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...

My article on Why Smartphones are a Really Useful Tool in the Maths Classroom has been published in Teachwire https://www.teachwire.net/news/why-smartphones-are-a-really-useful-tool-in-the-maths-classroom

I recently submitted a short clip for Craig Barton’s podcast on the theme of Slice of Advice: What have I learned this year?  In this I suggested two things that had had an impact on me this year: the use of graphing apps on smartphones and diagrams representing functions as mappings between number lines. Graphing apps on smartphones I’ve been using GeoGebra for over ten years now and it has had a huge impact on how I think about mathematics and teaching mathematics. I’ve also been massively impressed with Desmos though I don’t know it inside-out in the way I do with GeoGebra. My use of these graphing tools, and Autograph before it, was always based on using them on a computer and this means I have a preference for the computer software over the phone apps: I find them much more usable on a large screen with a proper keyboard and mouse.  This works fine for me but, as I’ve commented on here before, I think the greatest impact of technology in the mathematics classroom is ...

I've noticed a couple of tweets recently about the importance of being playful when doing mathematics and this has brought to mind an insight I had about simultaneous linear equations that occurred when I was being playful with them in technology. As a result of this I now have a different method for solving that I  prefer to the standard textbook approaches. Playing with simultaneous equations In trying to construct a pair of linear simultaneous equations where the solution went through a given point. I can't remember the point but I'll use (3,2) for the example. I did this by creating a point A at (3,2) then two more points B and C and finding the lines that went through these and A. This gave me the simultaneous equations: 3 x + y = 11 x + 5 y = 13 I then moved the points B and C around to find some different equations that would have the same point of intersection. This is probably best displayed here by showing all the different lines I got in a...

EEF (Education Endowment Fund) have published a report today on "Improving Mathematics in Key Stages Two and Three". The report is a meta-analysis of research into teaching and learning strategies and can be access in full at: https://educationendowmentfoundation.org.uk/evidence-summaries/evidence-reviews/improving-mathematics-in-key-stages-two-and-three/ The report has been widely publicised, mainly for what it has to say about calculator use. Although Key Stages Two and Three are outside my area of expertise I think there are useful reflections that can be made with reference to the use of technology, including calculators as well as other tools, in GCSE and A level Maths. Calculator use has a positive effect on students’ calculation skills  The conclusion in calculator use states: "When calculators are used as an integral part of testing and teaching, their use appears to have a positive effect on students’ calculation skills. ... When integrated into the teachi...