huge coincidence!

° I am still wondering if there are any more ways that we can use Fibonacci numbers, Like prime numbers are useful in a coding security.

° This unit helped me discover that maths is used everywhere and we even we use maths without thinking thinking about it.

° Learning about the Fibonacci numbers really pushed my thinking about how maths connects with everything in the world.

° I had never thought of the question we began our unit with before: Does nature use maths? It is still on my mind when I look at nature these days.

Some comments:

° I discovered different ways and patterns to find area and perimeter. There are lots of connections between them and I liked how we had to find them ourselves instead of being told. It made me feel proud when I found new patterns myself.

° Area and perimeter was the most hands-on activity unit that we had. My personal favourite was measuring the football pitch because there were shortcuts, and we were outside. During this unit, we had an equal balance of group and individual learning.

° This unit helped me understand how and where we use maths in real live. I learnt new strategies and I found out the area of my house.

° I discovered that open ended activities can really develop my mathematical skills because I am the one who is responsible for my own learning. This unit showed me that if I ask more questions to find out then I will deepen my learning. This was the unit that made me realise how I can be a very effective mathematician.

° This unit helped me to understand a bit more how we use maths in real life.

Some comments:

° I always found data handling more difficult than other parts of maths, but I realised that when you draw it out onto some type of chart of graph, it makes finding average, mean, maximum, minimum etc, easier!

° There are many new ways of data handling like graphs, the mean,median and mode etc. I never new that all these ways are for handling data.

° This unit was very fun because we got to make our own graphs and learn in a more creative way, like racing and finding the time. This helped the learning to be more engaging and increases the chance that we will remember the unit.

Some comments:

° During this unit, I learnt how Fractions, Decimals, and Percentages are all connected with each other. The activities that we did made me think about how we use them in our daily lives, which put a new insight to my thinking.

° It helped the class see how we can find maths everywhere even in humans, and art.

° I liked how we had to think where we were with our understandings of fractions and then chose what we should learn next. 

Some comments:

° Why is it the one that changes the number most first, even if it is an unknown value you can still solve it as you get to it, what example is there that clearly explains why you need brackets, even if you did it left to right then why left to right?

° BODMAS was just for geniuses I thought but actually all you have to master is the strategy and the order of operations and then you have turned something hard to easy.

° In this unit I learnt that WHY is very very very very very important. When we understand why, then it all makes sense.

Some comments:

° This unit was a lot of fun because we got to discover new things, like how much my pencil case weighs, or how much water you have to put in a scale to match the mass of a orange. And it was especially fun to think about how much I weigh on other planets!

° This unit made me realise how connected science and maths is.

Some comments:

° Negative to positive strengthens my understanding of how the world works and different strategies to find when working with positive and negative numbers.

Some comments:

° In this unit we were always making theories and testing them to see if they were true or not. They have many connections which was fun and helpful.

° In this unit I realised that prime numbers are like building blocks of composite numbers like primary colours are the building blocks to secondary colours.

° In this unit I started to feel like ciphers, codes, internet security, and encoding writing are very interesting for me.

Some comments:

° Maybe someone could say that something hasn't anything to do with maths, but this unit made me think that every-single-thing has a connection to maths.

° This was my favourite maths unit because we had to test our theories all the time and we did fun and engaging activities. I especially liked making paint colours using ratios. That made me understand what ratios are in a deep way.

Some comments: 

° I finally discovered why people in America have different units of measurement.

° This made me realise how much we use maths in our real lives and that decimals are really important to understand. 

Some comments:

° From this unit I discovered that column strategies is most faster and very useful but I also discovered that some people have different strategies that can solve questions easy.

° I liked how we had to decide which strategies were more effective. I really liked learning the area model strategy because it finally made me understand what i am doing when I am multiplying big numbers. Before I couldn't understand.

° We had to be responsible for ourselves in this unit by choosing strategies to enquire into and then decide which is better to use.

After some time making our reflection comments on each slide, we discussed how impressed were with all the learning we had done in one year and others remarked on how much they had changed as mathematicians. One student remarked how she thought it was amazing that we did an entire year of maths without any textbook and not even one worksheet!

I then gave them a quick google form survey to find out further:

Our base 10 number system unit was our first unit of the year. Being so long ago, I had figured it wouldn't rank very high as children tend to think of things they did more recently.

Seeing this high result has made me realise that the unit should very much stay next year.

I also found it interesting that it was primarily number units that they found more interesting than the more hands on measuring units. 

Again, the base 10 number unit ranked high. I think it was the first time that they started understanding why discovering the WHYS of maths is so important and interesting.

Seeing these results makes me rethink of how long I schedule units for next year. Clearly, I should be giving them more time for children to enquire into. 

How have you changed as a mathematician this year?

At the beginning of the year I only knew adding and minessing.
At the start i hated math and never understood it then as time passed i understood and saw how and why we have math.
I feel i've expanded my knowledge on math a lot this year and i also like math much much more this way than the everyday math book.
I learnt what math was, not just equations: It is a mixture of knowledge and creativity.. My thinking about math changed after have learnt that.
I change with fibonacci numbers because I know nothing about fibonacci numbers befor.
At the beginning of the year, I was just adapting to enquiry based learning, so throughout the year I got used to learning the WHY something happens not WHAT it is!
I can not believe how many of my thoughts have changed this year because mr. a has told me things that would have never gone through my mind which strengthened my understanding of mathematics dramatically.
In year 5 I really disliked math because we usually did it in books which annoyed me but in 6a we don't have books and we do more visual activities so we actually understand what we are trying to understand a look at.
(for the previous question I think ratios and base 10 but in reality understanding and knowing about ratios I think will probably help more than understanding why the base 10 system works that way) I think mostly now I understand to really really stress the WHY.
A little bit
At the start of the year, I knew how to do things and I was quite fast, but now I know why we do those things. I also have become much more enthusiastic about maths throughout the year.
I have changed as mathematician because i can do more complicated stuff and so math has become a little bit easier for me.
I think I changed very positive!!! I learnt a lot, lot, lot of new things during this school year! This school year added a lot more knowledge to me. I will miss you!
I have learned a lot about maths itself and I have also really improved at things which I didn't know about. Also by doing open ended activities I was able to be more creative and in yr 6 I have gotten better at investigations in maths.
My changed was having fun and have a interest on math because before year 6 I got bored on math because we needed to use math sheet and that makes me boring and I had no curios because unit that I did is what I already did in Japan . But in year 6 it changed because Mr.Anshaw choose interesting topic for me.
I have observed this year that I have changed quite a lot in math this year, I feel that I am enjoying it more than I was before and I feel that the subjects we focus on make me push my thinking the the deepest spot in the sea (I do not normally challenge my thinking that much in math class). Over all I think that in math I have become much more knowledgeable about the importance of math and that should be why I have challenged my thinking more that I would usually do.
Before this year everytime I had maths my brain would say "NOOOOO not maths!! Well, here comes some more boring worksheets" after this year my brain is saying " YAY MATHS!!! I wonder what we will do today!?" I love maths now, and I know that it is not just about staring at numbers sitting on a peice of paper it is actually a wonderful way to learn with creative thinking and enjoy playing around with numbers!
I have changed a lot in Year 6 since last year. Last year, I didn't learn many things because in Year 5 you don't learn ratios and advanced fraction, percentages and decimals. This year I have learnt many new things and explored new things like fibonacci numbers.

Explain why you think so:(18 responses)
because I learnt a lot
I hated those math books and found it boring later when we started I loved it and understood way more
Because i have really liked this way of learning and it was really interesting to see all the things about math that most people dont know.
Because you always had creative ideas but for the home learning ,probably give us interactive home learning, not paper work (worksheets from time to time).
Because I have found now lots of different creative but useful was to learn.
In my old school, I never had to think this deeply about a math topic. This year, you challenged me EVERY SINGLE TOPIC!!! I liked the challenge, and I was impressed by how much more I could understand something by knowing why it happens!
I think mr .a has helped my personally very much because you built lots of neuron pathways and connections in my head with makes me a better mathematician because i am able to remember topics and strategies more easy so i think mr. a has made me a better mathematician
Because you would explain it really well ( the best ) so everyone could understand how to do it and you helped me become a bit more enthusiastic about math because of the more visual activities we did . Thank You :)
Because I already thought that maths was very interesting and you made think that maths was more interesting than what I thought.
Because I dont Hate it as much
I think Mr Anshaw was Very Successful because our feelings toward maths have changed quite a bit in year 6.
I think you were very successful because everybody loved your activities that you did including me.
Before year 6 I didn't think math was that interesting and does not use creative thinking at all. Now I think math is very interesting an d it does use a lot of creative thinking.
I think so because the way taught was different from any other teacher and you taught how maths is your investigation and all the connections it has so much that I can't explain it but, my opinions have changed in a good way.
I think so because I got bored in year 5 but in year 6 I had a fun time to learn math .
This year the learning in math that we have done in class has been very different (in a good way) to what I used to do. The learning is much more interactive then before which makes us think more deeply I think. Activities like the running data, The ladybird city, the fibonacci number plants etc etc all helped us more to understand the importance of math and things like creative thinking or the world all connect to each other.
I love math now! It is super fun and creative especially with you (Mr Anshaw) as a teacher! GOODBYE WORKSHEETS AND WORKBOOKS! I DON'T NEED YOU! I love the creative thinking during our lessons and I found out that maths is playing around with numbers and seeing what happens when you add it or subtract it or square it etc. I hope math is still as enjoyable when I am in middle school.
Last year, maths was my least favourite subject. I really found it hard to think about maths as a fun way but this year you have taught me that mths can be a whole new world.

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