Digital technologies for learning mathematics

I've been asked again this year to contribute to Craig Barton's end of year podcast: Slice of advice - what have I learned this year:  http://www.mrbartonmaths.com/blog/slice-of-advice-2019-what-did-you-learn-this-year/ The main thing that I've learned this year is how few teachers are familiar with Richard Skemp's ideas on instrumental versus relational understanding. I meet a lot of teachers in my job and I will often have only one or two teachers in the room who have read it. These ideas have been fundamental to my development as a mathematics educator and I see it as the key concept that is most illuminating when considering ideas about teaching and learning in maths. It is also one of the main reasons why I am so passionate about the use of technology in maths. Instrumental versus relational understanding Skemp published his ideas in the 1970s but they are still available via the ATM website at:  https://www.atm.org.uk/write/MediaUploads/Resources/Richard_Sk

In 2011 I completed an MA in ICT and Education through the University of Leeds. My critical study was on "Using Dynamic Geometry/Graphing software to set students open-ended mathematics investigations". It can be downloaded from:  https://drive.google.com/file/d/1pgFvIjkuEQRpzUm4uJ_KZ1mnql6UZfJ9/view?usp=sharing

Over the past week I've been exploring CloudReady from Neverware. The idea behind it is that it takes an old laptop and effectively converts it into a Chromebook. I took an old Windows laptop (I'm not sure of the exact age but I think it was about 10 years old). It was running so slowly that it was practically unusable. I replaced it with their operating system, which is based on the Chromium OS, to turn it into a Chromebook. The process was pretty straightforward - it required me to make an installer on a USB stick and then I ran the installation. Overall it took less than an hour but it would be quicker if I were to repeat it. It was a full replacement of the OS, but given that the laptop was destined to be disposed of, this wasn't a problem. I've now got a fully working Chromebook and I'm really impressed with it. It runs really quickly - the browser is at least as fast as my current Windows laptop and I can watch/stream videos on it clearly. You can see a pi