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## MyMaths Update

Thought I should provide an update on last nights post.

This morning the MyMaths team must have come into a deluge of tweets as they started work tweeted that they apologised for the message on these slides and were working to update this lesson.

True to their word, by the afternoon this lesson had been updated and the first slide is now the following

They have also published this blog post about when they update content.

While I don’t think it was very good that the original slide ever existed I am very impressed with how quickly they have acted on our feedback and changed their slides.

Thank you for doing this – it is good to see such a negative message removed.

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## Another MyMaths Post

I’ve written about a pretty awful MyMaths question before and this is another post about MyMaths – I promise I will keep it brief.

When I saw the screen shot below that had been tweeted by Michelle MacDonagh (@michellemacd) I genuinely thought it was a photoshop by someone. Alas, it turns out that this is not the case:

For a product aimed at the maths education market to promote this idea in any way is unbelievable.

To be fair to MyMaths, clicking through reveals the next part

Personally, I don’t think this mitigates what is at the top of the page. Many students will be looking at this lesson on their own, and perhaps not pick up on the obvious untruths that have been written above.

Unfortunately, clicking next one more time reveals this ridiculous pearl of wisdom from MyMaths

What a great way to promote the importance of understanding behind a concept…

I cannot think of any justification for this… I would be very interested to hear MyMath’s reasoning behind this.

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## #Mathsconf5

Yesterday morning I wasn’t as positive setting off early to #mathsconf5 in Sheffield as I normally am due to having felt really ill on Friday and I still wasn’t feeling great on the Saturday morning. Giving a workshop in the first session meant that not going wasn’t really an option and I was very thankful to @Miss_J_Carter for offering to drive. I’m also going to put not being sure if I recognised Hannah (@MissRadders) in the queue for car park money down to my poorly-ness!

When I arrived I was (incredibly) excited to be given this tea towel by Julia (@tessmaths):

I hope she understands just how happy this tea towel made me!

The conference started as usual with a presentation by Andrew Taylor of @AQAMaths – he helpfully put his slides online here. I was particularly interested to hear about the KS3 assessment materials that they are going to be releasing.

Following that we had the speed dating 🙂 The first one ended up being more of a general chat though. For the second someone who isn’t on Twitter shared the idea of having a grid that students work through to formalise the process of solving an equation for example. I like this idea as it provides a bit of structure and would hopefully lead to better written mathematics from students. The last person I spoke to is also not on Twitter and talked about using tools such as Secretive which I have used a couple of times before but then also mentioned Mentimeter which I haven’t used before. A friend of mine recently mentioned the graphing capabilities of Mentimeter so i need to look at this soon.

I’m going to briefly highlight the best bits of each session, but I didn’t take as good notes as normal so they are definitely not comprehensive!

Session 1:

I was delivering a workshop entitled “How to enjoy (and Succeed at) Your NQT Year” during the first session of the day. I’m not going to say a lot here as I plan to write about it specifically (hopefully tomorrow, definitely by Friday) but I enjoyed the discussions I had with people attending my workshop. It was particularly nice to have @dannytybrown in my session.

[prezi id=”http://prezi.com/-dz30jtfabtw/?utm_campaign=share&utm_medium=copy&rc=ex0share” align=center width=600 lock_to_path=1]

Session 2:

For Session 2 I had chosen @dannytybrown‘s workshop “Time to Slow Down?”. It wasn’t what i was expecting but I really enjoyed it. I was sat on a great table where we had a lively discussion about the initial slide

What do you notice? I had never really considered looking at the formula for the sum of an arithmetic sequence in conjunction with a picture of a trapezium before – some great points were made by people in the audience.

We then discussed an account of a conversation between Danny and someone else about an observation of a particular A Level lesson. The conversation is hopefully viewable in these photos of the handout:

It was interesting to consider this as it raises many important questions. I certainly think becoming emotional and letting yourself be annoyed means that as a teacher you don’t reflect properly on a lesson.

Session 3:

Luke Graham (@BetterMaths) chaired a session where attendees collaborated to come up with a list of topics that they are wanting ideas of how to teach in the new GCSE and then some ideas of how to do this. I had been asked to oversee a table looking at the Statistics strand – there really isn’t much in the new GCSE on statistics. The result of this session is shown in Luke’s tweet

I’m looking forward to seeing where he takes this.

The TweetUp:

During a nice long lunch break ( the mini pies were pretty good) the TweetUp organised by Julia (@tessmaths) took place. This is becoming a bit of an institution and I was on the QRCubed table again which embarrassingly I had forgotten how to solve. Lots of people were getting involved with Pete Mattock’s (@MrMattock) STEP questions, Jo’s (@mathsjem) selfie booth and the various other activities on offer. The “TweetUp and do Some Maths” is a great part of the day and if you haven’t been to one before make sure you come at #mathsconf6.

Session 4:

This was the first session that I decided on. Bruno Reddy (@MrReddyMaths), Craig Jeavons (@Craigos87) and Matt Fox (@MFx15) have recently returned from Shanghai and this session “Sh****ai Is Not ADirty Word” was dedicated to them sharing some of the things they experienced and noticed.

I was interested to learn that the students do eye relaxation techniques every day – perhaps something we should implement over here, I’m sure it would help me at least! I think the fact that teachers in Shanghai work in 5 year cycles and must log 240 hours of CPD in those 5 years in order to progress to the next level is significant. This is much more than in the UK and surely improving teacher’s practice is the thing that will lead to the biggest increase in assessment scores (whether we want this to be the focus is another question!).

The quick ramp up in difficulty of the questions concerning the simplification of surds shown on the slide below is very interesting. Question 3 is significantly harder than question 1.
I would be afraid to use such varied questions (where the difficulty increases quickly) in a “quick response” activity as shown below.
I liked the evidence of students who are equivalent to Year 10 using the $$\because$$ and $$\therefore$$ symbols to explain their mathematics. I firmly believe that we should be encouraging this sort of formalism in our students, certainly at A-Level.

The variation in the index law questions above is striking. In the UK we would normally do lots of similar questions such as:

Because of this our students aren’t being exposed to as wide a variety of situations where the index laws can be applied – this leads to difficulties in the future, for example when cancelling algebraic fractions down.  James Pearce (@MathsPadJames) has written about this in a great post yesterday.

Session 5:

Kris Boulton’s (@Kris_Boulton) talk on the “Stories of Maths” had been one that I was really looking forward to and he didn’t disappoint. Writing about it really can’t do it justice and luckily I recorded it, so if you missed it download the file (it’s about 1.6GB) from here and watch it – you won’t be disappointed.

I particularly enjoyed the reading about Sumerian (I think!) shepherds and how they could find out if all sheep had returned before the invention of counting. Will definitely be using that in class. The origin of the word “sine” was also interesting as I didn’t know the full story there.

Overall it was a really good day, and as ever great to catch up with people. Mark McCourt has written a blog post outlining the philosophy of the mathsconfs that is worth a read.

Looking forward to the next one on the 5th March in Peterborough…..

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## A Love of Romanesco

I was pretty excited to discover that my local Aldi had Romanesco cauliflower’s for sale – from Nottinghamshire no less.

Above are some pictures at various levels of zoom.

I really like looking at Romanesco cauliflower as it is possibly the closest approximation in nature to a mathematical fractal. Because of nature’s many approximations to fractals, fractal growth is incredibly important in computer games to create life-like environments.

If you are interested in coding a simple fractal check out my old post on Barnsley’s Fern

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## The Second #mathsjournalclubarticle has Been Chosen

So the day to announce the next #mathsjournalclub article as come, and it was a landslide victory, garnering over 52% of the votes.

The article you have chosen is “Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts” by Colin Foster, as published in the International Journal of Mathematical Education in Science and Technology.

• In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the expense of more independent engagement with richer, multifaceted tasks risks devaluing the subject and failing to give learners an authentic and enjoyable experience of being a mathematician. Thus, there is a pressing need for mathematical tasks which embed the practice of essential techniques within a richer, exploratory and investigative context. Such tasks can be justified to school management or to more traditional mathematics teachers as vital practice of important skills; at the same time, they give scope to progressive teachers who wish to work in more exploratory ways. This paper draws on the notion of a musical e ́tude to develop a powerful and versatile approach in which these apparently contradictory aspects of teaching mathematics can be harmoniously combined. I illustrate the tactic in three central areas of the high-school mathematics curriculum: plotting Cartesian coordinates, solving linear equations and performing enlargements. In each case, extensive practice of important procedures takes place alongside more thoughtful and mathematically creative activity.

This looks a really interesting article and I hope that many of you will join us (despite it being term time) for the discussion on Monday 19th October at 8pm.

The second and third place articles will now go through to the next poll, along side some other suggestions.

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## A Sixth Form PRET Homework

One of the many jobs that I had wanted to do over the summer was to create PRET homeworks for the A-Level modules that I was going to be teaching this coming year. Along with the website design this didn’t really happen, so now I am doing them throughout the year as I go.

I thought I would share one I made this week as I am trying to do at least one resource post and one more general math/education/math education post every week.

Jo Morgan (@mathsjem does a great job collating all the PRET homework that people contribute at her PRET homework site, so make sure you take a look to see all the wonderful homework for KS3,KS4 and KS5 that are available. The one I contributed this week is for “The method of differences” which is in the Edexcel Further Pure 2 module.

The use of the method of differences to sum infinite series isn’t often touched upon in A-Level and so I included that in the research part. For the skills section i tried to make most of similar to the ones in the official A-Level text book, apart from Question 4 which is harder than you tend to get for the current FP2 syllabus. It is only harder as I don’t give the function you require to apply the method of differences; the students only need to remember that the function tends have a power that is one order above the terms you are trying to sum and it drops out fairly easily. The stretch questions I have taken from the old Rostock and Chandler books that I love, these are harder than the ones typically seen at FP2, but definitely not insurmountable.

This sheet is available here or in the Algebra section of Jo’s site.

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## Demonstrating a Love of Learning Maths in Lessons

Today I am hostingthe first #mathscpdchat of the new academic year. Between 7pm and 8pm we will be discussing the following topic: “How do you demonstrate to your pupils that you have a personal love of learning maths?”

Since being asked to host this, I’ve been thinkning quite a bit about this and this short post briefly distills some of that thinking.

Of course there are some areas of math that I have a personal leaning towards, but I would say that I love learning about any are of maths. How to demonstrate this to a class at school is somewhat harder to pin down. Rightly or wrongly, teachers are often perceived by their students as all knowing and so as far as they are concerned there is no more learning for us to do – I beleive it is important ot challenge this perception.

Below are some things that I think can help us show a love of learning.

• This is probably easier with an A-Level class, but I will normally choose exercises to do on the board that I haven’t looked at before. This serves two purposes in my opinion;it slows me down so that I don’t gloss over any exposition that may be key to someone else’s understanding and it also demonstrates that I need to try different approaches, or learn a new technique in order to be able to master it.
• If possible talking about current mathematics research that has made the news is good for many other reasons than just showing that I enjoy learning about mathematics. For example, the new result about tiling pentagons is accessible to anyone with a basic understanding of interior angles of a pentagon.
• Promoting the love of learning of any subject by being interested in discussing any topic or subject with a student. I think the love of learning is infectious and so showing that you enjoy learning and see it as something rewarding in itself has to be a good thing.
• Being positive when teaching any topic. Students seem to be scarily perceptive of whether we like (or value) a particular topic – I have definitely made this mistake before.

I’m looking for better ideas than this to demonstrate my love of learning mathematics. It seems very hard(to me at least) to convey the excitement I feel when working through a new problem or learning some cool new result.

I’m looking forward to discussing it in just over half an hour. Join in tonight’s #mathscpdchat at 7pm (UK time)!

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## The End of This Year’s #summerblogchallenge

Today was an inset day for me, so technically yesterday’s post was my last #summerblogchallenge post, however I thought I would briefly round off the challenge tonight.

Overall I have enjoyed it, but I am looking forward to relaxing a bit and not having to post every day. Some days it was hard to find a topic that enthused me to write about! Having said that, there are plenty of things that I considered writing about but didn’t get around to, and these may make appearances over the next few months. In particular, I remember saying that I will be writing about the Cauchy-Schwarz inequality so I will try to do that some point soon.

I have loved reading all the other posts by my fellow #summerblogchallenge people and I have tried to select my favourite post from each of them.

• Christine Norledge (@MissNorledge) – this post about the top 5 resources for rich tasks and problem solving.
• Mark Wilson (@mwimaths) – I enjoyed reading about his joining into maths in this post
• Kim Thomas-Lee (@kimThomasLee) – great post about various activities at a “Numeracy Challenge day”.
• @funASDteacher – This post has added a book to my reading list

I’m not really sure if I have a favourite post but I did like the one about the first #mathsjournalclub discussion as I was very glad that the discussion went well.

I’m contemplating doing the #summerblogchallenge again next year….

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## A VideoScribe Video

During the last week of the holiday I was inspired by some videos that Jo Morgan (@mathsjem) has produced (as seen in her great blog post on Behaviour Management) using the VideoScribe software to produce a Classroom Expectations video of my own to use.

I am looking forward to using this piece of software some more.

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## Proof School

I was wondering today how many people in the UK had seen the article about Proof School in the San Francisco article.

I saw this article on KQED.org towards the end of July and found it fascinating. The idea of a school dedicated to helping the most gifted at mathematics excel really appeals to me. Personally, I feel that the most gifted students of maths, particularly in state schools, sometimes don’t get the maths education that that they deserve. I remember that when I was a student, it was a widely held view amongst other students that the “top set wasn’t really cared about as they would get the grades needed for the school without particularly inspiring or good teaching”. I certainly, now that I am a teacher myself , don’t believe this is a widespread view held by teachers and generally I think teachers do the best they can for all of their students. However, it is a fact that in many schools top set classes are generally bigger than the lower attaining classes resulting in each individual having less teacher time spent on them. This means that there is, necessarily, less dedicated time spent on developing that gifted individual’s mathematics – to me this doesn’t seem that fair.

Teacher expertise is also an issue – the most gifted students at mathematics by the time they are at secondary school are probably significantly better at maths than most teachers of the subject (I’m definitely including myself here – I just know a lot about one tiny tiny area of maths!), and whilst things such as IMO and UKMT exist I think it could be nice to bring the most gifted students in a region together for sessions where they are taught (or allowed to are discover for themselves) some mathematics that is of a much higher level than they would normally be exposed to in school.

I would urge anyone interested to take a look at the Proof School’s website. I particularly found the academic information interesting (additional languages offered are Latin and American Sign Language – no foreign language which is a bit strange). The structure of the mathematics curriculum is very much more like a University level structure with some really interesting topics included. I like their description of a “maths kid”

Their characterisation of a maths kid as someone who loves maths is really nice, I firmly think love of maths not ability should be celebrated. If someone loves maths then they will soon be able to excel at maths I think. 2.5 hours of maths in the afternoon would have been a dream for me when I was at school.

The school has axioms that are used to define the school

Number 3 is something that I think should be talked about more – mathematics is a social and creative subject, not just an intellectual pursuit!

I wonder if something similar could work in the UK – I would possibly be interested to be part of it if it was tried – the closest that I can think of are academies with a specific STEM focus, such as the newly opened NUAST Academy in Nottingham.

What do other people think of the idea of a school where maths is given much greater prominence (though other subjects aren’t neglected) than it is in most schools?