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I had intended for a different post to go live today, but it looks like the post that was scheduled didn’t save properly so I have quickly thought of something else to write about. Looks like I will get it posted just in time so it is probably going to be shorter than some…. 

I enjoyed reading yesterday’s #summerblogchallenge post from Christine (@MissNorledge) concerning her top 5 sites for starters. Unfortunately though I was reading it on my iPad and consequently some of the links reminded me of one of my great pet hates. 

The two things that drive me round the bend with my laptop is the seemingly constant need to update the Adobe Flash plugin and the Java plugin: neither of these update in a “clean” way, they take far longer than you would expect and break my workflow. I’ve hated Flash for a long time; when I first had a Mac, Flash  would regularly crash safari because of some unexpected error. Unfortunately I can’t write as eloquently about my dislike of Flash as Steve Jobs did in 2010 in his famous “Thoughts on Flash” but suffice to say that in general I am extremely happy that neither my iPad nor my iPhone support Flash and I think that the Internet would be a better place without it. 

The only niggle is that there are some great maths resources out there that have been written in Flash and Christine’s post highlighted some of them and reminded me of this. Ideally I look for resources that are robust and will work on whatever device I happen to be using. This is especially true of I am intending on letting students access some of them – I know that se of them don’t have a computer at home but do have an iPad so anything incorporating Flash or Java applets is a no-no. 

I appreciate that recoding resources to avoid Flash is a massive undertaking but with the completely open standards of JavaScript and HTML5 I genuinely think it is worth the effort. More and more people are using iPads as their primary computing device, some schools are adopting a one-to-one iPad policy and so using the more modern and open standards is surely a no brainer. 

I’ve made my pentominoes resource using CSS, HTML5, JavaScript and the fabric.js library for this reason. I have a few other small resources in various stages of development and am hoping that I will be able to get them completed over the summer. Any of the Geogebra worksheets that I embed in HTML pages (such as this on conic sections and this investigating graph transformations ) use HTML5 so that they work on all devices. I also recently became aware of the website amathsteacherwrites from Jeff (@jeff2869). On this site (as well as some interesting blog posts) there are some great draggable maths activities, such as this matching graphs activity that work on any device. The wonderful Times Table Rockstars developed by Bruno Reddy (@MrReddyMaths) also works on iOS devices (though I understand that there will be dedicated apps coming out which will no doubt improve the UI experience even further for these devices). 

I hope that, over time, more resources which avoid the use of Flash come out and I will try to do my bit and add to them myself. 

Just a short post today where I thought I would share a resource that I found almost a year ago and have used with multiple classes since. This resource works as a starter, main activity or plenary depending on the class and where in a sequence you want to do it.

This resource is from William Emeny (@Maths_Master) and was posted on his excellent Great Maths Teaching Ideas website. It is a card sort of famous number sequences as shown below

  
The high resolution pdf version can be found on his site here. I think it is great how for each sequence you are matching the name, a pictorial representation, a way to produce the sequence, a fact about the sequence and the first few terms of the sequence. There are six sequences contained in this card sort

1. Even numbers
2. Odd numbers
3. Square numbers
4. Fibonacci numbers
5. Cube numbers
6. Triangle numbers

Thanks again for sharing it!

Apparently it was my first WordPress Anniversary on Saturday so I thought I would quickly re-share my first 3 blog posts:

1. Hello World – A First Blog Post
2. Why Teach
3. Thoughts on the Draft Maths A Level Content

I wasn’t as regular with posting when I first started ……

Last week Jo Morgan (@mathsjem) posted a picture of a Wordle formed from all her tweets since she joined Twitter. This led me to think about my Twitter history.

Back in 2009 I had experimented with Twitter, but didn’t stick at it and kind of forgot about it until I set up my “professional” Twitter account (@DrBennison) on the 1st of May 2014. I then sent my first tweet on the 7th of may, tweeting a photo of some resources I was cutting up for a Year 8 problem solving lesson.

Inspired by Jo I downloaded my twitter archive and used wordle to create the following Wordle from all my tweets. 

  
  I really value Twitter for collaboration with colleagues across the country (and further afield) and would encourage anyone to sign up and start talking to people. I haven’t met anyone on Twitter who isn’t friendly, encouraging and always happy to provide advice and share resources. As you can see from the above picture, I must have engaged with quite a few people repeatedly for their twitter handles to come out large.

For the next week or so I have pre-written my daily blog posts and the main tweets announcing them as I am going away up north for a break. I may not have such a good reason to not be able to write my posts on the day as @MissNorledge but I have stolen her Twuffer idea and am giving that a go.

It seems timely to write about something that I think is very important as a teacher to give yourself a break sometimes. It is very easy to constantly be thinking about work, marking, preparing resources and planning lessons. And, now there is the added addiction to Twitter that takes more time up…

I love having access to the internet, and to be honest I do often find it a bit of a panic when I haven’t got at least 3G on my phone. However sometimes it is really nice to have a break and be free from it all for a while.

This is of course possible during the holidays, but to a lesser extent I think it is important to try and manage it during term time too. I try to do no work on a Saturday for example, preferring to work more during the week and do a bit on a Sunday. I think having a day completely away from teaching is really beneficial and helps keep me sane – it would be one of my top tips for anyone new to teaching.

I also think it is important to be aware of “the law of diminishing returns”: you can spend hours trying to make a resource completely perfect, but as you spend more time on it you have less and less impact on the actual resource. I once remember spending 6 hours trying to get a piece of Excel to do what I wanted it to do for a 10 minute segment of a lesson – definitely not time well spent!

Please wish me luck with having a bit of a break, I do struggle to turn off to be honest. Good luck to you too if you are doing something similar 🙂

Yesterday’s post was a bit mammoth, so today’s post is much shorter! I’m sure you are all releived by this. 

Back in April I posted on my Mathematical Journey and in that post I mentioned how I felt lucky to have a granny who was a maths teacher. 

Ever since I can remember she would talk about maths with me, set me problems to do and send me coded messages in the post. As she taught at the Royal College for the blind this included teaching me Braille which sadly I can no longer remember. Whilst sorting through some stuff last night I found some old letters etc so thought I would share a photo here 

 
My handwriting hasn’t really improved much since then to be honest. 

So, here is issue 88 of the Math(s) Teachers at Play blog carnival. This acts as a round up of some cool blog posts that have been published since issue 87 over at cavmaths. As usual people have submitted entries, which I will supplement with some posts that I have really enjoyed reading in the last few weeks.

It is tradition for the post to start with something about the issue number so here goes!

Firstly, here are a few calculations that result in 88 (taken from Zoo of Numbers

\( \begin{align} 88 &= 23^2 – 21^2 \\ &= 13^2 – 9^2 \\ &= 4^2+6^2+6^2 \\ &= 2^3+2^3+2^3+4^3 \\ &= 3+4+5+6+7+8+9+10+11+12+13 \\ &= 17+ 19 + 23+29 \end{align} \)

88 is also an Erdos-Woods number. An Erdos-Woods number, \(k\) is defined to be the length of a chain of numbers \(n,(n+1),(n+2), \cdots + (n+k)\) such that each integer \(n+i\) for \(0<i<k\) shares at least one prime factor with either \(n\) or \(n+k\).16 is an Erdos-Woods number because for each number in the chain

\(2184,2185, \cdots, 2199,2200\)

shares at least one factor with either \(2184\) or \(2200\). TheErdos-Woods numbers are sequence A059756 in the Online Encyclopedia of Integer Sequences, the first few are as follows

\(16,22,34,36,46,56,64,66,70,76,78,86,88,92,94,96,100 \)

I am now wondering if there is a nice way to compute Erdos-Woods numbers, yet another thing to look at when I get the chance…

Right, I had some really interesting submissions this month.

Jo Morgan (@mathsjem) shared this great post about Teaching Foundation GCSE (Grades 9 and 10 in the States) classes. This is one of her most popular posts of all time, and it contains some great tips for engaging those students who really struggle at maths – I know I will be returning to it when I am teaching Foundation GCSE.

Lisa (I can’t find her on Twitter unfortunately) shared an article she has written for the Huffington Post titled “Reconsidering Math as an Art Form”. It was inspired by Paul Lockhart’s essay a “Mathematician’s Lament”. I agree with Lisa and think this should be essential reading for mathematics educators. I particularly liked his comparison of the teaching of Mathematics to the teaching of music – I fundamentally believe mathematics is as creative as any of the creative arts and it is a massive shame that a lot of school children don’t see this side of maths.

Stephen Cavadino (@srcav) shared this amusing post linking a “Quirk of Probability” to a mobile game. I really enjoyed reading this before I received the submissions, and it was nice to be reminded of it.

April Freeman (who blogs here) has a post about using bundles of popsicle (or ice lolly sticks) to help with the understanding of place value for her daughter. I think this could be a useful technique to help with the visualisation of place value.

This nice review of a year of running a maths club for 4th and 5th graders by Benjamin Leis is well worth a read, there are some great tips that are applicable to general teachers as well as those running extra-curricular clubs. The Yearly Topics Map on his blog also contains links to some really nice resources.

Mrs E (@MrsETeachesMath) has shared this fairly short post on introducing proof. Proof is always a topic that is relatively challenging to teach. The ordering a story idea is a nice analogy to emphasise the importance of logical thinking when completing a mathematical proof.

Christy (@housefulofchaos) is a homeschooler based in Ontario and she submitted this on “Minecraft Multiplication Practice”. I confess I’ve never played Minecraft, but I am now very intrigued by this detailed post on a way to make multiplication more interesting. I’m also very curious about the online course she is running on Minecraft Maths, I wonder if I would be allowed to join?!?

Pea has shared a post on using concrete manipulative to teach the addition of fractions. Too often addition of fractions seems to be based on rote learning and I like how the understanding is at the fore-front of this approach, and I like the fraction discs.

Denise Gaskins (@letsplaymath), the organiser of this carnival has shared this fantastic post on introducing infinite series to children  with a puzzle courtesy of Don Cohen and an additional puzzle for older children from James Tanton. The infinite series approach to the solution of James Tanton’s puzzle is amazing, and I certainly don’t think I would have come up with it – I used similar triangles! I hadn’t seen Don Cohen’s “Map of Calculus for Young People” before, or looked at Don Cohen’s site; I’ll be spending more time here!

The final submission comes from Manan (@shahlock) who has shared his comic for Pi approximation day. I love Manan’s comics, make sure you check out the others.

I came across this site examining the maths of banknote patterns, it is a really interesting read. I had n’t really considered the mathematics behind these patterns and I will certainly be exploring them more in the future. I came across this article thanks to Colin Beveridge (@icecolbeveridge) who tweeted it alongside this Desmos sheet . Colin has also recently shared his Mathematical Journey (in response to this post of mine), it is a really interesting read, and contains some useful advice for any budding mathematician.

Danny Brown (@dannytybrown) has, in the last couple of days shared this long post about mathematical teaching styles. I promise it is worth spending time to read to the end!!! Get involved in the conversation about it on Twitter to.

Because of my background I am very interested in computer programming and the benefits this can bring to mathematics education. I have been looking at some early programs designed to be used in the maths classroom for the BBC Micro and have discovered an emulator by Matt Godbolt (@mattgodbolt), he has a video describing the coding of this available here.

Finally a few of us our taking part in a challenge to write a blog post every day of the summer holiday, the index is available here. At the moment it is me, Christine Norledge (@MissNorledge), Kim Thomas-Lee (@kimThomasLee), Mark Wilson (@mwimaths), Archbishop Sancroft High School maths department (@ASHS_Maths), @funASDteacher and Jennifer Stice (@mathchick5) taking part. We would love you to take a look t our posts and maybe join us in the challenge?

The next edition of this blog carnival will be at Mrs E Teaches Math.