Digital technologies for learning mathematics

This is my favourite technology-based maths problem, and possibly my favourite maths problem.  It needs to be attempted in software that has linked geometrical and algebraic views (and preferably some others too).  GeoGebra or TI-Nspire are ideal for this. Start with a square of variable side with one vertex on the origin and one on the positive x-axis: The problem is to create a rectangle with the same area as the square whose sides are in the ratio 2:1. Creating the initial square in GeoGebra Add a point A at the origin. Add a point B on the x-axis. Use the Regular Polygon tool selecting vertices at A and B and set the number of vertices to 4. Creating the initial square in TI-Nspire Add a new Graphs page. Add a point at the origin by finding the Intersection Point of both axes . Add a new Point On the x-axis. Display the Coordinates of this point. Use Measurement Transfer to transfer the value of the x-coordinate to the y-axis. Add a line Perpendicular t

Mechanics is more than just an application of algebra and geometry, it is the primary application of geometry and algebra.  Newton’s development of calculus was to answer problems in what we would now call mechanics and much of his work was geometrical in nature.  However, students study less geometry than they use to and this, along with difficulties in algebra, can result in issues when they start studying mechanics. As a remedy to this software that links geometry and algebra is perfect tool in which students can practise modelling situations in mechanics.  This can complement their studies in mechanics and enhance their skills. In particular two main methods that lend themselves well to being represented in software are interactive force diagrams and animations of position. Interactive force diagrams Interactive force diagrams can be created where the vectors for the forces acting on an object are represented dynamically. The diagram below shows the forces acting

In a previous post I wrote about how Computer Algebra Systems (CAS) are really useful tools for teaching when writing questions: http://digitalmathematics.blogspot.co.uk/2011/08/using-cas-for-writing-questions.html  This focussed on teachers using them for preparation but not necessarily exploiting them in the classroom. Many teachers are reluctant to use them in lessons when they aren’t allowed in examinations.   There is also the view that the purpose of mathematics lessons is for students to learn processes and therefore a tool that can perform those processes will hamper students’ progress. CAS is out there There are free tools available online that have CAS built into them such as websites like Wolfram Alpha , and software such as Geogebra and Microsoft Mathematics .  If students find these they can use them when set basic algebraic tasks.  A series of questions on factorising quadratic equations can be performed very quickly on Wolfram Alpha! Once students are aware