Category Archives: Maths

Mathematical Mindsets – Jo Boaler.

I am working on (and shall be over the summer holidays) an online MOOC – Mathematical Mindsets, run by Jo Boaler.

If you haven’t come across Jo before, find her on the Twitter, google her or read her books. I love her methods for maths and the way she links them with growth mindsets.

I intend publishing some of my work here.

In my first piece, Jo shared three pieces of research onto brain growth with us and asked us to share our feelings about how this should impact schools.

 

Taxi Driver Evidence.

“You may have seen me show the evidence from London black cab drivers who have to undergo complex spatial training, at the end of which, they have a significantly larger hippocampus in the brain. At the end of being taxi drivers, when they retire, the hippocampus shrinks back down again.”

 

Taxi driver response:

This research shows that a brain that is being used develops and grows and that when the brain is not being used it regresses to its initial state. So in school I guess this means that we need to keep children thinking about their maths. The children who probably end up thinking about their maths are the mid-ability ones upwards who, if we are not careful are fed a diet of ‘more of the same with bigger numbers’. These are the children who are ‘high fliers’ who then plateau in their maths learning.

We need to use real-life challenging problems and investigations and games with all learners to ensure brains keep growing.

 

 

Half-Brain Case-study. “You may also have seen me show the girl who had half her brain removed. The doctors expected her to be paralyzed for many years or even for her whole life, but she shocked them by regrowing the connections she needed in a really

short space of time.”

 

Half-Brain response:

This research shows that the brain is a wonderful thing which scientists are still understanding…slowly in some cases.

In school we need to encourage our children to make connections within their brains to ensure that they keep developing. Brains don’t get full! We need to share this learning about re-wiring of brains with the children so they come to associate hard learning with something like a gym visit or fitness training – a development; and improver.

 

Stanford Case Study: “They brought 7 to 9-year-old children into the labs at Stanford, and half of them had been diagnosed as having mathematics learning disabilities, and half of them hadn’t. And they had these children work on maths under brain scans.

And lo and behold, they found actual brain differences. And the children diagnosed with learning disabilities actually

had more brain activity than the other children, more areas of their brain were lighting up when they worked on maths.”

 

Stanford response: Initially, this research seems to show that pupils who are thought have learning disabilities are working harder to keep up with (and by definition be not as good at maths as) their peers. Their brains are working harder, which means they will feel more tired during a maths lesson, be more stressed and require more breaks. We need to think in schools how we treat these children who are working harder, and it’s certainly not good enough to say X is not good at maths. It also suggests that schools need to find time to work closely with our ‘poorer maths attainers’ to get an understanding of where there learning is and to give them strategies to learn and develop their maths. – In an ideal world this can be done through group work and talk partners also.

Educational reforms.

As soon as the PISA results came out, the questions, accusations and incriminations began. Blame it on the CfE, blame it on the SNP, blame it on the boogie. I’m not going to blame anyone, there’s plenty of stuff written by plenty of people on the internet already, indeed I’m not sure the PISA results are something to aim for or worry about – Finland seems not to be too concerned – but I am going to write about working through major education reforms in my career to date.

The two major reforms which took place whilst I’ve been a teacher occurred in England and Scotland. In England, I taught through the time of the National Literacy Strategy, the National Numeracy Strategy, the QCA units, the QCA unit plans, SATS tests and OfSTED inspections every four years in a range of schools in England.  In Scotland I’ve taught throughout the implementation of the Curriculum for Excellence, and seen at first hand via The Girl, the national assessment procedures.

The reforms in England were massive and to a large degree micro-managed. The Government wanted improvements in literacy and numeracy and wrote strategies to make sure this happened. If there was debate around what ‘good’ literacy and numeracy should look like, I wasn’t part of (I was in my 20s though, so I knew everything anyway). The strategies were written by a group of literacy experts and then rolled out to schools in the autumn and winter to be put into place for the start of the next school year.

I recall the literacy strategy being rolled out in 2 hour staff meetings after school – I hate after school meetings, I’ve done a day of teaching, there is assessment to do and I’m tired: You’re not going to get the best out of me. These meetings were scripted by the government, the trainers read out what we needed to know and we worked through units of work which explained how the strategy worked, how we should plan, how we should teach reading,writing and spelling. We soon spotted that the answers to the trainers’ questions were usually on the next page of the document! For this training we were given a complete strategy, various unit breakdowns of our own, resources (which we needed to make up in school) and some examples of expected work. It was a slog but by September we had stuff in place and away we went with it. The lessons I taught from the strategy weren’t perfect, but there was a structure in place to help me.

Of course, your school didn’t HAVE to follow the literacy strategy, but if you didn’t and the OfSTED or local authority came a calling, your school literacy strategy had better be an improvement on the national strategy. If your SATS results weren’t up to standard then OfSTED might make an extra visit and again, you’d better be getting the national strategy in place or else (or else usually meant your HT retiring or resigning).

Once we had successfully implemented that – well actually by October of that same year – the National Numeracy Strategy was launched. If you’ve had the misfortune to chat to me about this, you’ll know I love the NNS! The Government spotted some of the problems with the literacy strategy and made some key improvements.

The NNS contained examples of questions and ideas you could use, straight out of the folder. The document, like the NLS had learning objectives for each term of each year group (meaning for differentiation there was a progression mapped out). However, the NNS was supplemented with two things I thought were brilliant.

Firstly, there was a 5 day maths course for every teacher in the UK. 5 days out of class (in a hotel at times) to discover the document, talk about it with colleagues from other schools, plan how you would implement it with your class, look at all the resources. Like the NLS it too was scripted, so the Government really were leading this change in EXACTLY the way they wanted it to go. The 5 days were back to back. A full week thinking about nothing more than numeracy. It changed my teaching approach to maths from ‘here’s the book kids’ to something I love to this day. And really it bloody well should have done, bearing in mind the cost of this to the UK taxpayer.

The other wonderful thing was the resources the NNS team made and shared. They created some wonderful teaching programs which I use to this day and they wrote the unit plans. These were highly detailed documents for each unit of work. Unit one was place value it contained 5 plans, one for each day of the week. Each plan was A4 and was pretty much a script for the lesson. There in the same folder (and latterly on CD-ROMS) were the resources (including worksheets) you needed for the lesson. Differentiated. The idea was that these plans were a start point, you changed them to suit the needs of your class. Lots of teachers did and that was great, but even if you didn’t (because you were, like so many teachers lazy 😉 what you delivered was good quality, written by numeracy experts, lessons. If you were new to the job it allowed you to know where to pitch an average lesson and how to piece your maths teaching together over a term. I loved them and still did out the ideas for a concept which my class find tricky to see if I’ve missed anything.

After a year or two, the Government did it again. They released the QCA topic documents. These detailed the teaching for all of the non-core subjects on a lesson by lesson basis. Again, all the information you needed to teach the lesson was contained in the folder. You adapted it, changed the order, added bits in, took bits out but the basic lessons for all your Art, DT, History, Geography, Music, Science, RME and PSE were there. Concurrent to that, the Government noticed that problem solving and investigations was not progressing as well as they wanted, so they created more problem-solving resource and ran another 5 day maths course for two teachers in each school to upskill them in teaching this. Again, resources and knowledge I still use to this day.

Looking back, it seems a great time, with resources aplenty, cash aplenty, but it was hard, hard work at times, with the pressure of OfSTED ready to pounce and the pressure of SATS scores needing to meet targets for school and local authority. For me, giving me start points close to a finished article of a lesson plan or termly plan allowed me to focus on the delivery of the lesson, moving children to their next target (of which they had many) and how I might make these at time dry lessons interesting and meaningful for the children. For teachers, new to the profession it certainly offered a proven scaffold to begin their careers. I loved the support the strategies and unit plans gave me and the time it freed up to think about the needs of the children in my care.

I will discuss the education reforms since I’ve moved to Scotland in my next post. I think it’s possible I moved out of England before things took a turn for the worse, but I’m happy to hear comments from people who disagree with that thought or with things as I recall them from the late 90s and early 2000s

Daily Maths Work.

I’ve been using a daily maths sheet which I found here, in addition to our brilliant in-house Minute Maths resource recently. I loved it as it reinforced so many aspects of maths which needed a steady drip feed before they became confident and embedded.

I decided that some of the parts of the sheet were still required this term, but I also wanted to add some aspects of maths which we still needed practice with. So, I made up my own sheet and adapted it to the needs of my class. In line with my last post, I’m offering it for free from here as a PDF, or e-mail me for the adaptable publisher doc. I’ll also put it on Pinterest.

 

Maths Map – Edinburgh

I originally wrote this 3 years ago. In reorganising my website, I have included it as a post rather than a page.

Tom Barrett has come up with a fantastic idea for using google maps to create maths maps. The idea, like many brilliant ones, is simple. You find an area (I did Edinburgh as it’s local, so I know it) and put in place markers in certain areas and attach maths questions to them. Children can then work through them in and out of school and answer the questions.

Because of the way google maps is shared people all over the world can collaborate with these maps (including children as part of their learning). You can use different coloured markers for different levels of questions. I’m really looking forward to trialling it in school during our maths week.

Here is a link to my maths map.

Here is a link to the maths map area of Tom’s blog. http://edte.ch/blog/maths-maps/

And finally here is a link to Tom’s blog, which I think is brilliant. http://edte.ch/blog/

Low-tech mental oral starter 2

Another popular low-tech starter is a version of the memory game ‘I went shopping.’ In the maths version children take it in turns to say

‘I went shopping with £x.xx and I bought something (let the children choose, it adds to the fun) that cost £x.xx, what change should I get.’

This activity lends itself to circle time maths and pretty much to any age groups which have worked with money. Older children could add the ideas of a % discount or price rises too. The children will really enjoy making up problems to extend their friends maths skills!

Low-tech mental oral starter!

Just a quick post. I got reminded listening to my partner’s daughter this evening that the most interesting and effective things in teaching can also be the simplest.

Her maths teacher uses a variation of the ’11’ game to practice counting down, through hundred barriers.  To play you would stand up all the class and begin with a random child and a number near a hundreds barrier (214 for example). Each child subtracts either 1,2 or3 numbers from 214 until some child says 197. The child who says 197 sits down and are out. So a sample game might go,

214,213,212,

211,210,

209,208,207,

206,205,

204,203,202

201,200,

199,198

197 OUT!

You play until only one person is left in.

You can also use an extension to this game. That is for the winning player’s table to get a reward of house points etc. The children then have to use a planning strategy to try to keep their table’s members in.

I’ll be giving it a go with my maths class tomorrow!

Using tutpup in my classroom.

I was introduced to Tutpup through Year Six Teacher’s Blog in this article. It is an online mental maths and spelling game in which the children play against children around the world, in realtime. It is also free.

To begin, the teacher needs to sign up first as… a teacher. Once this is done you can create classes for your pupils to use. I currently have two classes, one for my class and one for my maths class. You set a class code for each of your classes and the children need this when they sign up. It would be possible for one teacher login to run many of the classes in a school but I wouldn’t recommend this. Each teacher would be better creating a teacher login as they then have access to the data on how their children are progressing, and can move their children onto the games which will develop their pupils skills appropriately. Once the teacher has logged in and created a class or classes the children are ready to be introduced to the program.

The children create their own login using this simple interface. They choose a colour, animal and then a number and that is their playername. They then need to create their own password – on a side issue password creation, remembering and retrieval is a skill that our children need so much now for their lives inside and outside of education, do we discuss this enough with them? – and the enter the class login that the teacher creates in their login process.

You may find that some of the colour and animal combinations have gone (i.e. they do not have any numbers left), but the children in my class really supported each other in this. As soon as one child had found a colour and animal that had numbers, they told the class who then went to that combination and created their login.

Continue

Drench.

A new game which I’ve introduced to my class is drench.  I’m not sure where how I found the game, I thought it was via the Guardian Technology Pages but it was actually via a comment on their report on ‘Games to relax you’.

The game involves the player selecting one of 6 colours and trying to change all of the board into 1 colour in 30 moves or less. Drench has proved very popular with many of the children in my class, although not with myself as I am very colour blind and find I cannot tell a 2 pairs of the colours apart from each other!

To find a winning strategy children (or adults) have to plan what colours lie around the ‘active’ area (the area which they can change the colour for) and plan 2 or 3 moves ahead. It develops spatiality and thinking ahead, and like many of the best games contains simple gameplay which remains challenging through successively harder levels.

I find using it in the final 2 minutes around play or break works really well with my class and I have tried children working in table groups to complete the puzzle as quickly as they can. I also  use it in plenaries and also introductions to maths sessions to revisit bit of spatial learning.

Spatial awareness, as I have mentioned previously, is an area I feel ICT (especially games based learning) can make large developments as children have the opportunity to explore spaces in an enjoyable context.

Wii Sports for Mean, Mode and Median.

My final lesson of the week to involve the Wii used the practice option for batting on Wii sports baseball.
I decided that I wanted to create a larger range of numbers for the children to find the median number of. Wii sports baseball batting practice allows you to have 10 swings at 10 pitches. It records (quite quickly) what the distance is that you hit it. It was this data we recorded for our averages lesson.

As with the bowling, there were 10 numbers to record, meaning we had to split the 5th and 6th numbers to find the median.
After a discussion about the best way to do this, we managed quite well and got better at it as we progressed through the tables taking their turns at batting. The children were by now quite good at finding the mean and mode for the range of numbers.

One of the more interesting discussions we had whilst using the Wii for averages, was the way the modal average differed between the bowling game and the baseball game. In the bowling game, the mode was 10, and the mean average score was frequently around 9. The children could clearly see that the mode and mean were closely related in that scenario.

However, despite some of my group being ace sluggers, (the record was 7 homers out of 10 attempts!), the mode for each set distances was 0. This was not close to the mean average, which was around 110m. We briefly discussed the reasons behind this and talked about which average is most useful in which situations.

One final thought about the Wii bowling. The scoring of bowling is quite complex when spares and strikes are involved (which with my class they always seemed to be) I wonder i there is some maths to be investigated  in how the scores are made, maybe with a secondary class devising new scoring methods for bowling and using the Wii bowling game to see how they would work, comparing the scoring methods with each other.

The children throughout the week certainly enjoyed our use of the Wii, and they seem to have learned how to calculate the mean, mode and median averages for a set of numbers.

An enjoyable and productive week in maths.

Wii for Mean, Mode and Median – The Outcome.

I thoroughly enjoyed our maths session on Monday, using the wii and I think the children did as well. As ever, I’ve learned a few things which would lead to a few ‘tweaks’ if I was to do it again. Before I discuss those I must say the P7 children are all far better ten-pin bowlers on the wii than I am and had a range of entertaining styles all of which proved to highly effective!

The lesson had a sparkle to it to begin with as the class noticed straight away that the wii was set up. ‘Are we using the wii in maths?’ was a popular question!

That moved on to ‘We’re not using brain training are we?’ which I found interesting and probably reinforced the point that just having a wii on for maths isn’t enough. It needs to be properly targetted and integral to the lesson, not just the lesson itself.

We formed our teams and each team played out their first frames, and we got used to recording our scores. Bowling is good for this, as you can pause between throws to make sure everyone is up to speed.

On the second frame I introduced the idea of modal average. The skills on show ensured that we quickly identified 10 as the modal score. The class found this quite easy.

After the third frame for each team we introduced the mean average. We needed a bit of calculation help on this to get the division by 12 done. We also spent some time working on rounding to 2 d.p.

After the fourth frame we began to find the median also. In hindsight I shouldn’t have had 4 teams, as it meant we always had an even number of scores to find the median for, and this made understanding of this concept harder.

We carried on and completed the game. I changed my idea of getting the averages onto the board and adding on points as I felt I didn’t want to pressurise the groups too much! We also dropped finding the mode after 6 frames as it was always going to be 10!

In summary the class and I enjoyed it, the lesson had an exciting feel to it and I feel the children learned the objectives I had for them at the start of the lesson.

[youtube=http://www.youtube.com/watch?v=FugD_CIjrDY&hl=en_GB&fs=1&]

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