Edexcel admirably give you access to detailed question by question data from their Maths exams with the use of Results+.  However I have always found that it does not come in a format that is particularly useful for teachers or individual pupils.

I have created a spreadsheet that analyses the data at a class and individual level and presents both in what I hope is a helpfully colourful manner.

To use the spreadsheet you need to download the paper analysis from Edexcel for Paper 3 & Paper 4.  Copy and past the raw data into the data entry sheet and watch the magic happen on the other sheets.  The individual sheet should be sized so that you can print the data for each child on 2 sides of A4 paper.

I hope this is of use to other Maths teachers / leaders.  Please feel free to adapt / share as you see fit.

Any questions, feel free to leave me a comment here.  File here: http://db.tt/xevYyYl (data included is anonymised version of my own so you can see what it should look like).

Data Entry Sheet

Class Analysis Sheet

Individual Analysis Sheet

No related posts.

David is the author of http://www.informationisbeautiful.net/.

Worked through some fantastic infographics from his site, go look at them now.  Better still see his TED talk:

Some interesting insights from using Google InSights to track search terms.  Great tool for use in the classroom.

Nice talk about needing to compare proportions rather than totals, in the concept of military spending.  Love the Maths of normalising figures for population.

Take data and use it as a lense to clarify your thinking.

Like Stephen Heppel’s learners David is self-taught in his technical skills using the likes of Youtube.

What happens when you make data beautiful?  Visualisation helps make the mind envisage scale and proportion far better.  Can condense a huge amount of info into a small amount of space.

Nice graphic of the difference between the Left & Right in American politics.  Helps you to see where someone else is coming from.

Information design is about solving information problems, something we have lots of now.

Fascinating and enlightening talk – a breath of fresh air after the intense debate from previous session.  And to top it off his book is on sale at Amazon!

No related posts.

Inspired by Sugata Mitra at the SSAT National Conference I decided to try and ape his ‘minimally invasive education‘ within my own Maths classroom.

In a really tough December week this two hours shone out as a great teaching and learning experience.

Before going any further, please head over to my previous post to read about the inspiration for this lesson.

In a nutshell, Sugata discovered that children can teach themselves with the aid of the Internet.  His hole-in-the-wall experiment inspired the book that inspired the film Slumdog Millionaire.  He has since been investigating how to apply these findings in Western school systems.

I followed some basic rules that Sugata has developed.  I split the students into groups, each with a computer and then gave them a problem to solve.

The rules are simple:

• Students were told to get into groups of their choice of around 4 children.
• They had one laptop per group.
• They could walk around and cheat, looking at what the other groups were doing.
• They could move groups if they wanted to.
• No input from me other than some encouragement and praise.

My Year 7 class (11-12 year olds) are an able group who I have done a little group work earlier this year.  I gave them a simple question:

Who was Pythagoras?

And with it, the text (but not diagram) of a typical GCSE question:

A ladder is leaning against a wall.  It is 5 meters long, the base of the ladder is 3.5 meters away from the wall.  How far up the wall does it reach?

At that point, I pretty much put my feet up and left them to it for the next two hours.  The maths involved is traditionally not taught to pupils of this ability for at least another 2 1/2 years.  It would be considered as being about 2-3 National Curriculum levels above their current ability.

To say I was surprised and delighted with the next 90 minutes would be an understatement!

Two groups in particular shone at this task and took very different approaches to reaching the correct solution:

Mathematical Logic: An enthusiastic group of girls split into two pairs, one pair hit Google and quickly found Pythagoras’ Theorem, a diagram of a right angle triangle and the formula a²+b²=c².  The other pair started drawing a scale drawing of the problem and within minutes had a fairly close estimate of the ladder problem.  These girls had done little algebra before, they had certainly not substituted into equations, let alone rearranged them.  However I watched them equate the ladder and wall to the example right angle triangle, substitute in the values I had given them in the problem, and begin a discussion about how to find b².  They correctly deduced that to find the missing value “if they are added together, then we need to subtract the 3.5² from the 5² to find b²”.  Perfect mathematical logic!  They then got a little stuck as they had never come across the concept of a square root before.  Halving their value was the first attempt, but they quickly saw that this was nowhere near the value they had got from their scale drawing.  Dividing by 3 was the next logical step for them (a triangle has 3 sides afterall they declared!), again this didn’t work out close enough to their estimate.  At this point they went back to the Internet and found some examples of solving problems of this nature.  Here they stumbled across the square root sign, quickly understood the concept of a square root and then found the button on their calculators, and next the correct solution to the problem.  Quite amazing!  They produced a poster to show their learning:

Other than a little confusion with square and square root symbols, an impressive effort.

Search and yee shall find: A group of three boys attacked this problem by searching for information using both the laptop and also the resources in the room.  They found out who Pythagoras was thanks to Wikipedia.  But they also started looking through the GCSE Maths books in the room and even found a revision guide.  They found an example question in one of the books that was another leaning ladder question.  They used this to quickly find the answer to the problem that I had set them.  This might not have involved the mathematical deduction that I had watched the girls use, but it was an impressively efficient effort, and is just how I learn things these days.  Search on the Internet, find some examples of what I want to do and adapt these methods.  I put another question on the board, this time finding the hypotenuse of the triangle.  The boys found a great ’3 quick steps to solving Pythagoras’ from the revision guide and applied this to the problem in no time at all.  They produced this presentation of their learning:

Of all the groups, these two groups developed a good understanding of Pythagoras’ Theorem with no help at all.  Two other groups got there after a little bit of peeking at the work of the first two groups (well within the rules), and two groups did not get very far.  This was down to a lack of teamwork, something we can work on in coming weeks, these pupils are only 11 years old after all.  Overall in the two hours we managed to learn: Pythagoras’ Theorem – done!  Square roots – done!  Substituting & rearranging algebraic equations – well on the way!

I will be interested to see how well this learning is retained.  Sugata Mitra’s work seems to show that months later retention from this form of learning is impressive.  I’ll be delighted if the class can solve a problem next week, and even more so if it’s still there after the Christmas break.

This was such a success I will try it out with all my classes this week.  It’s the last full week of term, always a tricky time to keep the pupils engaged, it seems an ideal time to try out a different way of learning.  I’ll be intrigued to see how this works, particularly with my lower ability Year 8s.  I think the success I had with this trial was in part due to the excellent learning habits that class already had and in the pitch of the question.  It offered just the right amount of challenge, and was relatively easy to search for online.

With that in mind, this week I will try the following:

• Year 7 (NC Level 5-6):  Independent Probability: How do you find the probability of two independent events happening? What is the probability of winning the lottery?  What is the problem of getting 5 out of 6 balls in the lottery?

• Year 8 (NC Level 3-4):  nth Term of Sequences: How do you find the 100th number in a sequence?  Present with a sequence problem from diagrams e.g. matchsticks and ask for the 100th term.

• Year 10 (GCSE Grades E-D):  Sine Rule: How do you find the area of a scalene triangle? Present with triangle to find area of.

• Year 11 (GCSE Grades D-C): Transforming Graphs: What is the equation of this graph? (Transformed sine wave – pupils have not come across sine waves before)

What do you think?  Are these suitable questions?  Have you tried anything similar in your classroom?  Will you try this method of enquiry based learning now?  I’d be really interested to here your views and experiences.

As this is a fairly hands-off form of teaching I may try and live-tweet the lessons – we’ll see how things go.

No related posts.

I’ve been trying to use my iPad in the classroom as much as possible, as a device for use in schools it is close to being perfect.  One of the drawbacks has been working out how to get what’s on the iPad to be projected onto my classroom wall.  You can connect it with the iPad VGA connector to a computer and project that way, but only a handful of apps support this.  This can apparently be expanded somewhat by jail-breaking , but I don’t really want to go there.

Then last week Wes Frier alerted me to an App called Air Sketch.  Air Sketch is a fairly simple drawing application with a killer feature, it will broadcast whatever is on the screen across your network to a webpage.  If you open that webpage in a HTML 5 browser from any machine attached to the same network you will see the iPad screen.  Any updates made on the iPad appear almost instantly on your PC or Mac.  Air Sketch was £1.79 but there is also a free option to try.

So I can walk around my classroom with my iPad and write on it with my Pogo Sketch Pen.  Everything appears as if I was stood at the Interactive Whiteboard using SMART Notebook.  Just being able to do this from anywhere in the room is a great help, I can get pupils to demonstrate work quickly without getting them to the front of the classroom.  We have GCSE exams next week, so spent a lot of Friday working through old exam papers, this meant as soon as I spotted a common problem in the class I could demonstrate a solution from sitting next to whichever child had the issue, but for the whole class to see, or better still get one of the pupils who did understand the answer to demonstrate it to their colleagues.

Air Sketch allows you to import both PDF files and images into the software ready for you to annotate over.  Air Sketch adds itself to your ‘Open In’ menu, so you can open a PDF straight from the Mail app, or Dropbox for example:

The PDF import is a useful feature and a good idea, but I had some issues with the clarity of the documents when they were imported.  Pogo Sketch works in landscape mode, and my PDFs were in portrait, zoomed out they were too small to annotate and too small to read on the projector:

Zoomed in they lacked clarity:

I found the easiest way to work around this was to open the PDF (or indeed Word, Powerpoint etc) document in the standard iPad viewer, zoom into the section I wanted to display then press the Home and Power buttons simultaneously to take a picture.  I could then open Air Sketch back up and open the image from the Picture menu:

The little toolbar along the bottom of that screen allows you to rotate the image and fill the screen with it ready for annotation:

Overall this is a great utility, it’s not perfect but is really exciting.  Surely it’s only a matter of time before other app developers build this technology into their own applications?  I hope Air Sketch itself gets an update soon to allow better importing of other files, more brush options, some hand-writing smoothing and other features that some of the other note-taking apps have been perfecting on the iPad.

Have you got any other apps you couldn’t live without in the classroom?  Do you think the iPad will soon offer a serious alternative to an Interactive Whiteboard?  When you consider the cost of this solution versus an interactive whiteboard or a tablet PC I think the market leaders in those areas must be running scared.

This works beautifully with the new iPad Software 4.2 – the ability to multi-task is a killer. More on that in my next post….

No related posts.

Scrolling through things I had starred for holiday reading, I noticed that Gapminder.org has been updated.  I have blogged previously about Gapminder and the fantastic Hans Rosling, it is a fantastic tool for visualising a wealth of World data on lovely scatter graphs that animate changes through the years.

Watch one of Hans Rosling’s classic TED talks to see what it’s capable of:

There have been a number of great updates which can be seen in this diagram I’ve borrowed from Gapminder.org:

You can see the blog post detailing these on Gapminder, but to summarise:

• More data;
• Downloadable data – each set is available as a Google Spreadsheet ;
• Data displayed as scatter graph or plotted on a map;
• News & videos. (Bookmark their RSS feed in your Google Reader!)
• For Teachers section that is soon to be updated with teaching ideas & resources.

How have you used Gapminder in your classroom? I’d be fascinated to hear.

PS: I also note that Google (who bought our Gapminder a few years ago) have a little strangely brought out a very similar tool: Google Public Data Explorer.  This has some nice alternative data sets to investigate.

PPS: Another short Hans Rosling video – just because he’s great

No related posts.

I have just completed the second edition of the SHS E-Learning Newsletter.  This issue’s focus was:

1. Google Maps/Earth Special!
2. MFL – Street View
3. History – Historical Imagery
4. Science – Tours of the World
5. Maths – Collaborative Maps
6. Further Reading / Ideas

Check it out here, or sign up for the next edition over on the right in the sidebar

No related posts.

Following yesterday’s use of Twitter in the classroom, I was walking to Period 5 (same class as yesterday) after lunch, when inspiration struck.  I remembered this post from @tombarrett .

Go and read it.

Go on!

I threw my lesson plan out of the window and did exactly what Tom did, here are the replies: (click through for them all)

This caused great excitement and interest in the topic, and really helped us look in to the language and mathematics of describing chance.

This class have really been inspired with the idea of my network, I had to stop them spending the rest of the lesson bombarding you all with further questions!  Bringing global connections into the classroom is a real attention grabber, and like it or not we are entertainers!

Nothing more to say – thanks Tom –  a great idea, and thanks to everyone who contributed to the lesson.

No related posts.

I had an observation lesson today and decided to pull out all the technology tricks!  We happened to be at a point in the scheme of work looking at data handling and collecting data in particular.  I decided I’d develop the Questionnaires lesson which I used at interview last year.  60 minutes should be enough to do it more justice.

So here’s the plan:

• Discuss data quality based on previous lesson
• Tweet a link to my questionnaire and a Wallwisher for feedback on the questions
• Fill out my questionnaire full of deliberate mistakes in class
• Look at the live data spreadsheet
• Groups look at the data for one question, suggest problems with the data collected, and suggest improvements to the data.
• Discuss findings, looking at key points of: Leading Questions, Bias, Open/Closed Qs, Personal Qs, Options Boxes, Group boundaries etc.
• Look at Twitter feedback on Wallwisher, compare to our own thoughts
• Each team leaves one learning point on our own Wallwisher.
• Compile new Qs into anew Questionnaire

A lot to pack in to 60 minutes, but time for individual, group and whole class work and reflection.  My class have a high proportion of special educational needs, I feel there is a good mixture of learning styles catered for here and certainly not much time to get bored!

To complete the technological marvel, this was all wrapped up in a Prezi presentation:

As you can see I took charity as a theme – we had been collecting that morning for Haiti so it seemed appropriate.

Here’s my questionnaire – complete with deliberate mistakes galore:

I tweeted out a link to the form and my lovely personal learning network took care of the rest.

We completed the form individually in class while the live spreadsheet was up on the board:

Each group then worked through one of the questions, looking at data problems, and how to improve it.  This allowed me to differentiate the work, stronger groups could look at the tougher concepts and vice-versa.

Here’s the worksheets they worked on:

At this point we had some, lively, discussions about this and looked at the feedback from the Twitterverse on Wallwisher:

As you can see there was an awesome level of feedback here – I can’t thank everyone enough!  I was losing things a little by now, whole class discussion is hard work!

Finally we moved on and I asked each team to go to our own Wallwisher and put one point that they had learned today. This was tough, verbalising this level of Maths is not easy for them.  There were a few little nuggets in here, and although each pupil couldn’t put into words exactly what they had learned, I’m convinced each of them made good progress today.

My favourite (and it wasn’t me – a pupil using my logon) was:

“don’t ask the names cus the peepz won’t be honest”

Linking the fineries of English language questioning, with different data collection boxes through to the raw data that comes out of the other side is pretty complex stuff.

To blow my own trumpet, I think this is a pretty good way to teach Questionnaires & Data Quality.  Looking at the problems with the data produced from poor questioning makes it much clearer how to phrase and design them in the first place.  Has anyone else got any other novel ideas for this part of the curriculum?  I’d be fascinated to hear any ideas!

Finally, thanks to the fabulous TeachMeet BETT 2010.  The ideas of using Twitter in the classroom is one that I was reminded of at BETT, and particularly the use of Wallwisher.  I’ve seen it before and always forgotten to integrate it into the Maths classroom.  The ideas are fab, and the copy of Camtasia I won for emailing my use to tmbett2010@gmail.com will be really well used at school!  So a big thanks from me, and from the pupils for an entertaining lesson

No related posts.

I attended a SSAT training day today about ensuring Maths progress for all. This included a 30 minute section about using IT within Maths. During this Paul Hynes from the SSAT demonstrated an augmented reality program that the Trust are currently working on.

For those new to the term Augmented Reality it involves overlaying virtual images on top of a live video stream. Some of the first examples are on the iPhone and the PS3.

Here is an iPhone example called Nearest Tube, directions to the nearest London Tube stop are overlayed onto the image from the phone’s camera:

Another on the iPhone that I have used is the excellent Yelp app, overlaying the nearest restaurant, bar, shops etc onto an image from the camera:

Recently released on the PS3 is the ‘game’ EyePet, this uses a camera pointed at your living room floor, the PS3 then overlays a virtual pet who plays with you on your floor. Stuart Rideout has written a great little post about this. Please go and read that article, and take particular note of the little pieces of card that that software uses.

The system I saw today was similar to this, the camera picked up the distinct patterns on pieces of card and created a 3D image in their place. The team from the SSAT are creating some applications with these cards, some examples that were mentioned were cards that represented different tectonic plates. These could then be moved together by the teacher, and the project image on the IWB would show the plates meeting. Another was some cards to attach to the joints of your arm, when your arm moved, the image on screen showed the bones and muscles moving overlayed onto the video image.

The team are creating these little programs at the moment, and when done all that would be needed would be the software, a webcam and a projector/monitor. They are really engaging and certainly have the wow factor!

This is where you come in, Paul is looking for ideas to create some Maths software with this technology. The obvious thing is some virtual 3D shapes, but we can do better than that! If you have any ideas, rather than putting his email up here, I will pass on to him details of this post. If you could then leave your ideas in the comments section hopefully Paul’s team will put together some of them over the coming months.

My first thought was using this to teach balancing equations. Cards could represent numbers and letters and operations, these could then be presented as the old fashioned idea of some scales balancing an equation. With a bit of animation, the idea of doing the same operation to each side of the equation could be shown.

So over to you, can you think of anything more original?

No related posts.

I’m doing a quick presentation at Teach Meet North West tomorrow night in Manchester.

If you haven’t been to a Teachmeet before it’s an ‘unconference’ where enthusaistic teachers get together to share ideas, usually with an E-Learning theme.

I’m doing a 2 minute nano-presentation on Google Forms, based on my interview / blog post from earlier in the year.

Here’s the presentation.

Hopefully I’ll see some of you there

No related posts.