Bring Your Own Device: Equalising learning in A level Mathematics?

An earlier version of this article appeared in the Mathematical Association Journal: Mathematics in School (November 2020).

In July 2019 I was fortunate to be able to speak at the GeoGebra Global Gathering in Linz, Austria. I gave a presentation about how allowing students to use mathematical software on their own devices, both to support their learning in the classroom and as a tool they can use within assessment, is a potential solution to:

1. Harnessing the power of technology to improve the teaching and learning of mathematics
2. Increasing equality of access to technology for mathematics students.

This article is a summary of the talk I gave there.

Why should students use technology in mathematics?

When I first started teaching there was an activity that I used with students to give them a strong conceptual understanding of differentiation and what the derivative of a function expresses. The activity was for them to plot the curve for y=x² on graph-paper, draw some tangents at different points, measure the gradient of these tangents, tabulate them and form an expression for the gradient of the tangent at a point. The strength of this activity was that it helped the students construct a strong impression of what the derivative represents in terms of graphical, algebraic and numerical representations of it. This was a much more solid foundation than just meeting differentiation as a rule: “multiply by the power and reduce the power by one”, and one that was a very helpful basis for much future work on calculus.

As good as this activity was, it had some fairly significant limitations: their tangents were often inaccurately drawn, the students had a limited sense of how the gradient changed as the point varied and, perhaps most frustratingly, it took a long time for students to sketch the curve and the tangents. These factors, in particular the length of time the activity took, meant that in the following years I decided not use it, even though I believed it improved students’ understanding. 

Fortunately there is a solution to the problems with this activity, and many tasks like it: dynamic graphing/geometry. It is now possible for students to use software such as GeoGebra to plot a curve, add a point and a tangent and then measure the slope of the tangent. All of this can be constructed in a minute or two and has the added advantage that the diagram is dynamic: they can move the point and see the gradient change.

 

Exploring the gradient on y=x² in GeoGebra

This potential for students to develop an understanding of mathematical relationships through using technology is why the Ofqual  A level Mathematics guidance for awarding organisations, published in 2016, contains the statement:

“The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics.”

There is an appreciation from Ofqual of the power of technology to enhance students’ mathematical understanding. The intention of this statement is that part of each student’s experience of learning A level Mathematics should be for them to use mathematical technology, and not just watch a teacher use it.

Current use of technology in A level Mathematics classrooms

For many A level Mathematics students the only mathematical technology that they will use in their study is a scientific calculator. In the current examinations for A level Mathematics students are allowed to take a graphical calculator into an examination; however, it is not compulsory and many students will just use a scientific calculator. Assessment is a strong driver of classroom practice and because graphical calculator use is not compulsory, scientific calculators are often the only technology used by students in the classroom.

It is possible to utilise graphing technology in the learning, even if students only use a scientific calculator in the assessment, but alternative devices are needed for this.  This can be difficult as the technology infrastructure in schools/colleges is very variable: some are fortunate to have class sets of laptops, Chromebooks or tablets and some issue every student with a tablet. Unfortunately this is not universally the case and, even when class sets of laptops are available, these are often very old and slow. One solution to this problem is to allow students to use their own devices. This approach is often named BYOD: bring your own device.

BYOD in learning

One of the most frustrating aspects of the lack of hardware in schools/colleges is that many students already have a device that is capable of running mathematical software. Programs such as GeoGebra and Desmos are easily available and free for laptops, Chromebooks, tablets and Android/iOS smartphones. Operating a Bring Your Own Device (BYOD) policy means that schools/colleges do not need to address the lack of hardware issues. 

The power of students using technology has already been discussed but it is important to manage this so that students are supported in how to use it to effectively support their learning. The example provided earlier was about exploring the derivative of y=x²: this was a well-designed activity from the old SMP 16-19 scheme. This task was ideal for me as a novice teacher as it had a clear structure along with teachers’ notes to accompany it: these suggested what I could expect the students to achieve, as well as appropriate questions to ask. A similar level of support is beneficial when teachers are considering using technology in the classroom. For this reason, MEI has produced a series of tasks which describe graphs/constructions for students to enter into the software, along with suggestion for how to explore them and suitable questions for the teacher to ask. These tasks are also accompanied by teacher guidance.

MEI has developed 50 such tasks for GCSE, A level and Further Mathematics, all of which have a similar structure. They feature:

• Construction steps for the students;
• Questions for discussion;
• A mathematical problem (often to be attempted first without technology);
• Further/extension problems.

The purpose of these tasks is for students to explore and discuss a mathematical idea, using the power of dynamic graphing to allow them to observe relationships, then to consolidate this learning by attempting a more conventional problem. An example task is given below. In this task students are expected to consider the shape of the curve of the derivative function in relation to the shape of the curve of the original function.

Example of a student task

All the tasks are freely available via the MEI website at: https://mei.org.uk/resources/?terms=desmos and https://mei.org.uk/resources/?terms=geogebra

Concerns with BYOD in the classroom

A BYOD policy often covers students bringing in their own laptops, tablets or smartphones. Most teachers are comfortable with students bringing in laptops or tablets but the use of smartphones in the classroom is a very contentious issue. There are some advocates for completely banning smartphones in schools and a number of schools have enforced such a ban. When I speak to teachers the picture is very mixed: some work in schools/colleges that have banned smartphone use; some don’t ban their use, but don’t make use of them; a few are using them successfully. The experiences of teachers who have used them have been positive: none of the teachers that I’ve met who have used graphing apps on smartphones with A level Mathematics students have reported any classroom-management issues when using them. 

One of the very understandable reservations teachers have about allowing the use of smartphones in class is that students will be using them for distracting or disruptive purposes, such as browsing social media or taking photos and videos. One simple solution that I've heard from a few teachers is to make it compulsory that when phones are used they should be face-up on the students' desks in full view and not held in the students' hands. The strategy is sufficient in many classrooms to ensure they are used appropriately.

If the "face up, on the desk" strategy isn't sufficient then there is a feature built-in to GeoGebra and Desmos that is a very effective classroom-management tool. This feature, known as exam or test mode, locks the phone down so that the app cannot be exited and other apps cannot be used. It’s straightforward to leave the app but it stops the clock. I would highly recommend the use of exam mode for classroom management to any teacher that has concerns about the potential disruption of using smartphones in class. The feature can be accessed from within the app for GeoGebra or by downloading a separate app for Desmos.

Example of Desmos Test app

Another concern I’ve heard from teachers is that the screen on a phone is too small for it be an effective tool for mathematics. This is a concern I’ve heard from teachers but not students! As part of MEI’s work on the Advanced Mathematics Support Programme we worked with teachers on using Desmos and GeoGebra in the classroom and recorded some videos on it. The Using Technology in Further Maths video at https://amsp.org.uk/resource/pd-videos-further-pure shows the teacher expressing that he thought that the screen would be too small but the students were used to working on a small screen and had no problem with it.

When implementing BYOD there is the worry that students will not have a device that is suitable for them to bring into lessons. This can be addressed by the school/college providing a small number of tablets for this purpose at a cost that is much less than providing them for every student.

One final issue raised that I have much less sympathy for is the question “why use this in the classroom when it’s not allowed on the test?”. My response to this is that there are many classroom strategies which teachers use the classroom that are not allowed in tests, such as asking the teacher a question, looking something up in a textbook or discussing ideas with other students! Use of technology in the classroom should be judged using the same fundamental criterion as any other technique: does it help students understand mathematical relationships better? 

Trying BYOD in the classroom

For teachers who are interested in exploring student use of technology in the classroom BYOD offers an opportunity to try tasks without any financial investment. There are many activities available, such as the MEI GeoGebra tasks (https://mei.org.uk/resources/?terms=geogebra) and MEI Desmos tasks (https://mei.org.uk/resources/?terms=desmos). The exam or test modes in Desmos and GeoGebra are highly recommended for teachers who have concerns about the distractions of using smartphones in class.