In my last blog I talked about the change in our approach to Year 7 and 8 maths classes and the theory behind it.

When our students were presented with new material, some of them were showing classic signs of distraction and, more significantly, failing to spot the ‘clues’ in the questions. So we worked at encouraging them to develop a more systematic approach to questions and maths activities; boosting their resilience and engagement in the process.

In this blog I’ll share some of the activities we used to help them.

We thought there were four main reasons for our students’ lack of resilience:

  • not trying through fear of failure
  • inattention
  • tactical inattention (choosing to focus on a distraction; perhaps because of fear of failure)
  • ‘Tevs’ (not seeing the value or benefit of doing an activity).

You can read more about these in my last blog and read on for more on the approaches we tried, to help combat these habits.

Develop students’ observation skills

I tried to reduce students’ apparent fear of failure though lots of low-stakes activities. The idea was to get them used to changing their working hypothesis without seeing it as a failure on their part and to the idea that, in maths, the justification of the solution is important too – it’s not just about the solution itself.

I used some activities that are easy to engage with and encourage pupils to form a hypothesis, and then – crucially – refine it in the light of new information that they spot afterwards.

I started off with some really easy, simple images, with very few words, so that pupils could quickly pick up inconsistencies between the image and the words.

I used this image of a bag of ‘onions’ early on.

As the students started to get comfortable with the activity, I introduced examples with more words or that needed more careful observation to spot what was wrong, such as this painted road sign.

I gradually ramped up the  difficulty with images that require closer observation to spot what’s wrong. I used this photo of a cycle lane sign and then this great photo of an american freeway sign.

There are more examples of the Observation Station board on my Pinterest page.

These gave students an opportunity to say what they thought and share their ideas without fear of ‘failing’, and, in doing so, they showed none of the characteristics I had noticed before when meeting new material.

Once our pupils were happy with this idea, we started to introduce images with a mathematical overtone. There are lots of pricetag errors, such as this set from the Huffington Post.

Or this example:

6 onths free

We then extended the ‘what’s wrong?’ premise further.

We introduced graphs and got them talking about correlation and causation, and whether to reduce global temperatures, we simply need to have more pirates.

Screen Shot 2017-04-05 at 07.58.04.png

Number of pirates (approx)
 Global temp (°C)

You can find the classic pirates vs global temperature graph here.

There are loads of great ‘bad maths’ and ‘bad stats’ graphs available on the web, which you can hunt down to illustrate the same point.

Encourage pupils to think about what they see

From there we started to provide pupils with images and data that required them to come up with a reasonable explanation for what they notice is wrong, or to give examples when there are a number of valid conclusions.

Having built them up to it, they were much better at the task.

What might be the explanation for what’s happening in this picture ?

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Once the pupils were talking about and developing and articulating their ideas, I started to look for other sources of data that they would need to think hard about.

There is some fabulous data about changes in bird populations for geographical areas, so you can select a species that has increased or decreased over the last 10 years in your area and ask the pupils to come up with ideas as to why that might be.

For me, it was ‘what might be the explanation behind this change in the number of tree sparrows?

This map (and many others that I’ve used) comes from the British Trust for Ornithology (BTO) blog , but there is data from the BTO on many bird species, so you can find one that shows interesting trends near your school to help the pupils put their hypothesis into context.

There is also lots of great health and life expectancy data on the OECD that could be used for a similar purpose.

Set questions that take a long time and don’t have a single answer

Pupils are well schooled in the ‘series of 20 minute activities where the teacher gives you the answers’ lesson structure. However, giving them the opportunity to wrestle with a problem over a long time, where they don’t get clues or prompts – and even the teacher does not know the answers – makes for a really useful assessment opportunity.

The example of the birds above is one such question. No one really knows why the number of tree sparrows has changed. We all have ideas and some of these are more popular than others, but none are certain.

What really grabbed the attention of my class were ciphers and clues. The GCHQ code book had just come out, so I threw out a few questions from it and then came up with my own idea.

In our school each member of staff has a sign on their door telling the pupils what book they are ‘currently reading’. I was reading a book from the Ruby Redfort series at the time; so I used that as basis to create simple ciphers for the pupils.

This example is a replacement cipher, where each letter is replaced by the same code each time. You can work it out using letter frequency and identify the vowels, or notice that these are coordinates working on a 5-by-5 grid and link that to the 26 letters.

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Once they had solved it, the solution gave the location of a box in my room. When the pupils looked in the box there was a sheet of information about Vigenère (the so-called ‘uncrackable’ cipher), the grids he used and a second cipher using the Vigenère method.

I did not give them the keyword – that would have been too easy – but they were able to work it out with a bit of perseverance. This decoder/encoder is a great site and will save you lots of time.

Here is the message the pupils found:

iees vanx jgpe uywmkbuy qxiljfs. Gvo kon oshe pvjwew vmf hhd lte opyqnxyw iokrk oag djutx tw m Mnzaoae jjkpmvydaf?
Tj Srtosy.
I can tell you that the key is 5 letters long. Good luck.
Mr Graham.

The students found the Vigenère cipher sheets in drips and drabs; usually three or four a week, but sometimes more. The ciphers tended to be worked on by small, self-selecting groups of two or three pupils. So I suspect more than 20 pupils were able to crack the first cipher. At least two groups found the Vigenère key.

Six months in, I am really pleased with the outcomes. My students are far better at approaching new material and they are more confident at looking at the clues and responding appropriately than they were in October.

As a department, we have already started a similar approach in Year 8 and we think Year 10 will be next.

I’ll keep you updated with progress. In the meantime, if you find any great images or links that could be used for this, do send them my way.