Digital technologies for learning mathematics

Last week I went to two events where the subject of programming came-up, and specifically how useful a tool it is for the learning of mathematics.  Essentially to be able to program a computer to perform a process you need to understand it first and also the process of thinking about how you would construct a program can help you to understand an idea. Project Euler At both events Project Euler was mentioned as a great resource/community to encourage people to learn maths through programming.  Michael Borcherds ( twitter.com/mike_geogebra ) suggested that I might be interested in it at the Computer Based Math summit: www.computerbasedmath.org/ .  Then a couple of days later Matt Parker ( twitter.com/standupmaths ) promoted it at MathsJam: mathsjam.com/ . Project Euler ( projecteuler.net/ )  is a series of  mathematical/computer programming problems that require some mathematical insight and a little bit of programming knowledge to solve.  However, an u...

Many mathematics classrooms are installed with interactive whiteboards (IWBs); but I often get asked by teachers how they can use them to their full potential.  There is a lot more that can be done with an IWB other than displaying a static demonstration.  The Ofsted report of 2008 highlighted that the full potential of IWBs is not being capitalised on in Maths lessons: “... too often teachers used (IWBs) simply for PowerPoint presentations with no interaction by the pupils.” (see http://www.ofsted.gov.uk/node/2255 ).  I discussed some of the problems with PowerPoint in my previous post: “ What’s wrong with PowerPoint for Teaching Maths ”.  In spite of this there are some features of IWBs that make the particularly useful for teaching maths relating to the immediacy of dynamic software. The immediacy of dynamic software  When using an IWB the projector is (almost) always on therefore it is easy to use a piece of mathematical software for a small component of ...

There are a lot places on the internet where the are negative opinions about Powerpoint.  I don't want to repeat these arguments here, instead I wish highlight particular problems relating to the use of Powerpoint in the teaching and learning of mathematics.  These are that: It reinforces a view of mathematics that it is a series of algorithms to be rote-learned; It can reduce the amount of student-centred use of ICT in learning mathematics; It is usually a static form of mathematics and there are many easy tools for creating equivalent dynamic forms of mathematics. Reinforcing a limited perception of mathematics Many Powerpoint presentations for mathematics feature a question with the stages of a solution presented.  This can have a negative impact of students' perceptions of mathematics.  There is a link between students' perception of mathematics and how successful they are.  Students who perceive maths a series of unrelated recipes for solving probl...

There are many sites on the internet with data that can be used for teaching statistics but one of the best, and most topical is the Guardian Data Store.  The Guardian Data Store can be found at http://www.guardian.co.uk/data Raw data on many topical news stories The data store contains the data associated with stories that are in the news including such varied items as the riots and deprivation, the attendance of MPs and the full data on all the Doctor Who villains.  For many of the items there is a Google Docs spreadsheet of the raw data to download. Importing the data into software Whilst it is possible to analyse that data within a Google Docs spreadsheet you can do a lot more by importing it into a statistics package.  Two of the easiest to use are TI-Nspire and Autograph.  With both of these it is very quick to just to copy the data in the spreadsheet and paste it into a list.  All the analysis and the diagrams built-in to these packages can then be...

Computer Algebra Systems (CAS) are very powerful tools for mathematics but they are underused in the classroom probably because they aren't allowed in examinations (at least in the English school system).  This lack of use by students means that teachers often overlook how useful they could be for themselves. One time-saving use for teachers is writing questions with certain properties.  For example if you know you want a cubic with a repeated root you could multiply out appropriate brackets by hand, or you could use CAS to do it: Similarly you may want a quadratic with specific complex roots: Most CAS engines also feature calculus tools too so you could use the integration function to find a function with a specific derivative: In addition to using CAS to write questions teachers can also use to check students' answers. There are many CAS tools available.  The three that I have used here are: TI-nspire http://education.ti.com/html/nspire_uk/   (this is a...

Spreadsheet algebra is a very powerful tool that can be used to teach algebra to students of all abilities and all ages. The major reasons for this are: It is a genuine example of how algebra is used in the outside the mathematics classroom It reinforces the concept of a variable It reduces the likelihood of numerical errors obscuring the underlying mathematics It emphasises the importance of correct syntax Many students do not see the ‘point’ of algebra. However, they are aware that they may need to use a spreadsheet after they’ve left school and entered employment and so may be more willing to learn mathematics in format that they perceive as more relevant. Many students do not fully understand the concept of a variable. The use of x as the unknown is alien to many students and can produce misunderstandings. This is not helped by the fact that many students’ first experience of algebra is to solve equations. The result is that they see x as an unknown quantity whose value shoul...

I’ve been playing with the Euclid iPhone app this week.  It’s a fantastic app and very addictive.  The basic idea is to turn the process of ruler and compass geometric constructions into a game.  You start with some basic constructions, such as midpoint, and as you progress you get set more difficult ones, such as square roots. The progressive levels of difficulty, as you would expect with a game, works really well and contributes to a sense of achievement when levels are completed!  A particularly nice feature is, as you would expect for something based on Euclid’s Elements, is that when you have completed some of the constructions, such as perpendicular bisector, this then gets added as a tool you can use. It’s really pleasing to see maths envisaged in a puzzle game format in this way – I’ve certainly learned some geometry from playing it – and would be interesting to know if any teachers have used this with students.  The app can be downloaded from: ...

Last Friday saw the launch of the latest version of the TI-Nspire software - version 3.0. This has a few new features in addition to the already excellent version 2: Adding images You can now add images to Nspire pages, including as the background to a graphing or geometry page. This is a really powerful tool for relating mathematics to students' experiences outside the classroom. Differential equations You can also plot first order differential equations on version 3.0, where the derivative is a function of x and y. It plots a slope field indicating the shape of the general solution and particular solutions can be shown by entering initial conditions (as a single value or list). 3D Graphing The 3D graphing will plot graphs of the form z=f(x,y). The graphs are displayed really nicely and the window is easy to move. I'm very hopeful that later iterations of version 3 will have the ability to add points and vectors to the 3D graphs so it could be used to for the vectors/...

I’ve recently been exploring Microsoft Mathematics. Microsoft Mathematics 4.0 is free software that can be downloaded from http://www.microsoft.com/education/products/student/math/ .  It has a number of features that are implemented very well in an easy to use format.  The ones that I have used are the in-built CAS, the equation solver and graphing screen. CAS The CAS engine appears to be the same as many others – it gives the same results as Maxima for many things.  It’s easier to use than Maxima though: entering and editing are straightforward and there are some useful options, such as differentiation/integration, that are offered immediately upon entering an expression.  Using CAS can make writing questions easier as shown with the example below. Equation solver The equation solver will solve any equation, as a normal CAS engine would do, but it also includes the option to display detailed solution steps.  Where there are a couple of usual methods, s...

This blog is called “Digital technologies for learning mathematics” and not “ICT for learning mathematics”.  Why the distinction? The name ‘Information and Communication Technology’ has an impact on how ICT is used in teaching and learning as it implies that the two main uses of technology are for disseminating information and communicating. These two uses of ICT are very important: for example many learners are able to access mathematics through the opportunities for disseminating information and communicating that ICT offers. However, the name Information and Communication Technology can steer teachers down a route where they think ICT’s only roles are for disseminating information and communicating. Only using technology for disseminating information and communicating overlooks the opportunities that are available, especially using mathematical software, for learners to develop their relational understanding by working in an ICT-environment through exploring, investiga...