I’m lucky enough to have a sparky class of Year 10 students. At the school where I work we recognise that GCSE mathematics on its own is not enough to prepare them for the Higher Level Mathematics at IB. Hence, I take every opportunity to stretch them with work from beyond the syllabus. The idea of extension is an interesting one, but I’ll save that for a future blog. I’m keen to introduce students to the concept of proof from an early age so the Pythagoras’ Theorem seemed an ideal opportunity to do just that. As a warm-up activity we looked at a task to demonstrate the theorem by matching the areas of the smaller squares to the larger one (the puzzle was part of an activity on the proof of Pythagoras’ Theorem which can be found here ).

I’m a big fan of dynamic geometry, but I really feel that cutting up the shapes and reassembling them by hand has something over a demonstration using Geogebra, for example. However, an issue I often have with any cut-up puzzle activity is that there is no record of the learning that has taken place for the students. I suppose it would be possible to glue the finished pieces and even keep a before and after image but a static reminder like this never does justice to the process of re-arranging the pieces. A recent INSET on using video cameras reminded me of the potential usefulness of recording film in the mathematics classroom so I asked the students to prepare a demonstration and video it. Straight way I noticed the interest of the students was sparked by the idea and they were keen to get to work. Here are a couple of videos they managed to produce in a very short space of time.

Captions and background music. Simple yet engaging.

This one surprised me as the students tried a less obvious (to me anyway!) method. I like the way that they sped up the video too.

Advantages of Digital Memories

So what does his add to the activity? Here are a few thoughts I had:

• Cementing the knowledge – Anyone who has tried to make a video with commentary will know how the live performance makes you really think about your words. The refining and re-recording is a great way for students to think carefully about their work.
• Checking their work – I don’t think I could have got round to the whole class to see their demonstrations. However, I was able to enjoy watching all their videos in my own time.
• Celebrating students’ work - It’s nice to be able to share students’ work with the rest of the class. It is also great to be able to show a wider audience what goes on in the classroom (or on the floors of the corridor outside the classroom in this case!)
• Providing memorable experiences – I often forget that students have 6 different lessons in a day, but when I do remember it makes me wonder what they retain from their maths lessons. I would hope that they would remember this activity!
• Motivation – Making a video is good fun and allows the students to demonstrate some creativity. Movie Maker , a free piece of video editing software, can be used to add effects to give the video some extra punch. Students love it!

Videos & Photos – Where else?

Here are some other activities that lend themselves to being recorded digitally using photo or video:

Pyramid Model - This is a lovely practical activity to help students visualise and derive the formula for the volume of a pyramid.  By constructing square based pyramids (10cm by 10cm) with height 5cm then fitting six of them together to make a cube of edge 10cm they realise the volume of the pyramid is 1000/6cm². Students could make a PowerPoint presentation made up of images of them assembling the cube. I’ve used the photographs to make a worksheet so that they can explain their steps in this demonstration.

Human Loci - Human Loci is a fun and revealing activity that gets students representing various loci by positioning themselves according to the rules given. I have photographs of the students posted on my classroom walls. What a great way to remind them of the different loci.

Solving Equations – Here students were charged with the task of solving a linear equation. They made great use of the interactive whiteboard and it was great to be able to record their work and share it with the school community.

Human Coordinates - Students act as coordinates on a huge grid.  Holding A3 sheets of white paper up when a rule requires it, they will plot coordinate pictures and straight line graphs following instructions such as, “Hold up your sheet. Does your x and y coordinates add together to make 9!” Students always seem to mix up equations x=2 and y=2. What a great way to remind them by showing them photographs of themselves sat in a grid.

Human Transformations – Students create transformations of functions like y=x² and y=2x² using their bodies. The video then provides a useful aid to memory.

Dancing Vectors - Introduce vectors through dancing! This is a great fun and effective activity where students imagine vectors as dance moves! The vectors are combined to make a dance routine. Get the whole class up and dancing this routine to Donna Summer's hotstuff! It is a memorable experience and really helps students get to grips with this concept.