Wednesday, 13 April 2016

Use of Technology in the new A level Mathematics qualifications

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:

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 available, we expect an awarding organisation to explain and justify in its assessment strategy for that qualification how this statement has been reflected in the qualification’s design.

I think this is very good news in terms of the design brief given to the awarding bodies and, if it applied in the way it is intended, should result in greater and more effective use of technology in the A level mathematics classroom.  I look forward with interest to seeing how the awarding bodies justify that their assessment strategies are ensuring that technology permeates the study.

Strategies I would like to see

There are two main strategies that I would like to see employed: an explicit and an implicit one.

I expect to see questions that explicitly refer to the use of technology.  This could be through means of a statistical test that a candidate would perform on their calculators or by referencing spreadsheets in the questions.  It will be clear to teachers that in order to prepare candidates for the assessment they should be using technology in the teaching and learning.

In addition to this I would like to see questions where, although there is no requirement for the candidates to use technology in answering them, they will be better prepared for them if they have using technology in their studies.  For example a question asking a candidate to explain the impact of the parameter b on the graph of y=x²+bx+4 is likely to be answered better by students who’ve been using graphing tools to explore curves in their study.  This is an implicit strategy but can still be very powerful in encouraging use in the classroom.

I look forward to seeing the specifications and sample assessments when they are produced!

Tuesday, 15 March 2016

Maths on a Smartphone

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.


Problem to try: What’s the maximum product of a set of positive numbers that sum to 19?


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.


Problem to try: What’s the effect of varying a in the graph of y=x^3+ax+1 ?


GeoGebra is a very powerful mathematical package that I’ve discussed many times on here.  Currently the app is available for Android but not iOS.  You can see my thoughts on the app at 

In addition to the app you can also open files from the extensive set of materials at using a browser.  At the time of writing there are over 360,000 materials on there.

iOS: not currently available for iOS phones

Problem to try: Add the points A and B on the x-axis and C on the y-axis.  Find the equation of the quadratic that will always go through A, B and C wherever they are moved to.


Sumaze! is a mathematical puzzle app that requires you to move a block around a maze with various routes involving operations or restrictions on the value of your block.  It’s a great puzzle and features lots of maths including arithmetic, inequalities, the modulus function, indices, logarithms and primes.


Thursday, 14 January 2016

GeoGebra App for Android phones

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 device that is very personal to them and this means students are more likely to be well-disposed to software on it.

Having GeoGebra on their phones means that students can harness the power of the software wherever they are: at home, on the bus, ...  However, many teachers have reservations about students using phones in class.  There are concerns that this presents a major classroom management issue.  This is an ongoing debate and there is some evidence that banning phones  in schools has a positive impact on achievement: A lot of these arguments focus on general mobile phone use in class and it would be interesting to see some experiences based on students using subject-specific apps such as GeoGebra with effective tasks designed to improve their understanding using the software.

Downloading the the Android app

The Android app can be downloaded from: