BYOD Geneva

Computers in classooms 24/7

This page is set up for the BOYD professional development day at the International School of Geneva, Campus des Nations, May 21st 2013. The focus is on the impact of having computers at your disposal all the time on mathematics teaching. Resources that are used during the training day and more can be found from this webpage both on the day and afterwards.

Technology has had a profound impact on the teaching and learning of mathematics and continues to do so. Technology as a medium has changed education irrevocably but in mathematics it is so much more than just a medium. Schools of the future will be dependent on permanent access to technology and moving to a BYOD program is a huge forward step that means teachers and students will be able take advantage of technology in a completely different way!

A Natural Medium? - a n intersting debate from the blogosphere about this question which as a key one to consider when thinking about bringing tech in to schools.

Population growth

So this is an activity to get us started and is intended as an example of how technology might be blended in to lesons. This Population growth sheet shows population growth over the last two hundred years in billions for four main regions of the world. Africa, Asia, Europe and the Americas. The activity involves aksing students to fill in the gaps. Having done so and had the corresponding discussions, we might ask the question about what we want to do next. So now, get the data ourselves and try and model it with an algebraic function! Use Autograph or Geogebra as you prefer.

This is part of a project we did recently across a lot of age groups and subjects and with students from primary as well. Details on the project can be found here World Village.

The issues

The following is a brief presentation that sets out the issues to be considerd when moving towards permanent access to technology. Accepting that the technical issues are not to be taken lightly, this page will not focus particularly on technical issues.

Blending With Simulators

As already mentioned in the presentation above, one of the biggest changes involved is the increased potential for what I have called 'blended lessons' where only some part of a lesson takes part on computers. The following three examples are all about investigations that we might like students to do at different points in the curriculum. In my view, they are all much better when started without technology, but can be taken an awful lot further when technology is allowed!

Frogs - This is a classic and I highly recommend doing this with students moving around. The physical involvement adds so much to the thinking required. It helps students to think about the strategy required for the least number of moves and then, later, to think about the difference between slides and jumps. Then, when the number of frogs gets a bit cumbersome and we need more involvement for all of the students, we can switch to the computer simulator. this allows all students to attempt the ptoblem and collect data.

Tower of Hanoi - This is much the same as the above!

Monty Hall - This is a classic probability problem and really is a game that should be played before anyone tries a simulator!

Google Docs

I am just going to show a couple of ways google docs can come in to the BYOD classroom and perhaps we will think of others. The three key points are

  1. Using a google form to colect live data,
  2. Collaborating on a shared spreadsheet,
  3. Collaborating on a shared document.

Wisdom of the Crowd - We will look at the results from this which hopefully some of you have managed to do!

Here are the Wisdom results

UK Number Ones - Looking at the history of number one singles and spliting up the task!

Here are the documents we will collaborate on..

Wisdom averages

Wisdom Summaries

The following are examples about using google forms to study independence tests.

Political PersuasionBirthdaysGender and pets

Independence day - Expected frequenciesIndependence day - What if?

Animated Questions

This section is intended as an example how BYOD can help us to expand our definition of what a task is.

Can you reproduce this animation?

Further examples of this idea of question seting can be found here Animated Questions.

Tools and Ideas

The following are just some examples of different ways to use technology in mathematics teaching. You can find others by browsing the activity pages of this website. How much time we get to look at these in any detail is uncertain!


Often overlooked because graphing and dynamic geometry are so much more obviously engaging! Wih computers on offer all the time, spreadsheet activities can be a regular feature. The main advantage offered from a teaching point of view is about programming spreadsheets with formulae to do what you want them to do and make tasks easier. Below are two great little puzzles that take on a whole new life when being tackled with spreadsheets.


 Concentric Magic Squares

Below is a a new task I am developing. It is based on the idea of creating data sets with certain features ultimately leading to a data set with a normal distribution! We all recognise and can test for a normal distribution and know that they are everywhere, but can we create a data set with 20 data that is normally distributed?

Making a normal Distribution

1 - That has a mean of 10
2 - That has the same mean, median and mode (Is there a technique for doing this for any given value?)
3 - That has a mean of 10 and a standard deviation of 2
4 - That has a mean of 10 and a standard deviation of 5 (what are the limits of these values?)
5 - That has the same mean, median and mode and a standard deviation of 2
6 - Is a normal distribution!

Dynamic geometry

This is a huge area that I cant possibly do justice to in a short paragraph. This is one of the biggest developments in maths education in my view and profoundly changes the way things can be explored. The key issues for me are that it doesnt have to be complicated and that getting students to make and program figures for themselves is at least as valuable as getting them to manipulate ones that have already been made.

 Circle Theorems

 Indestructible Quadrilaterals

Both of my colleagues have run training on using geogebra and have published some of their trainin resources here...

ECIS Lisbon 2011




here are a couple of ideas about teaching trigonometry.

Making a trig Calculator

3D Uncovered

Graphing and Modelling

See  Algebra Activities page for modelling examples


Scratch is an online programming application. Making Spinners is one example of an application. See more ideas and get started on the main weblink.


Gapminder - This is a truly wonderful resource with lots of potential. Follow the link to learn more about it and for some ideas about how to use it in the classroom.

Real Data

This is a real advantage of the internet era and has a big impcat on the ability to bring context to activities.

 Predict the future

Learn more about data sources on the web here.

 Data, Data, Everywhere

Virtual Manipulatives

These are wonderful tools and a qucik search often yields the sort of thing you are after. These tools can offer an alternative or indeed an enhancement to various concepts. The key for teachers here is to think about how you want o use it before hand. In most cases, teachers will need to sructure an activity around the manipulative in order to add focus. Here are a couple of examples.

 Plans and Elevations


Other tools

PadletscattertasticBlogging - pink mathematicspocket seismometersflickrgoogle picasa - data week examplegoogle public data, google sketchup3D Geometrymeasuring gradients with Autographblockposterpreziedmodongram examplesvernier physics app

Google Trends, Google correlateGoogle NgramTwitter Venn,

Desmos, Instacalc, NLVM


My Interactive Whiteboard!

Putting the 'I' in IWB

I have always made a clear distinction about this particular 'I'. For me it simply means that that the user, can interact with a projected image of a computer screen with their finger or a pen. It does not mean that use of IWB guarantees an Interactive lesson. For the IWB is simply the evolution of the whiteboard and as such belongs in classrooms. I would not want to be without one. This blog from David Wees For whom are interactive whiteboards interactive? Presents the issues nicely by asking the intriguing question. In response I wrote the following about my priorities...

Its definitely the right question to be asking! I have been a big supporter of IWBs since I first saw one and my jaw dropped. Since then I have convinced two schools to dip their feet and they are now widespread in both. I think I agree with the view that the interactivity benefits the teacher as a user most, but that, as such – if used to its potential – it can benefit students as well. I like to think I know what I am doing, but, like most things, there is usually more potential there than you think. Where I work I am lucky enough that it doesn’t have to be a choice and in this case, I would not want to be without an IWB. I consider it part of the evolution of teaching and learning tools and would miss it horribly. This makes me think about a priority list I would make if I had to….

1. Computer for the teacher (I guess many teachers still don’t have this)
2. Digital projector (obviously no use without the above)
3. Computers for students (and/or handheld devices) – I might put this first, although it seems unlikely to happen without the top two.
4. IWB software – I have found this particularly useful with or without an IWB and for making tasks that students can do with computers.
5. IWB

In this sense I am definitely agreeing with the notion that devices for individuals are of more value than an IWB and if a straight choice were required then it would be easy. BUT I will still defend the IWB as an evolutionary device that would be part of my ideal classroom! If a future classroom would have no board at all then fair enough, but if a place to write, draw, create and record etc. is of use then mine would be an IWB – Although – I have heard of a school developing the concept of a Interactive wall - minority report style – Now that gets me going!

Thanks for making me think! I am now thinking about what I would say are the top 5 reasons I am glad I have an IWB – If I can’t do that then I’m in trouble!

Here then, are 5 ways in which I think the IWB (not just the software) can make a difference in the classroom.

  • Significant increase in the power of demonstration. Any part of a lesson that is considered 'whole class' is improved by an interacive whiteboard.
  • Specifically, the interactive whiteboard adds plenty of scope for increasing the interactivity of students in whole class activity. This can be added to even more so with a tablet interface that can be passed around the room.
  • When students are working individually or in groups, one group can be working at the IWB. This can be rotated or students might take urns to contribute to a collection of solutions at the IWB.
  • Student presentation. The IWB adds scope for students presenting to the rest of the class.
  • Multiple in put and output possibilities. The different ways there are to input to an IWB expand creative possibilities. Equally, the possibilities for output are similarly advantaeous.

The Mathematical Experience

A New Medium

For Working 

 Re-arranging Sohcahtoa

For Communicating


Smart Tasks

The main aim here is to think about what a task set as a notebook file can add. IWB software has capabilities that are not offered by other software and so can facilitate different tasks. The most obvious example is about matching exercises. I mean those that involve students matching different pairs by moving them around the page. On the IWB itself these tasks can be done as whole class with students coming forward one or two at a time. With access to computers each student can have the file for themselves and engage with the activity. All classifying style activities have this advantage along with the fact that the different answers can all be saved and shared.

I have provided some example files to demonstrate the point.

Another example might be oif you were all to try this Quadratic Links task on notebook software instead of with paper. Once you have a complete set of quadratics, take a screenshot and put it on a google doc so the whole class can see the evidence? It is also a nice way for students to keep evidence of their work.

Photos and Video

With all students havign access to technology, there is more scope for using photos and video in the work we do. As such we end up taking a lot more! See the below example of some photos and video that can be used.

World Village

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