Digital technologies for learning mathematics

In March of 2017 I was involved in creating a set of videos looking at aspects of using technology in A level Maths teaching. The full list of videos can be found at: http://furthermaths.org.uk/pd-videos-technology The first of these videos is on using graphing software for multiple representations. The video features an example of me using graphing software to highlight the link between graphical, algebraic and numerical representations so students can understand the ideas behind differentiation. Questions for reflection The video suggests three questions for reflection: What topics would you use graphing software for? What are the advantages of using prepared files? What questioning strategies are effective when using graphing software? Here are my responses to these questions: What topics would you use graphing software for? When teaching A level Maths, especially Pure, I can't think of a single topic where using software to display multiple representations w...

I was recently asked the following two questions in an email.  Teachers: What can the mathematics education community do to increase the use of digital resources by KS5 teachers? Students: How can time be found in the KS5 teaching programme to bring up the students’ skills in digital resources? I've reposted my response here: 1. Teachers: What can the mathematics education community do to increase the use of digital resources by KS5 teachers? I have a model for this of 10:80:10 for teachers who are really interested in technology/will use technology if it helps/will rarely use technology.  I think the most effective strategy is to concentrate on the middle 80%.  For these the single most important criterion to judge any resource on, including a digital one, is whether it is the best tool to help students understand the concept.  Many of these teachers don’t have the time to learn complicated software, such as Mathematica, but would use a graph-plotter in fron...

Last week the MEI new A level for Maths was accredited – the first full A level to be accredited of all the specifications.  The specification includes advice on using technology and the sample assessment materials have questions which lend themselves to the use of technology when teaching the topic. Use of graphing tools for families of curves The MEI specification includes guidance for activities that should be carried out during the course.  The first, and possibly most important, of these is: "Graphing tools: Learners should use graphing software to investigate the relationships between graphical and algebraic representations, e.g. understanding the effect of changing the parameter k in the graphs of y = 1/ x + k or y = x ² – kx " The ability to plot a family of curves, and observe the effect on the graphs of dynamically changing a parameter, is an incredibly powerful tool in helping students understand mathematical relationships.  Understanding how a mathemat...

Last Friday (8th April) the DfE published the GCE subject-level guidance for mathematics.  This guidance is for awarding bodies to help them in designing their specifications and assessments.  The full document can be found at: https://www.gov.uk/government/publications/gce-subject-level-guidance-for-mathematics Requirement for awarding bodies to explain how use of technology will permeate the study of mathematics In the Overarching themes and use of technology section: “ Paragraph 8 of the Content Document states that – 8. The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics. This statement should be interpreted primarily as indicating the desired approach to teaching GCE Qualifications in Mathematics. However, this statement also has implications for assessments. Consequently, in respect of each GCE Qualification in Mathematics which it makes available, or proposes to make...

I recently gave a talk about doing Maths on a smartphone.  I chose four of my favourite apps.  I like these apps because in all of them there are opportunities to think and work mathematically, not just passively observe prepared material. MyScript Calculator MyScript is really easy to use – you just write the calculations with your finger. Android: https://play.google.com/store/apps/details?id=com.visionobjects.calculator&hl=en_GB iOS: https://itunes.apple.com/gb/app/myscript-calculator-handwriting/id578979413?mt=8 Problem to try: What’s the maximum product of a set of positive numbers that sum to 19? Desmos Desmos is a very user-friendly graphing calculator.  In my experience most people find the interface intuitive and are able to work with it very quickly. Android: https://play.google.com/store/apps/details?id=com.desmos.calculator&hl=en_GB iOS: https://itunes.apple.com/gb/app/desmos-graphing-calculator/id653517540?mt=8 Problem to try: What...

GeoGebra have recently released a version for Android phones. Having played around with it it seems very responsive. The ability to select/drag objects and the speed that it updates appears to be really good - much better than when viewing GeoGebra worksheets via a browser. An example: gradient of the tangent to a curve at a point     This is an example that shows how the gradient of the tangent to a curve at a point varies with the point.  The app is so quick and easy to use that this took me 17 seconds to create (I timed myself!). Use of smartphones in classrooms This app presents a fantastic opportunity to put dynamic maths software into the hands of students.  As I've commented on before, I think the real benefits of technology come when students are using it.  In addition to this there are significant advantages when this is on a device that students have an attachment to and feel ownership of.  Most people feel their own phone is a devic...

Last week I attended the GeoGebra Global Gathering in Linz, Austria.   There were lots of fantastic ideas being demonstrated but these are a few of my highlights that I think I’ll be making use of … Students creating animations It was great to see some ideas from Fabian Vitabar from Uruguay about student tasks that involve them creating animations in GeoGebra.  There were two different suggestions for doing this – one was to get the students to create an animation such as a bouncing ball by animating points appropriately and then adding images to make the animation look like a real scene.  The other was to create some more pure maths based animations such as moving points around a polygon.  You can see a GeoGebraBook of his talk and some examples at: https://tube.geogebra.org/b/1408699#material/1408705 .  I think it could be very motivating to students to create animations like these and there is a lot of maths that they’ll need to sort out for themsel...