You won’t need me to tell you it has been a difficult year both in teaching and elsewhere. In this post, I’m going to pick out some of my most favourite parts, share some new resources and explore some things I have planned for the Summer and next year. You probably won’t be surprised to find out the Core Maths features heavily but there are some other things sprinkled throughout too.

**Lockdown**

The lockdowns were difficult but there were some positives. My classes really made good use of Desmos and the introduction of Google classrooms to the whole school has transformed setting homework. I can’t say we’ve totally mastered it yet but it has the potential to be a great long term time saver. Another bonus to Google classrooms was that it allowed us to share our workload and collaborate on projects/topics in a way we hadn’t ever really got round to before. Because other teachers were recording their instructions for how to do something, this has the potential to be a great CPD tool when we look back at these videos in the future.

**Tutor time**

My school uses vertical tutor groups so years 7 to 11 are mixed up and year 12 and 13 are mixed. I’m a 6th form tutor so I’ve had a year 12/13 tutor group for about 10 years now. Due to Covid, we split the year groups up so I kept my year 13s and inherited some others and, we’re planning on keeping them split next year too. This is something I’ve been interested in for quite a while so I’m keen to see how this works out. There is no real doubt that the needs of year 12 and 13 in September are very, very different so I’m looking forward to having a chance to really work with my year 12 tutor group and give them a proper introduction to 6th form life.

There are two things I intend to make use of as part of being the maths specialist tutor group. One is from the Great Gatsby talk that Cat and Rachel gave where I intend to show off some other career options to my year 12s. Some of them already have some idea about what they want to do but, whether that’s the case or not, I want to show them that there are other jobs out there (like urban redevelopment) that they simply might not know about. The second thing I want to do with my tutor group comes from Catherine Madden’s talk about visualising inequality. There is going to be a competition in the first term back and I’d like to get my tutees involved. Maths/Data can be visually appealing/creative and I’d like my students (and perhaps, the school newsletter) to see that!

**Core Maths resource updates**

As a result of the AMSP’s Core Maths Festival, I have updated some of my resources and re-uploaded them to the TES. These really are some of my best work and took an exceptionally long time to improve. I’ve used ideas from Dash’s talk and Jen’s (from Uk Data service) to improve my sampling and numerical data analysis material. These now include the bullet hole problem and genuine data from the NATSAL surveys to make a more authentic resource.

As part of the festival, I was given the honour of running one of the sessions about finance. It’s a topic that teachers ask about quite a lot as it’s just beyond most of our comfort zones. One of the things I really enjoy about running a Core Maths session for the AMSP (aside from the great help you get from Cat and Tom as well as the fantastic bunch of teachers that come along) is that it gives me a real reason to think really hard about something I teach and which I do it that way. One of the great things that happened in this case is that I’ve come to the conclusion that I’ve been misusing my time on the finance aspects by focussing too much on APR and not enough on some of the other aspects. I haven’t actually got round to updating my finance modules yet but they are in the pipeline. You can read more about that talk here and I’m sure I’ll update this blog once I’ve adapted my resources.

As part of the AMSP Core Maths networks, I spent some time discussing aspects of the specific course I teach with about 20 other teachers. Three things that have come out of that are:

- Critical analysis is difficult and there’s some scope for an easier introduction. I’ve incorporated that into my scheme of work and the resource that’s on the TES. More to come on this when I build the rest of that module.
- Fermi Estimations can be at there best if there isn’t an easily Google-able answer. I’m planning to see what questions I can think of that would fit that bill.
- Histograms may have a purpose! After quite some discussion, it might be that histograms have a use in comparing sets of data. I’ll have to do some more work on this but at least I have some reason to want to use histograms now!

This year saw my first attempt at a Quibans style article (about Marcus Rashford’s book club) and while I’m pleased with how it came out, I can assure you they are harder to make than you might think!

**Summer plans**

Rest.

Spend time with the family and do some reading.

Pick a couple of topics to continue to develop. It’s likely to be the finance and critical analysis but I might need to do some thinking about the Normal Distribution.

Accept that this is not going to happen quickly. Dash was right when he said that these things take time and I think a realistic aim is to get this course, the scheme of work and the homeworks all sorted to the standard I’d like them to be over the course of about 4 years.

**A nice way to end the year**

To round things off, I received a lovely email from Tom and Cat asking if I’d like to be officially recognised as a Core Maths Advocate. More details of that to come in the new year but it was a great end to a difficult year!

If you’ve got any comments, questions, requests for resources or anything else that you think I might be able to help with, please feel free to ask. I can’t promise that I can help but it’s usually worth asking!

I hope you have exactly the type of Summer you desire ðŸ™‚

A little while ago, Kerry sent this tweet:

*Anyone got a book/website/podcast list that is suitable for students who are half way through their #coremaths course. If not a list, then recommendations please so I can compile a list, thanks!*

Well, no-one had a list so she compiled one and has very kindly allowed me to share it here.

If you have any suggestions of your own, please message @KerryDunton or leave a comment here.

Thank you Kerry!

*In this series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. *

*The festival is finished now but there will be more in the next academic year.*

** Tom Button** (

**@mathstechnology**) is the MEI Mathematics Mathematics Technology Specialist and leading MEIâ€™s work on the development of Data Science courses and materials for pre-university students.

MEI has developed a free set of self-study resources to introduce Core Maths students to the wonders of Data Science. This is a series of lessons including videos and programming activities in Python (though no prior experience of coding is required). The lessons are designed to be studied as an optional course alongside Core Maths.

In this session we explored the resources and how they can be used with your students.

Tom introduced himself and then asked us to discuss how our students have used technology to explore data? It didn’t take long for my group to acknowledge that we hadn’t really done this much beyond using calculators. Some people had made use of spreadsheets but it all felt somewhat limited and with a real struggle to connect the desire to use technology with our own lack of experience and the considerations of what gets asked in exams.

Before looking at the course, Tom shared that he views Data Science as being the intersection of Domain knowledge (the context), Technology skills and Statistical understanding. Society is naturally producing huge quantities of data on a daily basis and technology is more advanced than ever so is now capable of handling this vast amount of data. An interesting point is that Amazon has the computing power to use its vast database as a census rather than even needing to sample.

The Introduction the Data Science course is intentionally a short course so as to be manageable alongside 3 A levels and Core Maths. It is free and self-study (so teacher input is not needed). The course uses real data contexts and includes the A level Large Data Sets (from all exam boards).

Also, an important pragmatic point is that there is no log-in or sign up needed to do the course.

Amongst other things, the course covers:

**How to pre-process data**. Including things like actually downloading data, converting CSV files to Excel compatible formats, cleaning the data.**Visualisations.**Obviously this links to the previous session by Catherine Manning but includes technology based ways of doing this.**Predictive models**. Scatter graphs are often used as an explanatory model. This course explores ways to use the data to be predictive.**Coding**. Tom talked about the course emphasising the importance of some beginner-level coding and how crucial this is for when data sets get beyond the capacity of spreadsheets.

We had a chance to explore the modules in the course and there is a great collection of videos from real data scientists covering a brilliant variety of subject areas. They mostly follow a format of a video, then 1 or 2 activities, then maybe another video and another activity. In each module there is a further reading section and a ‘meet a data scientist’ video.

In the second part of the talk, Tom gave us a brief introduction to coding in Python. This language is free, comparatively easy to get started with and also commonly asked for in job adverts. The Data Science course uses Python through a web-based coding environment called Kaggle. If desired, it is possible for students to share their Kaggle notebook with teachers.

Again, we had a chance to play with this tool and while I didn’t get enough time to look thoroughly, the parts I saw seemed pretty intuitive and easy to use.

Finally, Tom showed us how Kaggle can do things that spreadsheets can’t with a data set containing **all **of the national house sales from 1995 to 2020. The data set contains over 22 million pieces of data (!) which would obviously break Excel but was handled with ease by using coding in Kaggle. It was an impressive demonstration and has certainly made me think about what could be done with coding.

Some possible ways to use this course are:

- An optional summer project for students
- As preparation for any data-based Extended Project Qualification (EPQ)
- Working with teachers/students in other subjects

As a finisher, Tom told us that there are plans for a data science taught course in the Autumn term. It will be aimed at year 13 students that have completed the self study course and looks to be an exciting opportunity for students to really stand out from the crowd! More information on that is available here.

This was an excellent way to finish this series of sessions in the Core Maths Festival and it was great to have a change of pace/approach/style. Thanks to Tom for this session and to all those that have helped to make the Festival come together.

**My take aways:**

- I want to complete this course myself. I’ve already completed the first module and am looking forward to working through the rest over this Summer.
- I intend to offer this to my current year 12 students as I think some of them will enjoy the challenge.
- I am going to share this course with some colleagues at school. There are certainly some other maths teachers that would love it and I think there may be some teachers of other subjects that would benefit from it.
- This course does seem like a good way to provide some differentiation for the top end students that take Core Maths. A little bit of extra work that they could sink their teeth into.

*In thisÂ series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. *

*The festival has finished now but there will be a 4th Core Maths festival in the new academic year.*

This one is a special guest blog post fromÂ James MaloneyÂ â€“ thanks very much! It also has the slightly weird aspect of being about the talk that I gave. I’ve added my comments and thoughts throughout in *purple italics.*

As we entered this session of the Core Maths Festival with @reflectivemaths, the talk was of Englandâ€™s first knockout game of Euro 2020. There seemed to be an even split between those who cared and those who were working out what rule changes would be necessary for them to even begin to register a picogram of investment.

**Cake Emergency**

Dave knows what motivates Core Maths teachers though, and attention was swiftly on his session, with a question involving delayed payment for a cake from a parentsâ€™ evening.

(It might have helped my atrocious guesstimate had I properly noted the date of the parentsâ€™ evening!) Of course, it was very large number and Dave then talked about where he took the discussion then, revealing some of the questions students have asked in the past:

â€¢ How big is this?

â€¢ Compare it to the UK national debt

â€¢ What would happen with regards to payment etc?

â€¢ At what point does a debt become untenable?

â€¢ Could Dave go to prison?

â€¢ Was the brownie nice?

â€¢ Are Jaffa Cakes cakes or biscuits?

I really like how Dave acknowledged the seemingly more frivolous comments that may be dismissed as being pointless to explore, as these can often lead to deeper and different types of understanding. For example, asking whether the brownie was nice could lead to discussions about value, and that a lot of human decisions are not made on numbers alone but in conjunction with aesthetic or risk judgments. Similar approaches were discussed around Phone Emergency which led into Payday Loans and how Dave went through loans with his students. We had a quick discussion about how to use payday loans in Core Maths, now that legislature has limited the extent of the debt a person can build up. They have lost a little of their impact on student engagement due to this, but remain a useful hook. This year I have added in a discussion about the â€˜Brighthouseâ€™ model of buying electrical goods and appliances on credit, as I felt this business model had grown as the payday loan business model was curtailed by the legislation. Incidentally, Iâ€™ve also used this example for GCSE resits as instalments are common in exam questions there. **I’d be interested to hear more about this!**

**Timing** **and What is a Financial Question?**

We then had a poll on when we taught financial maths in our schemes of work. Dave revealed he allocated a lot of time for financial maths and noted that it wasnâ€™t the first topic, preferring to start with estimation. I was really interested to hear how Dave and the other attendees approached this as I wanted to compare it to my collegeâ€™s first year of teaching AQA option 2B, with a focus on different elements to our previous exam board.

Dave then focused in on APR, on which he spent a lot of time (showing his powerpoint to illustrate this) and wanted our views and ideas on whether it was worth spending so long on it. His grade 8/9 students liked doing the APR formula as it â€˜felt mathsyâ€™ and challenging but those with lower grades, well, not so much! So Dave went through his analysis of the syllabi of the exam boards. APR was only mentioned specifically in AQA and NCFE, though it was not ruled out from being examined in the other boards. A series of polls asked us what percentage of marks we thought were allocated to financial questions and whether we thought two examples of exam questions counted as financial questions.

Dave didnâ€™t get the answer he was expecting for either one, ** (I don’t really think this is a finance question)** but it was generally felt that any questions with money involved should be considered as financial in the exam. A table showed that AQA would consistently have 15-20% of marks related to financial maths while Edexcel and OCR were less predictable.

**APR or AP Arenâ€™t?** *(This could have been the talk title!)*

A discussion in break out rooms about how weâ€™d covered APR this year, led to comments from attendees and Dave that we probably should not spend too long on APR and perhaps it could be thought of as more of an extension opportunity. * (I do want all students to be aware of APR and what it means but I’m not convinced the technical breakdown of the algebra is useful for the majority of students.) *The year it came up on the AQA exam, it was a very poorly answered question according to the examinerâ€™s report.

*(Although it is fair to point out that it was a fairly tough variant of the topic.)*At this point, I was reflecting on having now taught AQA for one year, Iâ€™ll be reducing how long I spend on APR. In preparation for assessments, I had told students, if only from a timing point of view, any question on APR was likely to be involving only 1 or 2 years, or one of the simpler substitutions. My focus for next year will be more substitution into financial formulas in a broader sense (mortgages etc). Seeing past paper questions this year, Iâ€™ll be treating APR and AER as specific examples of the skills involved in substitution. Past papers questions have shown that AQA like to test the ability to work with any financial formula and sometimes they are linked to spreadsheets and iterative formulas. Students need to be prepared to use a financial formula they have never seen before, so Iâ€™ll be emphasising noting time periods and expressing percentages as a decimal and those skills that are common to financial formulae.

**Financial Maths Bucket List**

Daveâ€™s next question was, â€˜So what financial aspects should a Core Maths course cover?â€™ Dave gave us his list (see below,) based on what heâ€™d like his children to know.

Crucially his list wasnâ€™t just about topics that were specifically on the Core Maths specification and brought in other areas from the course such as critical analysis. I completely agree with Dave here, and it mirrors comments I suspect weâ€™ve all had from CM students along the lines of, â€˜I wish weâ€™d done this at GCSE!â€™

Then we came to the section where Daveâ€™s considered analysis set about inspiring tasks and problems heâ€™s used in his lessons along with the beginnings of ideas that are not yet fully-formed. They definitely got me thinking! As so often during the Core Maths Festival, my brain and muscles were scrambling to get the smorgasbord of ideas filed away for future reference, attached to a lesson from last year I wanted to change, or noting down how I was going to use them. These included

- Monthly budgeting
- “Car or Moped” (about students’ college transport
- Raising the pension by Â£10
- Gapminder’s Dollar Street
- Mortgages vs rent
- Claiming Expenses
- Food poverty
- Pay slips
- Student loans

We closed with a snapshot of Daveâ€™s alternative SoW with new titles to the lessons to create a more interesting sounding Scheme of Work. **(I know this needs some work but it feels far closer to how popular science books organise their chapters compared to how a text book would.)**

I like this idea, and Iâ€™m going to see how it goes down with my students. The Core Maths teachers in my department preferred to stick to our traditional topic listings however! *I’m a little surprised by this!*

A tiring but inspiring final section then, leaving me needing time to process everything. Any time Iâ€™ve attended a session with Dave, thereâ€™s been a wealth of ideas and resources presented. From there itâ€™s up to us to analysis, use and adapt what we feel will work best with our students. Dave always has a fresh and unique perspective and the common topics all of us spend our time thinking about and teaching. Thanks for another inspiring session, Dave and the Core Maths Festival! **Thanks. This is a very kind summary.**

**Main Takeaways**:

- Donâ€™t spend too long on APR!
- Teach substitution into financial formulas generally rather than specifically AER/APR.
- Students will be most engaged with financial situations most relevant to them.
- They still appreciate covering topics they wonâ€™t encounter immediately, like mortgages.
- Remember students will likely know less of the world than you expect!
*Finance is a good opportunity to cover some of the social inequality aspects that will crop up.**Anything that makes students realise how much money it costs to be an adult is time well spent!*

*In thisÂ series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. *

*The festival has finished now but there will be ones in the near future!*

**Dr Aoife HuntÂ **(@Aoife_Hunt) works for Movement Strategies, a consultancy that specialises in analysing the movements of people. Since finishing her PhD in evacuation modelling at the University of Greenwich, Aoife has worked with researchers across the world to figure out how we can use maths to make buildings safer.

In this session, we’ll explore some unexpected applications of maths in the world of large crowd flow. Aoife works as a consultant on some of the biggest events and venues in the world (eg Wembley and the Eiffel Tower) to make sure that crowd flow is efficient and safe.

Aoife started with a bit background in which we learnt that she was almost the face of the number part of Countdown (down to the last 5 but they chose Rachel Riley) and was also in a band. Aoife is the first woman to win an award for her research regarding fire safety from the SFPE.

Most of Aoife’s current job is working as a consultant to deal with crowd flow. She showed us some amazing computer simulations (similar to the SIMS game) and explained that it’s done both for safety and also to maximise enjoyment at events. Aoife shared some questions she’d been asked in her line of work, such as:

- I don’t know how many people are going to come to my parade – it’s between 30,000 and 100,000. Where should I put my barriers?
- Where should I position my toilets so that they are visible and accessible to everyone? How many do I need to make sure nobody waits for more than 2 minutes?
- Should I spend 2 million on an extra lift?

A very common question for large events (such as the 175 000 people at Glastonbury) is “How long would it take to evacuate?” We were asked to think about what you’d need to know to answer this and an important part is finding out how fast people walk. There were various suggestions for ways that students could experiment about this and Aoife showed us how to do this over a 10m distance. One method is to have people walked together within a hoop with an area of 1 square metre to get a sense of how density of people affects the speed. It turns out that speed of movement is mostly affected by the density of the crowd. Estimating this is very difficult to do but as a guide, the front of a music concert may well be 6 people per square metre.

One key term for considering evacuations is that of flow, where flow = no of people passing a point / time

Flow can be nicely modelled by a negative quadratic based on density on the horizontal access (peak flow when density is 2 people per square metre although the graph below, taken from here, doesn’t quite match that). Aoife assured us that every building since 1911 has been built using the quadratic model to think about the flow through that building. We saw some clips of genuine lab experiments of people leaving an area (wearing identical hats for ease of counting!)

Another good example of a useful model was the Normal distribution for time taken to choose, order, pay for and receive a drink for a food kiosk. Similarly, the same idea but for total time spent in the toilet (from entering to leaving, including washing hands). Aoife has actual co-authored a piece of research called The Toilet Paper looking at how long people spend in the loos at airports! Yes, this did involve literally hanging around outside toilets and timing people as from when they went in to when they left.

**After the break**, **we focused on the Maths of Social Distancing**.

As an example, Aoife told us that Old Trafford stadium had a capacity of 76 000 prior to Covid but there was some genuine questions about what the new capacity would be with social distancing (turns out it’s 23 500). We considered how much space someone actually needs if they are to socially distance and this lead to us considering circle packing. There’s also a really nice optimisation problem when people are sat down, with seats in rows, and what happens if they are sat in groups or not. For example, suppose you have 5 groups of 6, 4 groups of 4 and 2 groups of 2, what is the best seating arrangement to be able to offer more seats for sale while still maintaining social distancing.

This picture from the BBC (source here) is to illustrate the point.

One further example of social distancing is on the top deck of a London bus. If people are not allowed to sit in any seat immediately surrounding someone else or two seats in front or behind of anyone, what is the maximum you can get in? Here’s my answer with a red dot representing someone sat there.

A great follow up to this was that in an optimal packing, the even rows aren’t used but sometimes in real life, people make sub-optimal decisions with 8 people being the worst possible. If it costs Â£9 000 to put stickers on the even rows (saying don’t sit here!) and the tickets cost Â£1.60 each, how many bus runs a day are needed for the additional revenue to pay for the stickers?

Aoife finished by letting us know that in terms of recruitment for this job, the main qualities that she would look for are some element of common sense, an ability to communicate and a (relatively low) level of numeracy. After this inspiring talk, there were multiple members of the audience wondering if they had enough common sense to be qualified as working with Aoife sounds like an amazing job!

**My take aways:**

- I certainly want to incorporate the quadratic graph for crowd density vs flow into my KS4 lessons.
- I’d like to think about the flow vs crowd density scenario and see if I can incorporate this into my Isle of Wight/music festival project.
- Whether you like it or not, people are (for some reason) interested in issues regarding toilet usage. I am genuinely considering this as a theme for a block of lessons.
- “Should I spend Â£2 million on a lift” is a nice question to get students thinking about “what information would I need to answer this?”
- The top level of the bus scenario might make a nice starter activity or tutor time activity.
- Inspirational speakers really make a difference. It is amazing to know that I have been talking to the person that literally models venues and events to help save lives. I have found myself saying on a few occasions recently, “When I was talking to Dr Aoife Hunt, …” In other words, the Core Maths Festivals are amazing and if you weren’t able to make this series, see if you can possibly make the next set.

*In this series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. You can sign up for other sessions in the series here.*

**Dr Wanda Wyporska** is Executive Director of The Equality Trust, the national charity that campaigns to reduce social and economic inequality and is a regular keynote speaker.

Explore The Equality Trust schools resources and follow them on Twitter **@EqualityTrust**

**Catherine Madden** is an information designer and visual story strategist based in San Francisco. She runs visual thinking and data storytelling workshops, which help people to communicate complex concepts simply and effectively.

Follow her on Instagram and Twitter **@catmule**

This session is about inequality and creating data visualisations (and getting students to do the same) by hand!

We started off with Wanda describing the role of The Equality Trust and their role in campaigning to reduce inequality. Wanda explained that, amongst other things, inequality is literally a matter of life and death with it being a major factor in life expectancy. She spoke passionately about how important it is for young people to be involved and I can’t help but agree.

There was a good interview with Wanda involving some great questions. This was recorded and will be available when it’s ready.

Catherine gave us a tour of her background which started of as a graphic designer. This lead to her designing interesting ways to display data and becoming somethings of a ‘go-to’ person for this. She reassured us that it is common for people that think they are not good at drawing to actually be quite creative when suitably prompted.

We were given a nice task of trying to count how many 9s were in a bank of numbers, followed by the same task but with the 9s highlighted. Catherine told us that this is called pre-attentive processing and makes it clear that visualisations can help information be understood much more easily. She also pointed out that hand drawn charts are somewhat surprising (in a word of Excel based graphs) and are also easy to consume. They tap in to the empathy that comes with the obvious fact that a human must have been involved in its construction.

Next, Catherine walked us through an example she had prepared to give us a sense of the process of creating a hand drawn visualisation. It was fascinating to watch and somewhat daunting to be expected to create somethings ourselves soon.

**Five steps for the process**

1 Get to know your data – what is it about?

2 Get Curious – what do you notice? what do you wonder? what is most interesting to you?

3 Have an Idea Party – rapidly generate ideas with quantity more important than quality.

4 Evaluate and Iterate – look back at what you’ve done. Develop the ones you like.

5 Refine – Show a friend and ask them to “Describe what you see”. Discuss, refine and repeat.

Alongside clarity and being engaging, Catherine thinks that the following are necessary for a ‘legit’ graph: Title, Legend, Axes, Sources, Units and Context.

Next up, it was our turn to have a go. To get us into the drawing mood, we were asked to draw some squiggles on a page and then turn them into birds. This was remarkably good at making me think that my artistic skills shouldn’t hold me back on this!

After that, we were presented with the pie chart we were going to look at and completed the sentence “This chart tells me …” to which my answer was “fifths are not fifths”.

“What do you notice” and “What do you wonder?” were mentioned as useful tools that can lead you into the type of visualisation you draw.

Now we had 5 minutes to have an Idea Party. We were told to start a new design every minute and to prepare ourselves that this could well be chaotic and stressful. Here’s what I drew:

I was drawn (no pun intended) towards the idea of INKcome (pun intended) so thought about ink bottles or blobs of ink. This lead me to thinking that the wealthier you are, the more access to ink you have to get your point across.

Andrea helped me articulate this as – Does having more income give you more of a voice?

Now refine an idea and spend more time on it.

I thought about 1 letter (character) for each percentage point. A different colour per quintile. I don’t like that the jumble of colours makes it hard to see what’s going on.

Quite aware that the choice of words/letters is influencing the message of the data. I need to try and make each letter the same width. There’s no scale or title.

I can absolutely see how I could get absorbed into doing this and the whole process could take a while.

I know there are flaws in this presentation but I still quite like it, especially given the time I’ve spent on it. I am definitely aware that, to all intents and purposes, this is just a bar chart but I’m ok with that. I have no doubt I could choose better words and I know the spacing could be better. Still, all in all, I am proud of this.

I had an unfortunate wifi issue at this point but came back in to see options for allowing students to draw each idea on a separate post-it note and then put them onto a sharing wall. This allows a chance to group similar ideas and get those people to work together. This seems like a good plan to me.

This was a genuinely inspiring talk and it was fascinating to watch Catherine work and hear her talk about her ideas and thought processes.

There is going to be a competition for students to redesign a data presentation in the new school year. Thanks Catherine (and Cat and Tom) for an amazing session.

I’m off to go and draw some data now.

*In thisÂ series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. You can sign up for other sessions in the seriesÂ here.*

This one is a special guest blog post from James Maloney – thanks very much!

**Making Sense with Desmos**

A key online platform for many maths teachers over lockdown has been Desmos. A bit like a dog is not just for Christmas, Desmos is not just for lockdown. The focus of this session of the Core Maths Festival was using Desmos as a key tool in lessons; one which offers avenues of learning, understanding and assessment that will not be accessed even in face-to-face lessons.

We started out with some background from Natalie Vernon, of the AMSP, on how she came to get involved with Desmos and how her love for it has grown. We then had an interesting and useful comparison to Geogebra, which involved linking back to Tom Rainbowâ€™s â€˜Truth of Lies?â€™ session from earlier in the festival. Though it is hard to break away from what you are used to, the ease of working with large data sets in the graphing calculator alongside the activity builder really do support the use of the free-to-everyone Desmos!

At this point, Nat explained how the rest of the session would work. Having previously completed two Desmos courses with Nat, I was not surprised that this was going to be, â€˜watch me, then you practise.â€™ Having attending numerous CPDs over the years, I suspect Iâ€™m not the only one who appreciates this approach, especially when technology is involved! The support provided to work individually as much as possible, really is a mini-masterclass on how we can do the same for our students. In particular, Iâ€™m thinking about how my lessons on spreadsheets can use similar prompts and scaffolding.

*Investigating Divorce*

We then moved on to visualising the data. First, the mechanics of using Desmos from getting the data into the graphing calculator, to extracting the descriptive summary statistics, and then creating the visualisation of this data. At each stage, the activity was paced to pause at a slide requiring us to reflect on what we had just done. Nat highlighted here that Desmos allows the teacher to see ALL responses from students. Something that you really donâ€™t get in the classroom F2F. You can then pick up any interesting answers or get students to explain their answers further if you need to â€“ all leading to that deeper understanding for which we strive. The students can generate questions or points that change your next lesson or how you deliver the same lesson next time. The example here was getting Tom to explain how he came to his estimation of 20,000 for the number of divorces in England and Wales in 1912. With students, you could use box plots of their data, to see if theyâ€™d change their answers (which, perhaps, Tom should have done with a true answer of 587!)

Hereâ€™s the key thing and the reason this session has the title it does, and one that was reiterated throughout the session by Nat and Cat: all this procedure and process means very little if you do not place the statistics in context. The deeper understanding is not going emerge if students only work on methods without making connections. Cat mentioned the theme from examinerâ€™s reports that students who gained higher marks kept the context at the forefront of their answers and did not just correctly complete the procedures involved.

As a demonstration of that, we moved on to plotting the graph of the divorces in the UK since 1857. Nat gave us the line up to 1980 and asked us to sketch where we thought it would go next. Again she picked up comments and reflections from us, and built on the context, before moving into the lovely line of â€˜adding context to your context!â€™ And there, my questions and my reflections were getting answers (or sometimes further questions!) leading to my deeper understanding. In many ways, this path to my deeper understanding as a student was unavoidable, because of how we were working with and using the data.

*Life Stories*

Another nice touch throughout these activities, was the connection to personal stories. Nat linked her interest in the data to her personal history. Photos on Desmos were of interesting people with a tale to tell. Iâ€™d not heard of Margaret Molly Brown before and this sort of hook helps the student connect to the data, which quite often is hard to do. Particularly when faced with an iceberg of data!

We moved on to â€˜The Ship of Dreams,â€™ and data from the Titanic. The data for this came from Sheffield University and they have other data sets available. This is another site to add for one of my summer jobs of finding data to use next year. Our question about the Titanic was â€˜which was the greater factor in surviving â€“ gender or cash?â€™ Here we produced more graphs to demonstrate how often we cannot know the story of the data until we can visualise it. The next graph was always to gain greater understanding of the data, it wasnâ€™t just to make a pretty picture. No matter what processes we did, we circled back to the context.

Iâ€™ll be honest, at this point, I was always wrong with my predictions! Looking back I realise that, like the saying you never learn without failing, the moments I was thinking most deeply about the data and context were while I was searching for the reasons I was wrong. Desmos really facilitated doing this, as I was able to manipulate the data to answer the questions I wanted to ask, quickly and easily. How great is this for students? Where they donâ€™t have to worry about the time-consuming processes â€“ the how, and can concentrate on the context and reasoning â€“ the why.

*From acorns to oak trees*

We finished yet another inspiring festival session with a discussion of where you could go next with this. There are so many paths to take, and Desmos makes being guided by your students on where you need and want to go, so much easier. More importantly, it makes the journey more rewarding and the final destination of deeper understanding easier too.

**Key Takeaways:**

- Desmos was initially used by so many of us to deliver lessons online in lockdown, but itâ€™s much more than this. It can be a key learning tool of
*any*lesson (with technology access of course). - A common problem everyone seems to have is getting good, interesting and useable data. The session provided a number of links to where to find some.
- If you have the right data, you can arguably teach the whole syllabus from it!
- Context! Context! Context!

**Other points:**

I found it intriguing to try to think about what other teachers would be reflecting on at any particular point. I often think about what my students would be thinking during a task, but thinking about a fellow teacherâ€™s thinking did raise some interesting ideasâ€¦ I think.

â€˜The Ship of Dreams,â€™ reminded me of â€˜The Book of Dreams!â€™ and memories of using the Argos catalogue when teaching in schools. It was brilliant for so many topics!

Should I have a Core Maths Mantra? Should there be a set of questions I need to be asking every time about a graph or some data? What would they be?

We had a short discussion about whether we need to worry about sensitive topics so much? Other subjects cover them all the time, so perhaps we should use them more often. Particularly to strengthen the link between Core Maths and other subjects.

*In this series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. You can sign up for other sessions in the series here.*

**Jen Buckley** works at the University of Manchester and is part of User Support and Training team for the UK Data Service. She develops training to support the use of data in the social sciences and has a special interest in learning resources that introduce how data skills can help us understand society.

Find the UK Data Service on twitter @UKDataService

This session looks at using relatable and reliable data to create engaging lessons.

Jen started off by explaining that some of the data that is held could be sensitive so isn’t generally available while others are Open Data. There are plenty of Open Data sources and some really interesting, engaging options.

After discussing her background, we tried a Britain quiz with 8 questions on the mentimeter site. This reminded me of the Gapminder questions that check how well people understand the world around them. They covered topics such as household vehicles, smoking and people’s perception of stereotypical male/female roles. It was a good introduction to statistics and links easily to graphs and sampling.

Later, in breakout groups, we discussed how to get a representative sample of Britain. We decided this was rather difficult but went down the route of using postcodes and then some sort of stratifying within the houses to try to ensure some variation. After, Jen took us through a detailed example of how the British Social Attitudes Survey picked their sample. It was really good to see and accept that it cannot be perfect. She also dispelled the myth that a common starting point is the electoral role (as there are multiple people that are not on there).

**Resources and Data**

Jen showed us how to look up some data using the Nesstar data service. (As a starting point, click on *Research data sets* on the left and then *British Social Attitudes survey*.)

The UK Data Service are keen to find out what would be useful for teachers and already have some resources that can be found here.

We were shown some useful resources on topics that will definitely be of interest to students and are clearly from authentic surveys. There are some teaching ideas here and the public confidence in the police ties in beautifully with the recent talk from Dash Young-Saver.

Finally, Jen showed us some great spreadsheets including the data on Crime and Sexual views (Natsal) which is one that David Spiegelhalter mentions quite often.

**Conclusion**

As I was writing this, I found it hard to do justice to the level of interest that these topics caused. It was really great to hear from someone that actually has to deal with the ins and outs of sampling and also be able to have access to the vast data sets that are actually more easy to access than I tend to think.

Most importantly, it seems like this is just the beginning of the AMSP working with the UK Data service so I’m looking forward to more resources, possibly even tailored to Core Maths, in the future.

**My Take-aways**

A bit of a difficult one this but I want to adapt my sampling resources to make use of real data that’s available. I’ll have to work out how to do that of course!

*In this series of blog posts, Iâ€™ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. You can sign up for other sessions in the series here.*

** Ben Sparks** is a mathematician, musician, and public speaker. He gives maths talks and workshops around the world, to students, teachers and the general public. He is part freelance and part time with the Advanced Maths Support Programme (AMSP), and he’s based at the University of Bath. His work includes regular appearances on the Numberphile YouTube channel and shows with the Maths Inspiration and the MathsFest projects.

In this session, weâ€™ll explore how to use probability distributions, statistical analysis, and the exploitation of surprising number patterns to determine whether people are cheating, or whether youâ€™re being scammed.

We started with a Citizen Kane clip that linked to recent events in American polling.

Ben, quite sensibly I think, views Core Maths as being maths with ‘common sense’.

He talked about incorporating recent real-life events into our teaching and highlighted Mark Dawes’ blog quibans.blogspot.com as a great example of reacting to news articles that have opportunities for Core Maths lessons.

**Give me some data** – Ben gave us a dynamic example of real time data collection by asking for us to collect data on seemingly random things such as:

- How many twitter followers do you have?
- What was the price on a recent receipt?
- What’s your house number?
- What is the result of your birth year multiplied by your birth month multiplied by your birth day?

This lead, nicely (and surprisingly) to Benford’s Law when you look at the leading digits, even for this quite bizarre collection of values. He recommended Matt Parker’s Benford’s Law and Biden video.

Alongside these websites: testingbenfordslaw.com and benfordonline.net

In breakout rooms, we discussed: Could you use Benford’s Law in Core Maths lesson? Is it ok to do things that aren’t on the course?

My groups conclusions were a fairly clear yes to the second question, as long as you can find the time. The first one wasn’t quite as clear as, while you probably could use it, it might be fighting for other worthy ‘non Core Maths topics’ attention.

**Are you psychic?**

Next followed a spooky little test where a participant, Milena, correctly predicted 3 psychic events. Ben admits this was a cheat in some way but, maddeningly, refused to share how. We then used a site he’d made to test if we were psychic (spoiler- we weren’t).

**Find the Fraud**

Dream the youtuber plays minecraft and his wikipedia page mentions him being accused of cheating due to the unlikely events that happened in a speed run of the game. Matt again has a great video looking into the question of how lucky is too lucky?

A couple of things Ben wanted to draw out is that unlikely things CAN happen. Just because they have happened doesn’t automatically mean cheating is involved. He also likes the idea of new units (like Matt’s 10 billion human seconds) and micromorts to help people understand huge and small numbers.

To round things off, Cat suggested To round things off, Cat suggested this article and also linked to this Desmos activity What’s the significance? Smelling Parkinson’s â€¢ Activity Builder by Desmos, both of which revolve around understanding uncertainty.

Once again, this was an entertaining and engaging talk. Thanks Ben!

**My Take-aways**

- Use Benford’s law when teaching logarithms (in A level maths).
- 4.7% chance of a pearl in Minecraft will feature in my binomial distribution questions.
- Youtubers, Instagrammers and the like are hugely influential and a big part of teenager’s lives. I should try to find ways to incorporate this into my teaching activities.
- Geogebra has some nice probability tools built in that are easy to use.

**Tom Rainbow** (@CoreMathsTom) works on the AMSP supporting schools and colleges deliver Level 3 Core Maths. He loves all aspects of mathematics but has a particular interest in exploring ways in which mathematics can provide young people with a set of tools with which to make sense of the world they live in.

This session was about the idea that with so many information channels available to them, people today face an ever more common dilemma â€“ who can I trust?

We started with an activity that asked how our teaching connected with the Handling Data cycle from the old KS3 National Strategy.

The general consensus was that it’s a good process but difficult to use as a teacher. The focus tends to be on the bottom box and collecting data is difficult/time consuming to do. There’s also the sense that most exam questions would probably focus on that processing and representing aspect with maybe a cursory nod towards collection and interpretation.

Tom’s view is that this is applicable at all stages of maths and so the KS3 label should be removed. In Core Maths, there is time and motivation to do the full cycle, particularly with the evaluation section and going through the whole cycle again!

In the Shockwheat activity (Shockwheat memos | STEM) Tom got his year 10 students to run an experiment on the activity while his Core Maths students analysed the data. It’s about how many packets of cereals you might need to open to collect the whole set of free gift toys. His Core Maths students spotted outliers (which they didn’t know about at the time) and concluded that it was unlikely the year 10s were carrying out the experiment honestly. He questioned whether this is an authentic activity these days seeing as cereals have stopped putting toys in.

A recurring theme in the media is that of a North/South divide. He was curious about where it comes from and wonders if it’s linked to the dioceses of the Church of England.

This picture is from wikipedia and there’s an interactive version here. It is an example of a great ‘conversation starter’ picture as it immediately made me think of some questions (eg why is Southend and Nottingham pink? Why does the yellow bit go so far up?). However, Tom saw a TV program and wonders if there’s really more of an East/West divide and did some digging.

This does lead to a good opportunity to focus in on the “Specify the problem” aspect of the handling data cycle.

From the inews article, we get this image:

Again, it is a great conversation stater as it seems hard to initially tell what’s going on. Given that we were wondering whether the graphic is meant to show that the East is better off than the West or vice versa, Tom suggests going to the Office for National Statistics (ONS) and spending some time with students on this site. It’s not very, very easy to use but it does show students what they might genuinely need to deal with. This large set of data leads to the ‘process and represent’ section of the handling data cycle and, realistically, using software to do this.

For graph drawing software there are three good and free options: Autograph, Desmos, Geogebra. Tom demonstrated how non-intimidating using Geogebra can be to draw a variety of charts both for single data analysis and multiple variable analysis. Several people said they were impressed with how easily it can switch between different visualisations.

We had a chance to talk about our thoughts and my group’s discussion seemed to agree that even after comparing house prices, it was still very unclear. After hearing from some other groups, Tom showed us how you can develop a topic to follow up on what was suggested, such as considering whether London should be included. He commented that it’s really nice when a genuine curiosity leads you/the class into covering multiple parts of the course. We looked at a deprivation map and thought about how we could link this to the previous enquiry and also consider how to incorporate correlation and possibly financial maths too.

This was yet another great talk and a good reminder that we don’t need to reinvent the (handling data) wheel all the time. Find something your students are interested in and then work through the steps with them!

**My take aways:**

- I like the idea of using Core maths students to analyse something another class has done. This is also a subtle advert for Core Maths to those younger students.
- Some possible alternatives to the ShockWheat activity are: Lego minifigure packs, Pokemon booster packs and Football stickers.
- Geogebra can draw stem and leaf diagrams well!
- There’s never enough time to do everything so maybe some well chosen topics that cover multiple maths skills are the way forward.
- I need to book computer rooms more often or maybe even asked to be timetabled in there for some of my lessons.
- I really do need to find out what topics would interest my students!