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And rest

July 20, 2019 Leave a comment

Here we are, we made it. Another year done and another long summer holiday just begun. This time of year I find it hard not to reflect on what had been, what’s to co.e and what might have been.

It’s been a tough year in our department. We had a couple of people on mat leave and a number more who had to have lengthy spells off due to a variety of illnesses and injuries. This left me leading a skeleton department for a large chunk of the year when we were in the thick of it with year 11. It was tough and there were plenty of challenges to overcome, but we made it through and came out the other end. I was lucky enough to have great support from SLT and from the maths lead of our trust, who spent a lot of time in our school. He helped a lot with the additional leadership responsibilities I had to take on and he got really stuck in in the classroom. I feel that the experience has certainly had a positive impact on my own leadership skills and I think it had improved the team, who all went above and beyond to ensure we made it through. Whatever happens in August I know everyone gave there all and we couldn’t have done any more.

By the end of the year, everyone was back. We had a much more settled department and have a great foundation to move onwards into next year. I think we are in a great place to push on and improve further. We have a solid team in place, a great curriculum and have made some plans I feel will give the students a great chance of success.

This year I completed my NPQML. I feel that too has been a benefit to my development and I’m currently looking at options for my next learning venture.

I made it to a #mathsconf for the first time in a while and hope to get to more next year. I feel this has given me further things to think about in my own practice and I have already begun to implement some ideas and strategies in my lessons. Next year I plan to follow these through further and am particularly interested in trialling more use of manipulatives in my classroom.

This year I have been able to have great discussions with some former pupils who are now maths teachers,, and recieved news that another is looking to embark on a career in maths research and lecturing. This has been a source of much pride and enjoyment for me and I know they will all be brilliant in their chosen careers. I’m glad they chose mathematics.

I’ve also managed to start writing more on this blog, which I have neglected a bit over the last few years. I feel that this is something that really helps me frame my thoughts, improve my maths and reflect on my teaching, so I hope to keep the momentum up with it.

Now is the time to rest, to spend time with my family and recouperate ready for September, when it all starts again. Thanks to all who read this blog and those who interact with me on here and on social media. I hope you all have a great summer and continue to interact, as I feel you all help me to continue to improve.

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Categories: Commentary, Maths

Fun with Cusineire

July 18, 2019 Leave a comment

This is the second post in what I hope will become a long series about using manipulatives in lessons.

Last week I posted about how I was going to try and I corporate more manipulatives into my lessons, and that I’ve bought a set of Cusineire Rods for home to play with with my daughter. I’ve not manages to really do much in lessons since, the week has been disrupted by a couple of drop down days and sports day, and the lessons I’ve taught have mainly been around construction and loci, and symmetry and reflection.

I did, however, manage to have a play with some at home. My daughter was interested by the rods, and wanted me to show her some of their uses. First we looked at how they can be used to find number bonds to all different numbers, then we used this to look at adding and subtracting.

She uses Dienes base 10 blocks at school for similar so she started with just the 10 rods and the 1 cubes and showed be how she would use these at school. I then talked to her about how we could use our knowledge of number bonds to do the same thing but using all the rods. This was a fin discussion and allowed be to see some potential benefits to building number fluency with rods over dienes blocks.

She then showed me how she can use manipulatives to divide and to work out a fraction of something. The only fractions she really knew about were 1/2, 1/3, 1/3, 2/4 and 3/4. This led us to a discussion about the nature of fractions and their link to division. She knew that finding a quarter was the same as dividing by 4 and finding a half was dividing by 2 so I asked about finding other unit fractions showing her the notation and she made the link easily.

We then used rods to look at two of the fractions she knew. 1/2 and 2/4. She was surprised to see they always came out the same, and we used rods to investigate this and discussed the nature of equivalent fractions.

She then asked whether you could use the rods to multiply, I thought about it and came up with using them to create arrays:

This was 2 fives. Initially she was counting all the white blocks to get an answer, but after a bit when one of the numbers was one she could count in she started counting in those.

We looked at some where we were multiplying the same number together and I asked her if she noticed anything similar between these shapes and different to the ones we had done before and she picked out that these were squares and the others rectangles. This led to a good discussion as to why this was, linking to the basic properties of squares/rectangles and introducing the terminology square numbers and what that means.

I then looked at these two:

We had done 3 x 4 first then I said to do 4 x 3, she said “it will be the same because it doesn’t matter which way round they are”, so we did it anyway to check and talked about why that was. I tried to incorporate the cords congruent and commutative into the discussion, but I think they went over her head.

At this point her role changed to teacher and we had to teach all these things to her dolls…..

It was fun to play with Cusineire rods like this, and the mathematical discussion they provoked flowed very freely, so I can certainly see that thIs could be very helpful in lessons.

In other manipulative news: I had 20.minutes or so free earlier and spend it looking at Jonny Hall’s (@studymaths) excellent mathsbot website. In particular his virtual manipulatives section. I found what I think to be some good ideas for algebra tiles and double sided counters and think that virtual manipulatives may be a very good way of getting these things into lessons.

When will I use this?

June 4, 2019 Leave a comment

Recently I read a rather interesting article from Daniel Willingham about whether there were people who just cant do maths. It was a very good read and I hope to write my thoughts on it later, when I’ve had more time to digest the material and form some coherent thoughts, but there was one part that set me off on a train of thought that I want to write about here.

The part in question was discussing physical manipulatives and real life examples. Willingham said that there is some use in them but that research suggests this can sometimes be overstated as many abstract concepts have no real life examples. He then spoke about analogies and how they can be very effective in maths of used well.

This got me thinking, earlier on the day a year 12 student had asked me “when am I ever going to use proof in real life?”. This type of question is one I get a lot about various maths topics, and my stock answer tends to be “that depends what career you end up in”. Many students, when asking this, seem to think real life doesn’t mean work. A short discussion about the various roles that would use it and that its possible they never will if they chose different roles but that the reasoning skills it builds are useful is usually enough and certainly was in this case.

It does beg the question though “why do they only ask maths teachers”? Last week when a y10 student asked about “real life” use of algebraic fractions I asked him if he asked his English teachers when he’d need to know hiw to analyse an unseen poem in real life. He said no. I asked if he thought he would. Again no.

So why ask in maths?

The Willingham article got me thinking about this. There has been, throughout my career, a strong steer towards contextualising every maths topics. Observers and trainers pushing “make it relate to them” at every turn. But some topics have no every day relatable context.Circle theorems, for instance, are something that are not going to be encountered outside of school by pretty much any of them. So maybe thats the issue. Maybe we are drilling them with real life contexts too much in earlier years, and this means when they encounter algebraic fractions, circle theorems or proof and don’t have a relatable context the question arises not from somewhere that is naturally in them, but from somewhere that has been built into them through the mathematics education we give them.

Maybe we should spend more time on abstract concepts, ratger than forcing real life contexts. Especially when some of those contexts are ridiculous – who looks at a garden and thinks “that side is x + 4, that side is x – 2, I wonder what the area is?” (See more pseudocontext here and here).

What do you think? Do you think we should be spending more time lower down om the abstract contexts? Please let me know in comments or via social media.

Simultaneous Equations

March 10, 2019 3 comments

It’s been a while since i last wrote anything here. Which says more about how busy I’ve been than my desire to write, but I hope to start writing more regularly.

This week I was teaching simultaneous equations and a student asked a question that made me think about things so I thought i would share.

I was teaching elimination method and I had done some examples with the coefficients of y having different signs and I put one on the board with the same signs and asked the class to think how we may go about solving. One of the students in the class put uo his hand after a while and said he thought he had solved it.

5x + 4y = 13

2x + 2y = 6

I asked hime to talk us through his thinking and he said “first I multipled the bottom equation by -2”

5x + 4y = 13

-4x – 4y = -12

“then I added the equations as before”

x = 1

“Then I subbed in and solved.”

2 + 2y = 6

2y = 4

y = 2

“so the point of intersection is (1,2)”.

This wasn’t what I was expecting. I was expecting him to have spotted we could subtract instead, but this method was clearly just as correct. It wasn’t something I had considered as a method before this, but I actually really liked it as a method and it led to a good discussion with the class after another student interjected with her solution which was what I expected, to multiply by 2 and subtract.

It was a great start point to a discussion where the students were looking at the two methods, and understanding why they both worked, the link between addition of a negative and subtracting a positive and many more.

I was wondering, does anyone teach this as a method? Have you had similar discussions in your lessons? What do you think of it?

Another Year Over

July 22, 2018 Leave a comment

So this is summer, and what have you done, another year over and a six week holiday just begun. – What Lennon may have written had he been a teacher.

I know what you are thinking, “why are you up so early? It is sunday and it is summer!” And you are right to wonder. Usually its my body clock that makes it so, but this year my 6 year old daughter has taken on that responsibility. Argh.

This year has been a good one for me. Tough in places, but enjoyable over all. I work at a school where I like my colleagues, like the vast majority of the students, feel that the department I work in is strong and that the senior leadership know what they are doing and are making decisions that are pushing the school in the right direction. When I moved to my current school, which was in the process of academy conversion following a 4 Ofsted grading, part of the draw was the chance to be part of affecting a positive change and improving the chances of the students. In the 2 years I’ve been here I’ve seen massive improvements and can see the trajectory we are on.

There’s been some tough times, but there has been some good ones too and I look forward to next year and our next steps in the journey.

This year I’ve spent a lot of time improving subject knowledge amongst the department. I feel this is something that needs to continue. It was made necessary this year as we had a number of non specialists and trainees in the department and most of the experienced maths teachers had never taught the new content that is now on the GCSE. This is something that needs to conrinue next year. We have no non specialists next year, but do have NQTS, trainees and staff who still wont have taught the new content. These sessions allow not only for building content knowledge but also for discussing subject specific pedagogy and possible misconceptions.

I’ve also thought a lot about transition from KS2 to KS3, this has been driven in part by a need to improve this area and in part by a fascinating workshop we hosted led by the Bradford Research School. I hope to write more about the workshop and the fascinating findings I’ve had while looking at KS2 sats data, nationally and locally, and the KS2 curriculum. Suffice to say, if you are a secondary teacher who hasn’t looked, your year 7s probably know a considerable amount more than you think they do on arrival.

The KS2 sats provide some great data and there really is no need to retest students on entry. Except maybe the ones who have no data. I’ve always been averse to KS2 SATS but the data they produce is so rich I feel I’m coming round to them. Although I’m not sure I agree with the way they are currently reported and I certainly stand against the idea of school league tables.

I’ve not written as much as I would have liked on here this year, and I hope to change that going forward. I didn’t decide to blog less, it just sort of happened, so hopefully I can turn that around.

Now it’s summer, I’m looking to relax, have fun and to teach my daughter how to enjoy a lie in….

Eid and Exams

June 15, 2018 2 comments

Today is the day that all the students in year 11 at my school, and I believe a majority across the school, sat their final GCSE paper. It was a physics paper. Today also happens to be Eid al-fitr. Eid is a holy day in the Islamic faith and marks the end of the holy month of Ramadan.

Eid al-Fitr is an important day in the Islamic faith. Muslims start it out by attending the mosque for prayers, before sitting down to share a meal with their families, which will be the first time they have done this during daylight in a month.

I teach in a school where, I believe, around 30% of the student body practice Islam. This year has been particularly hard for year 11, as many have been observing the fast of Ramadan during their exam period and have had to miss important parts of their Eid rituals and celebrations in order to sit their final exams. Eid al-Fitr, and Eid al-adha – the most important Islamic holiday, follow the Islamic calendar and as such move year on year. Next year, Eid al-Fitr falls on June the 4th, the same day as one of the English Language GCSE exams, which ALL y11 students will sit, along with Business and music exams. This date will also feature A Level papers for English Language, English Lang and lit, art, RS and Chemistry.

Personally, I would advocate for all holidays of all the major religions to be made bank holidays as the UK becomes an increasingly wonderful multi-cultural and diverse place, but I understand we are a long way from that dream becoming a reality. However, I am certain that a more achievable goal is becoming a society that manages to schedule GCSE and A-Level exams around such an important event.

Many students this year have been disadvantaged this year because they have had an exam on a day that is massively important to them, their families and their religion. GCSE exams that fell today cover science, taken by the vast majority of students, and Citizenship, an exam I would argue was extremely important. A level exams that fell today were PE, Economics, English literature, Mathematics, Further Mathematics and Chinese.

In the 2011 census Islam was the second biggest religion in the UK behind Christianity, and also the fasted growing religion. There are many local authority areas in the UK where more than 25% of the population follow the Islamic faith. These included Bradford, which is where I work, Blackburn, Luton and Birmingham. Some areas are over thirty, which includes Tower Hamlets, which has around 35% of its population following Islam.

GCSE and A Levels are important examinations; they massively affect the future of those that sit them. The stresses on students at this time is massively high and I feel that it is hideously unfair to make this more difficult on one subset of students purely based on their religion. To have a few fallow days during the exam period would mean what? Lengthening the session by a few days?! Surely it’s time we stopped punishing students for what they believe in.

Angle problem

December 5, 2017 2 comments

Today has been quite a geometric based day for me. I spent a couple of hours solving non-RAT trigonometry problems with year 10 and then a while with year 11 looking at various algebra angle problems. Then I went on Twitter and saw this from Ed Southall (@solvemymaths):

A couple of nice parallel lines questions that I might grow at y11 tomorrow.

Both are fairly straight forward to solve. I looked at the first one, imagines a third parallel line through the join if x and saw x must be the sum of 40 and 60 hence 100.

The second I saw an alternate angle to the 50 in the top triangle and used angle sum of a triangle is 180 to spot that x is a right angle. I glanced down at the responses and saw the vast majority had the same answers as me. That would probably have been the end of it but then I noticed this response:

The same thought process for the first one, but a significantly different approach to the second.

It made me wonder what approach others would take, and which approach my students would take. I wondered if the first problem had led this respondent into this solutions the second, and if so why it hasn’t had the same effect as me.

I don’t know if either approach is better, I just thought the differences were interesting. I’d love to hear your thoughts on it and how you would approach it.

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