Digital technologies for learning mathematics

One of the fantastic features of dynamic graphing software is that you can animate how a graph changes as some aspect of it is varied. I'm particularly keen on making short GIFs of animated graphs that demonstrate interesting properties.  One advantage of animated GIFs is that they are really easy to distribute via Twitter. There are loads of them if you have a look at the hashtag #mathgif .  Parabolas I've been posting animated Maths GIFs to Twitter for quite a while now. Here are some of my favourites featuring parabolas: The midpoint of the points of intersection of y  =  x ² and y  = mx  + c lies on the line x = m /2. The tangent at point P to a parabola with vertex Q can be constructed by finding R, the point of intersection of the vertical through P and the horizontal through Q, finding the midpoint, M, of QR and then drawing the line through P and M. If the tangents at two points A and B on a parabola are perpendicular then the line AB goes through t...

The past few months have been a very chaotic time for teachers and students. Many schools and colleges are now back to teaching full time but this year is likely to be very challenging and teachers want to know that they can provide opportunities for students to learn, even if the normal day-to-day routines are disrupted. For me, one tool stands out as particularly effective in ensuring that students have interesting and engaging activities that will develop their mathematical understanding: Desmos Classroom. Desmos Classroom Activities  Desmos Classroom activities are collections of screens that provide students with the opportunity to interact and respond to mathematical questions. They can feature text answers, mathematical answers, graphical features, multi-choice, card sorts and many other types of elements.  There is a large selection of pre-made activities and it's really easy to adapt these or create your own. These activities are great for supporting students in think...

Most graphing tools have a feature to add a variable constant in a way that can be changed dynamically. In Desmos and GeoGebra this is by using sliders; in Autograph it is via the constant controller. When the parameter is changed you can view its effect on the graph and this can be discussed with students. You can even animate the change so you don't need to do it manually! This feature of being able to dynamically change a variable constant is a very powerful tool to help students build their understanding; however, to make the best use of it, it is useful to have some questions to ask to direct students' thinking. Effective questions when using dynamic graphs When I vary … how does it move and why? For what value of … will …? If I vary … how will it move? Examples using the intersection of a line and a parabola To exemplify this I'm going to use the intersection of the parabola y = x 2 with the line y = mx+c . To do this I've plotted: y = x 2   y...

My article for NCETM: "Ten calculations that A level students should be doing on a calculator: can yours?" can be read at: https://www.ncetm.org.uk/resources/54231