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M2, M4, M6, M8, Motorway!

I've always[1] wondered how far it was possible to go staying only on consecutively numbered motorways in the UK. I've also been looking for a reason to fiddle around with Graphviz since the eternally helpful Colin Wright pointed me towards it a while ago.

So I found a database of the UK's motorways and created a graph:

Optimistic October: Day 31 - What Gives You Hope for the Future?

It's the end of the month, the end of Optimistic October, and it's Hallowe'en...

And what is scarier, I ask you, than...


But anyway. Rules are rules:



  1. Friends. I have a small (ideal) number of excellent friends.
  2. Science. It's awesome and if we do it properly we can solve all sorts of problems.
  3. The belief that most people, deep down, want to be better.

Optimistic October: Day 30 - Purpose

I'm... supposed to have a sense of purpose?


I'm never quite sure what things like this mean, but that just gives me an opportunity to define it however like, doesn't it?

I guess a "sense of purpose" is when you feel like you're doing something that has a point to it, and I'm feeling that this is more of an external thing than an internal one: giving something back to the world, rather than making personal achievements.

I feel most like I have purpose when I'm teaching, so a goal set in response to today's challenge should probably have something to do with that. Generally, my goal is...
To be the best educator that I can be.
 ... but that's not exactly measurable. Part of my desire to undertake postgraduate study was so that it could provide some structure in working towards this goal, so I'm going to work damned hard on completing that as well as I can. As well as this, and at least equally important, is my network of educators that I keep tabs on via Twitter. I don't engage as much as I probably should with the broader teaching community, but I learn a lot, keep up to date, and am forced to think (and re-think) about various aspects of teaching and education. It is genuinely an excellent tool through which to build a learning network on various themes.

Optimistic October: Day 29 - Problem?

Perspective is everything.


I have far too much to do. I'm working on a new perspective for that and will get back to you just as soon as I am able. Please leave a message after the beep*.




* With some ideas about how to find a new perspective on that.

Optimistic October: Day 28 - This Week's Plans

It's important to have goals! This week is going to be a busy week so my top priorities are as follows:



  1. Prepare for my (working) weekend away.
  2. Do some reading for my assignment, making notes and noting references.
  3. Lay the groundwork for next week's work.
  4. Keep tabs on my mental state, and make sure I take the time to switch off for a little while each day.

Optimistic October: Day 27 - Be Kind to Yourself

I really need this one at the moment. I'm a bit behind on, well, everything, and I keep having to stop me beating myself up (not least because it takes time away from doing something productive).


I'm trying to take day 26's advice. And day 24's. Day 21 as well.

Anyway... I'm off to work on day 20.

Optimistic October: Day 26 - Same as it Ever Was

This question might not work for every situation, but it illustrates something which is, I think, a good habit to get into.


A question I (try to remember to) ask myself when I start worrying about something is...
Can I do anything about it?
  • If the answer is "no," then it's a moot point and not really worth worrying about (and the problem now turns into "how do I chill myself out about it?")
  • If the answer is "yes," (and that means I must have at least some idea of what I can do) then the problem turns into...
Should I do it?
If the thing that you can do is easy and less stressful than the problem you're worrying about, then just do it. Why wouldn't you?
If the thing that can be done is more difficult or more stressful than the problem, some of the questions I ask myself when deciding whether taking (or avoiding) any given action is worth raising my blood pressure over include:
  • Will anybody to die?
  • Will anybody be subject to specific torment, anguish, pain or discomfort?
  • Will I get into trouble?
  • Is it really my responsibility?
  • Is this more important than other things that require my time and/or energy?
These all boil down to various versions of the question does it matter? If the answer to all of these questions is "no," then I've got some ammunition to convince the whinier parts of my brain that, actually, we're all good here. We've got space. Breathe.

If the answer to any of them is "yes," then maybe it's time to go to red alert*.

Even in that situation, however, I find it's absolutely vital to remind myself that...
Panicking, flapping, and beating myself up is not going to achieve anything at all. 20 minutes spent breathing, calming, relaxing and planning is time much better spent than the same 20 minutes spent doing those other things.

Whilst writing this post I've had the following stuck in my head, placed there by the original challenge as worded in the post's image:








* Even if that does mean changing the bulb.

Optimistic October: Day 25 - Plan a Fun Activity

I'm posting this a day late, but as this is yesterday's post I think I can use today's activity to answer it...

** does that wibbly-woo thing from Wayne's World **


Tomorrow I'll be heading off to Waddesdon Manor with two ex-colleagues and a current one. This particular team tends to meet up once (or so) a year (or so) for an educational day out, which means cake, coffee and catching up.

I've been to Waddesdon before (a couple of months ago, actually), but tomorrow we went* to a part that I hadn't discovered before: the wine cellars. Here are a few photographs that I will have going to have taken from that bit tomorrow:







* I'm writing this from the future, remember? Keep up.

Optimistic October: Day 24 - Priorities, Priorities

I don't know about you, but I'm really really busy at the moment, and it doesn't show any signs of letting up. Life seems to thunder by at a terrifying pace; deadlines fly at you from the darkness, and in some cases just keep going past, receding again into the distance.

I cannot get it all done.


But you know what? We don't have to. We can't get it all done, and we shouldn't bust a gut trying to. We have lives to lead. What's the point if we're working so hard all the time that we can't sit back and experience life every now and then.

Part of the challenge is working out what needs to be done, and what can be set aside if needed.

Of those things that need to be done, then who needs them to be done? Are they things that we have to do or can someone else get involved.

Even with those things that we alone can do, and need to be done, we still have some wiggle room:

  • What needs to be done to our absolute best standard?
  • What can be done to a lower standard?
  • And what's just, when it boils down to it, a box-ticking exercise and doesn't deserve our hardest and best work.
What matters? Hint: It's not always what other people tell you to prioritise. It's up to you.

Optimistic October: Day 23 - Share an Inspiring Idea

Similar to day 17, this one.


Today I shared:


How about you?

Optimistic October: Day 22 - Show Me Yours?

You can read mine, but only if you show me yours.



  1. My first guitar lesson in years.
  2. Got an A in my first ever postgraduate assignment.
  3. I was surprisingly gripped by rehearsal performances of a maths, music and dance project that I'm part of.

Optimistic October: Day 21 - Not Great Expectations

You're never going to please everyone all of the time, but a lot of us beat ourselves up trying to do just that.


My mental health journey has to a large extent been about reducing the amount of time I spend floating around outside myself and making assumptions about what everybody else thinks - and expects - of me. In fact, when I'm at my lowest I tend to describe how I'm feeling as almost literally not being inside my own body.

What you think other people think is not what's important. What's important is:
  1. That you're doing what you're doing for reasons;
  2. That those reasons are good ones
Of course, everybody's ideas of what entails "good" reasons can be very different, so I think a decent number 3. to put on that list is you can justify those reasons and a number 4. could be and you're open to redefining them in light of new knowledge, understanding and evidence.

I find that it's a good idea to remind myself now and than that one of the reasons that what I think other people think is not important is that if I'm honest I don't and can't know what other people are thinking. Most of the time the unrealistic expectations of other people turn out to be my own unrealistic expectations of myself projected outwards on other people.

I'm sure they wouldn't be very impressed with me if they knew...


Optimistic October: Day 20 - Joy in Completion!

I tend to work on the least-close-to-finished thing, which means I have a million and one projects on the go, and none of them are finished. One easily visible case of this is in the list of books I'm currently reading. It takes me ages to finish anything... Though I did finish one the other day, so I'll say that's today's challenge complete!

Also, tomorrow I'll be playing my guitar for the first time in around a decade as I was gifted a Lead Guitar Masterclass for my birthday a couple of weeks ago. Excellent!


On Day 14 I set myself some goals and I promised I'd revisit them to see how well I'd done...
Here they are, colour coded: successfully completed goals are green, completely failed are red. Somewhere in the middle are yellow (not quite!) and orange (well, I started...)
  1. From Day 1:
    1. Do some work towards my assignment.
    2. Leave work on time at least once this week.
    3. Go to the gym at least once this week.
    4. Not exceed my self-imposed budget for the month.
  2. Look out for positive news and reasons to be cheerful. (Day 2)
  3. Work on prioritising things properly (from Day 3).
  4. From Day 4, be more conscious of my effect on the environment; call out antisocial behaviour when I see it; be an ally to decent people everywhere; seek out sources of positive news; and to challenge negative nonsense whilst championing the harmless stuff.
  5. From Day 5: read a few pages every night before bed.
  6. Extract something optimistic from the bad stuff (Day 6)
  7. Get on it. (Day 7)
  8. From Day 8, sandwich bad news between bits of good news.
  9. Not join in with that blaming lark. (Day 9)
  10. Look for the good in people around me (Day 10)
  11. Re-frame problems into opportunities. (see Day 11)
  12. Do some reflecting. (Day 12)
  13. Be spontaneous. (Day 13)
There's only one outright failure there... And a few bits of green. I'll chalk that one up as a success with things to work on...

Optimistic October: Day 19 - What are you Looking Forward to?

It can be very easy to dwell on the bad things that might happen, or the boring or less fun things that we know are just around the corner. But there are always some good things coming up too.


Some things I'm looking forward to are:

  • A guitar lesson (it has been ages since I played, and I got a masterclass for my birthday!)
  • My first ever visit to America!
  • Big MathsJam!
  • A good night's sleep...
  • ... and a little lie in!
Go on then: what's in store for you?

Optimistic October: Day 18 - Pat-On-The-Back Time

Oh, this is a good one.

I've been a little down this week, struggling against an invisible and ill-defined weight on my shoulders. Everything's seemed a little foggy and I have been (metaphorically) wading through treacle.


But there are things we do every day that, even though it feels like we're taking them in our stride, are actually little wins. Some of them are things we find tricky but push through them anyway. Other things are things that we may genuinely find easy but other people wouldn't have a clue.

Here are a few of my "actually, that was pretty good going" wins for today (if you get through them, send me some of yours!):

  • I went to London by myself.
  • I walked from Euston station to Southwark, having deliberately got an earlier train to do so.
  • I spent the day with strangers, immersed in unfamilar surroundings and concentrating on things that were far outside my comfort zone.
  • I walked back again...
Pretty pleased with that. All of those things will be a "so what?" for someone reading this, but for me, they're all a reason to be a little bit pleased with myself.

Optimistic October: Day 16 - Change for the Better

Things change. We know that, but it can often be much easier* to worry about things changing for the worse rather than looking forward to things changing for the better.


Having said that, in my darker periods over the last decade-and-a-half or so, it's been hard to shake the idea that existence is an unbreakable monotony. Funnily enough I listened to a fascinating TED talk on this (sort of) theme the other day, which I'll embed at the end of this post.

Before that, though I think it's worth saying that I think that today's challenge is a little asinine, or at the very least unhelpful. Yes, things can change for the better (I've got a new bike, woohoo!) but they can also change for the worse (my Granddad was recently diagnosed with lung cancer). Without any further advice the challenge seems a little flat.

I guess what they're trying to say is that it's easy to latch onto and expect the changes for the worse whilst ignoring the changes for the better. Following this change represents a mindset adjustment, and looking back over the last 15 years or so I think I've managed to achieve that, little by little. It takes time, though, and more than a little effort. Simply remembering that it can happen doesn't really help anything at all.

The TED talk I mentioned earlier might be good for viewing change from a different perspective. Here it is:











* At least, if you're me it is.

Optimistic October: Day 15 - Overcoming Obstacles

As mentioned in some of my responses to previous challenges this month something I really need to do is to become fitter and less, well, just generally less. Another obstacle is professional: I've been doing what I'm doing for ages now and whilst I enjoy it (largely...) there's no opportunity for career progression.


Regarding the first obstacle, I tested that new bike out today. I didn't cycle all the way to work as I didn't think it'd be sensible given that I haven't sat atop a bicycle for any distance for a decade or more. Instead, I cycled to the station (and from it again at the other end).

On the professional front, the steps to take are less obvious but I'm working towards broadening my mathematical horizons: when everything is related to cryptography this pony's tricks are rapidly dwindling in number. With this in mind I've been thinking about the MathsJam talk I offered as part of Day 13's challenge: It's definitely not going to be about anything to do with cryptography. I don't know what it is going to be about, but I've got some ideas and I'll collapse that probability function when (if) my submission for a talk is accepted.


What are your obstacles? If you can't think of a first step towards overcoming them talk to someone about them (me, if you like). Maybe you (we) can help each other along a bit.

Optimistic October: Day 14 - Goal Setting for the Week (and a quick review)

Today's challenge, to set hopeful but realistic goals for the week ahead, is generally a pretty good idea to be taking forwards. But then...


... the whole point of taking part in the Optimistic October challenge is lost if I don't make sure that I take something away from it all to keep for the future. So a recap (of sorts) is in order, with a few loose goals attached based on each day's challenge so far.

I will...
  1. As per the goals set on Day 1:
    1. Do some work towards my assignment.
    2. Leave work on time at least once this week.
    3. Go to the gym at least once this week.
    4. Not exceed my self-imposed budget for the month.
  2. Look out for positive news and reasons to be cheerful, as agreed to on Day 2.
    • If you'd like to help me with this, mention me in some happy, funny, cheerful and generally lovely news posted on twitter.
    • If you'd like help with this, I've added some links to positive news sources on the "More?" page of this site. If you know of any others, please let me know!
  3. Work on prioritising my daily work, as was the theme of Day 3.
  4. Keep up with my efforts to be the positive changes that I want to see in society. On Day 4, I promised to be more conscious of my effect on the environment; call out antisocial behaviour when I see it; be an ally to decent people everywhere; seek out sources of positive news (see #2!); and to challenge negative nonsense whilst championing the harmless stuff.
  5. Keep up with Day 5's pledge to read a few pages every night before bed. I haven't been perfect between then and now, but I've managed it most days.
  6. Look the bad, annoying or upsetting stuff in the face and extract something optimistic from it. Day 6 told me to, so it's happening.
  7. Get on it. Procrastination would be my middle name if it wasn't already Kenneth, so Day 7 has, is and always will be a challenge, but I'm going to get. On. It*.
  8. Respond to difficult situations constructively. Also, as I challenged myself on Day 8, I'll sandwich bad news between bits of good news. Feel free to give me a nudge if I slip on this one.
  9. Not join in with that blaming lark. Day 9 has a point. I will, instead, [see #7].
  10. Look for the good in people around me, as challenged on Day 10. Nobody's all good, but nobody's all bad either.
  11. Re-frame those problems. I guess Day 11 is just Day 10 in a different... frame. Also the chubster thing. I got that bike, by the way.
  12. Do some reflecting on what I achieve, as Day 12 dictated. I can use this post to do that. See you on Day 20?** 
  13. Live a little. Be spontaneous. Day 13 reminds me to not let #3 on this list take over.

How are things going with your challenges so far, and what are your main goals for the week ahead? Good luck with them, and let me know if I can help out!






* First thing in the morning.
** Hopefully before then, too, though.

Optimistic October: Day 13 - A Spontaneous Thing

Today's challenge is a bit of an odd one for me, because to-do lists are very much not my forte, so I thought I'd flip this one on my head.


I use todoist to keep track of my to-dos at home. I say "use," but really that means I use todoist to record a whole heap of things that I'm probably not going to get around to.

So, today I spontaneously did some things on my to-do list:

  • One was called "Q&A entry," which refers to a diary of sorts in which I am supposed to answer a daily question for five years. The entry was 211 days overdue. I caught up a bit (but not completely).
  • I'm going to America soon, and it occurred to me the other day that I'd need money while I'm there, so I put it on my to-do list (which is a surefire way to make sure it gets forgotten). I got that process in motion.
  • I put my name down to do a talk for Big MathsJam in November. This'll be my fourth (I think) Big MathsJam and I've promised myself I'll offer a talk each time. Now I've done it, if it's accepted I'll have no choice but to actually write it.
I can say with complete honesty that without any prior planning I decided on a complete whim to be not spontaneous today: what did you do?

Optimistic October: Day 12 - A Reflection on This Week's Achievments

Day 12, and I'm still going! Today's challenge is to take time to reflect on what you have achieved this week. I want to hear what you've done, either in the comments or over on Twitter!
My own achievements can be summed up as follows:
  • I took three days off work*! I almost managed not to spend any time answering work emails, too, but I can't really notch that up as an achievement. Still needs work.
  • It was my birthday week, and for the first time in as long as I can remember I didn't dread it. I could hear the Black Dog howling in the distance on Saturday, but managed to keep it at arm's length.
  • I socialised on Friday night. It's been a while since that happened.
  • I got the resource I've been developing for teachers (and their students) to test as part of my PGCert in Digital Leadership finished and sent out on time!

Magic. What did you get up to?








* I won't mention the fact that I worked on Saturday...

Optimistic October: Day 11 - Reframing Problems

This is a great idea... 

Problem: Stop being such a chubster.


  • The solution: I need to eat less and move more. Gah.
  • A reframing of that problem: If I eat less bad stuff and more of the decent stuff I can save a bit of cash. If I walk when I can (and make use of that bike I've got on order that I bought with birthday money so it didn't even cost me anything) I can spend less on petrol and rail fares.

What's your problem, and how could you frame it? Answers on a postcard (or in the comments)!

Optimistic October: Day 10 - Look for the Good Intentions

It's not just Optimistic October; it's also World Mental Health day and my birthday. Traditionally, I've struggled with this day each year.
This year, however, has been the best in quite some time. Not because anything specific happened today in particular. Just that I've gradually got a bit better at dealing with the Black Dog when it comes sniffing around.

I'll pull out something from today, though. There's someone who I often clash with, but today they did something for me which involved going out of their way. It was only a little something, and only the tiniest detour, but it was done nevertheless, and it was done with a smile.

I really appreciated that.

World Mental Health Day: Traditionally My 2nd Least Favourite Day of the Year

Today is 10th October, and it's World Mental Health Day. Oddly, it has traditionally also been my 2nd least favourite day of the year for most of my life.


Optimistic October: Day 9 - Avoid the Blame Game

I successfully managed this one, but then there wasn't really anything to blame anyone for. However, as this is Optimistic October, I shall do my best to mention something I'm trying to do more consistently that definitely helps towards my own mental health improvement goals. Also, hopefully you won't detect any virtue-signalling. Excellent.
One thing that pops up on twitter now and then is the (generally quite good) advice that one should apologise less in emails. You know, the one that suggests instead of typing "sorry for the delay," you should replace it with something like "thanks for your patience". I'm getting better at that, and in genuinely removes a little bit of that self-flagellation which it is so easy to surreptitiously in all areas of our lives.

Well, the same idea works in the opposite direction. If someone takes a while getting back to you, then absolutely nothing is gained by getting grumpy over it. Suck it up. Provide some suggestions. Set some deadlines for actionable, well-defined targets. Be clear, concise, informative and decisive.

If something goes wrong, apportioning blame very rarely helps matters. If others are wasting time blamestorming, let them get on with it while you set about actually doing something instead. Stick up for yourself more than you tend to*, and stick up for others even more than that, especially if they're in a less influential position than you are.

So ends today's sermon.





* Even, nay, especially against your own inner monologue. If you're anything like me, they're the worst.

Optimistic October: Day 8 - Doing Something Constructive

Today's challenge is something I try to do whenever I see a tricky situation brewing, but I'm not sure if I can honestly talk about much I've done towards this today specifically.

I have a challenge to offer, though. A challenge for me, and also for you, that I think fits today's Optimistic October entry.

The challenge goes something like this:

News these days is generally very negative. Bad news sells; good news seems to do less well. This doesn't do any favours for our mental health, so can we make some steps towards making that better? I think we can. Here's a challenge that I'd like you all to take part in, and I'd like you to help me to keep. Call me out when I get it wrong; pat me on the back when I get it right. Here goes:

When sharing anything at all on social media (or anywhere else) you are choosing to propagate that story and all of the values and emotions that come along for the ride. Every time you share something, follow this:

  • Is it good news? Is it positive news? Is it happy? Is it true?
    • Yes! - Keep it up. Share with wild abandon.
    • No - Does it need to be shared? Really?
      • Yes! - Sandwich it between something good, positive and uplifting. Don't share until you've found something heartwarming, and then make sure you share something else with an uplifting centre to it soon afterwards.
      • No - Then don't share it.

Who's with me? If you are, maybe you can pass this on to others and set them the challenge too.

Just for clarity, this challenge starts now, and it ends... Never.

Optimistic October: Day 7 - Disavoidance

Today's Optimistic October challenge is sponsored by My First Day Off In Months and The Obligatory Encroaching Headcold. Nevertheless I powered through the aching neck and sinuses and did some stuff.

I've been coveting folding bikes for a while and, having received an unexpected sum of monies from an undisclosed benefactor (or, if you like, a birthday gift from my grandparents) I decided to head out and buy myself one. This may not seem much like a "project or task" but it intersects with at least three broader projects lose weight, get fitter, and spend less. I hope.

Anyway, I went to the shop I've spent months choosing to purchase the bike I've spent months researching only to find the cycle section practically bare and having a refit.

So I went home and did some washing up and vacuuming and changed the bedsheets instead, which are all tasks residing under the housework project, which is something I generally tend to avoid as much as possible.

I also responded to some work emails, which isn't the best thing for a day "off", I grant you, but that will hopefully contribute to the inbox 2000 project*.




What did you get up to?









* Inbox zero is a long way off.

Optimistic October: Day 6 - Being a Realistic Optimist

This is a refreshing one. So often we're told to look on the bright side, but there's often a reason for darker days and it pays to take note of the bad things sometimes so that we can change them rather than just coping with them. I'm going through some difficult things at the moment, but today's Optimistic October entry is about focusing on the good stuff. So here goes...
A family member has had some very, very bad news in the last couple of weeks...
... but we've still got time left to spend together, and things worth reminiscing about.

There are some things about work that frustrate the hell out of me...
... but I work in a unique role and every day drops something new in front of me. I learn new things all the time, and get brilliant feedback from people I work with externally on a regular basis.

I don't seem to have any time to myself...
... but that's because I am, in some senses of the word, 'successful'. I am in enormous demand at work, and outside of work is full of stuff to do, not least the PGCert course I'm working towards. My social life is... well, I have one, which is streets ahead of where I was a few years ago. I'm certainly not bored!

Some of my favourite people who are most important to me are the ones who are furthest away...
... but I know they're there, and I know they care.


Optimistic October: Day 5 - First Steps

I have plenty of goals that I'm working towards at the moment (you can see some in Day 1's Optimistic October post), but today's challenge is to take the first step towards what I'm interpreting as a new goal.
I've been meaning to read more. This is not something that I think I should do, but something I know I enjoy doing and life often gets in the way of it. My first step will be a pledge:
I will read a few pages every night before bed.
There. I've said it. Now I'm going to do it.

G'night.

Optimistic October: Day 4 - Positive Ch Ch Ch Changes

Here's a real challenge for me. There are plenty of things that drive me quietly bonkers about society, but this is Optimistic October so I need to turn that on its head...

  • I'm working hard to reduce my consumption of single-use plastics and favouring the purchase of things that come with less packaging to throw away, regardless of its composition.
  • Rather than quietly seething when I experience people being racist, sexist, transphobic or generally intolerant of people, things and ideas that aren't in the slightest intolerable, I'm calling it out. I'm doing my best to let people know that that sort of thing is not something that I'm willing to tolerate, and I'm doing it in a polite, calm and civil manner.
  • I'm doing the best I can to be an ally to everyone who identifies somewhere (or nowhere) on the big, complicated and broad spectrum of humanity. If you're a decent person, I'm your ally.
  • I'm seeking out sources of positive news.
  • I will tackle head-on nonsense and ridiculousness of any type that has at least the potential for a negative effect on people, persons or peoples (whilst championing the friendly, harmless nonsense and ridiculousness that I enjoy so much).

Optimistic October: Day 3 - Starting Importantly

Welcome to Day 3 of my OptimisticOctober19 challenge!

Working on the assumption that this means the list in Day 1's challenge, I started off with a pull-up (baby steps...) which contributes to motivations behind #3. I started my work day with some development time on the mathematics resource that I'm creating to be trialed over the next two weeks by some volunteer maths teachers. That contributes to #1!

How about you? What did you get up to?

Optimistic October: Day 2 - Reasons to be Cheerful Part 1 (of 1)

It's Day 2 of OptimisticOctober19, and today's challenge is to look out for positive news and reasons to be cheerful.
I decided to do this via the medium of twitter, so I posted a few things that I came across throughout the day, and a few other people joined in too!

If you've got some positive news or a reason to be cheerful today (or any day) I'd love to hear it. Explore mine and those of the others who have joined in here (just click the little blue bird...):

I finished off the day with a re-watch of a really good movie.

Optimistic October: Day 1 - Gooooooals

It's day 1 of Optimistic October, and the first challenge is:

My top four most important goals for this month are...

  1. Do a decent job of my next assignment, due in early next month.
  2. Habitually leave work on time at least once a week (baby steps...).
  3. Go to the gym at least once a week.
  4. Stay within my budget for the month.

What are your most important goals for this month?

Optimistic October!

I've been challenged to take part in Action for Happiness's Optimistic October (by friend and colleague Claire). I'll be posting responses to the below challenges every day throughout October 2019, and I'll be tagging them with OptimisticOctober19.


That's the full calendar. Feel free to join in at home (and point me towards your own responses, or just post them in the comments, or tweet them at me...) or just egg me on, and PLEASE send me reminders!

October is a particularly pertinent month for me to be doing this as it's a month I've always had problems with. I can be a grumpy guy at times, but October, traditionally for me, is a time of the year that optimism is usually even more difficult to muster. In fact, historically it's been my second-least-favourite month of the year!

Enough waffling. First (proper) response coming up...

Join me?

GEM Conference 2019: Top Ten Takeaways

For the past three days I've been in attendance at #GEM2019, this year's conference for people working (and generally interested) in learning through museums and heritage. You can see my tweets during the conference in the embedded collection below the main post, but inspired by Sarah Cowie's Top Ten Quickfire Takeaways, I thought coming up with a list of my own might be a good way to reflect on what was an intensive, tiring and thoroughly enjoyable three days! The theme was Connection, Action, Innovation: Forging dynamic and lasting partnerships with communities.

The conference took place in Torquay this year. A long way away, but lovely!
Photograph © T. Briggs

Digital Maths Resources: Invitation to Take Part in a Trial

A little while ago a few maths teachers* were kind enough to submit responses to a survey designed to discover what mathematics teachers in the UK want from digital resources offered by museums. This survey was used to influence part of the work towards my PostGraduate Certificate in Digital Leadership, and I went on to provide a brief analysis of the results in my Reflective ePortfolio, which also included discussion around some academic reading I've done on the subject.


The next step is to use the results of that survey to inform the creation of a digital resource and then test it with some students. As a full-time museum educator I don't have any captive students of my own so I would very much like to enlist the help of some of the many innovative and excitable maths teachers that abound in my Twitter network and beyond.

All I'm looking for is a few maths teachers who would like to try out a brand new digital resource with some of their students. Full details and terms are in the embedded registration form below, but some key information in short:
  • The resource isn't quite ready yet, but when it is I'll email a link out to any teachers who have registered below, in time for testing to take place during the fortnight between 7th and 25th October 2019.
  • It will require around 20 minutes or so for students to complete, followed by a quick survey, so they'll need about half an hour in total. This can take place whenever is convenient for you (and them) during that two-week period, but all trials must be complete before the end of the school day on 25th October.
  • Students will need access to an internet-connected computer, tablet or mobile phone to use the resource and respond to the survey.
Interested? Fill in the survey below, and I'll be in touch in the next few weeks. Please do pass this post along to anybody in your personal and professional networks who may also be interested in taking part.






*113 of them!

Musings on the Science Museum's Maths Gallery

I love the Science Museum and visit regularly. Mathematics: The Winton Gallery opened in December 2016 and I was lucky enough to visit very early on as part of the Christmaths event organised by the highly influential maths resources twit[1] Jo Morgan, and I've visited a small handful of times since, including yesterday.

Photo by T.Briggs 2019: The H.P. 39 "Gugnuc" biplane that forms the centerpiece of the exhibition, surrounded by wibbly representations of airflow patterns around the machine in flight



Reflective ePortfolio: What do Secondary School Mathematics Teachers want from Digital Museum Resources?

With seven years experience as a museum educator and roughly the same amount of time before that as a mathematics teacher, I have an almost unique perspective from which to analyse the intersection between these two disciplines and this has been the driving force behind my decision to concentrate on the role of museums in mathematics education. De Freitas and Bentley (2012) say of museum-based integrated curricula that “students are afforded experiences that radically disrupt traditional philosophies of mathematics,” whilst Harrell and Kotecki (2015) assert that “authentic, in-person experiences with objects is crucial to make meaningful connections for students.” They also recognise that “experiences can be hindered due to geographical, financial, and time constraints of our audiences.” At my own museum and those of colleagues in similar roles elsewhere it is often also the case that these same constraints apply not just to audiences but to museums themselves. One response is to reach out beyond the confines of the physical museum space, and this can be done either in person or digitally. This assignment will concentrate on the latter, investigating the question; What do Secondary School Mathematics Teachers want from digital museum resources?

An Enigma machine and a laptop
For the purposes of this assignment the phrase 'digital museum resource' refers to any digitally-served learning resource offered by a museum for use off-site and without direct involvement of museum staff. It is recognised that there are digital museum resources that fit the latter condition but require staff involvement (for example, webcasting and videoconferencing), but these are not included within the scope of this research. This definition is provided as, during the course of researching the theme it was evident that some of the teachers consulted parsed the phrase as 'resources supplied by digital museums' rather than 'digital resources supplied by traditional museums'.

There are not many digital resources offered by museums that focus specifically on mathematics. Some of the providers and resources considered whilst researching this assignment are linked in the embedded Padlet below. Most of the resources encountered were printable pdf files designed to be used as worksheets or planning materials.

Made with Padlet

Academic literature

Initial searches revealed that academic literature relating to this specific topic is similarly sparse, but there is plenty on component topics: the benefits of museum learning opportunities to schools (with reference to the development of websites and other digital provision) and the relevance of digital technologies in mathematics education are two that I have concentrated on. It is also important to note that while there is a wealth of writing on some of these intersecting themes, much of it is a few years old by now.

Museum learning and schools

Lin, Fernández and Gregor (2010) discuss website design with relation to informal learning in the museum context. They argue that enjoyment is a key aspect of online learning and identify characteristics of materials that may help to promote this: novelty; harmonization (i.e. coherence of design coupled with appropriate learning content); no time constraint; and proper facilitations and associations (including external links and extra information). They also put forward some guidelines which suggest that enjoyable online learning experiences are: multisensory; story-based; (positive) mood building; fun; and have opportunities to establish social interaction. As mentioned by Martin (2004), “museum learning may be said to straddle the ‘formal’ and ‘informal’,” so these characteristics and guidelines may well be used to inform the development of digital resources designed to complement more formal learning in schools. These ideas are also supported by a survey of teachers conducted for this assignment which will be discussed in more detail later. One issue which permeates all of this is the subjectiveness of terms such as ‘fun’.

Digital technologies and mathematics teaching

With regards to the use of digital technologies in the teaching of mathematics, Rowlett (2013) reminds us that “Educational technology may not produce a benefit simply by its introduction, but a benefit may derive from a change of approach driven by the use of the technology.” Further, The National Council of Teachers of Mathematics (NCTM) encourages “mathematics lessons that take advantage of technology-rich environments and the integration of digital tools in daily instruction” (Nelson, Christopher, & Mims (2009) and Pierce & Stacey (2010), cited in NCTM, 2015) and states as part of its official position that “when teachers use technology strategically, they can provide greater access to mathematics for all students.” (NCTM, 2015, emphasis added). This supports some of the general guidelines discussed in the previous paragraph (but in the specific context of mathematics education) and also provides reassurance that museum resources that take advantage of digital technologies may find a welcome home in mathematics classrooms.

Digital skills

Also of interest is the comparative states of digital technology adoption and skillsets evident in the Education and Heritage sectors, which will almost certainly have a bearing upon both what can be produced by museum educators and what will be useful to school teachers. The Curriculum for Wales Digital Competence Framework is a comprehensive website detailing the digital skills that should be embedded at every stage in the Welsh school system. Its strands and elements are summarised as follows:

Figure 1: Welsh Government (2018)
This gives an idea of the kind of digital skills that should be embedded across all subjects in school curricula, and hence would not only be appropriate if embedded in digital resources offered by museums, but actively beneficial and desirable. Contrasted with this, though, there is a recognised deficit in digital skills in the museums sector (Parry et al. 2018, p. 1), with “Education and learning roles – creating interactive learning resources, delivering online resources and producing copies of objects for learning activities;” cited as a particular example of digital aspects growing in museum roles (Parry et al. 2018, p 18).

Teacher survey

But what do teachers want? In preparation for this assignment UK secondary school mathematics teachers were invited via Twitter to take part in a Google Drive survey which asked questions about their needs, hopes and experiences to date with regards to digital resources from museums. 113 usable responses were submitted and analysis and commentary of some of the data is given below.

Opinion of existing resources

Teachers were asked to provide some keywords that describe their general opinion of digital resources offered by museums to date. These were gathered as free text and the resulting words (and phrases) were sorted into categories under a theme, represented by a single word or short phrase. A word cloud was then generated, with larger text generally signifying more common themes:

Figure 2: Survey respondents’ opinions of digital museum resources.
By far the most common themes were those represented by the words “unknown”, “unaware”, “none” and “non-existent”, indicating that the maths teachers who took part in the survey were largely unaware that mathematics resources are offered by any museums. Of the people whose responses implied that they had come across such resources before, opinions were largely negative with a key theme being “irrelevant”. A handful of positive responses coupled with the relatively common “hard to find” and “never looked” may point towards the issue being exacerbated by lack of marketing rather than entirely down to such resources not existing. Conversations with a number individual teachers revealed inconsistencies regarding what constitutes a digital resource, which may also have affected the results. For example, a PDF lesson plan was considered by some to fit that description, but not by others.

The same process was used to generate a word cloud for the survey respondents’ ideal digital museum resources of the future:

Figure 3: Survey respondents’ wishes for future digital museum resources.
This time the responses were far more positive, with “straightforward” and “accessible” clear winners, and there were a greater variety of themes with 91 different words represented in Figure 3, compared with 55 in Figure 2. Generally, each respondent had more to say here as well, with the total frequency of words for the aspirational set reaching 236, and 151 in the responses for current provision. This may indicate that despite the slightly negative view of digital resources so far, there is still an appetite for and openness to the idea of future developments in this area.

Technical requirements

From informal conversations with school teachers, as well as regularly visiting schools around the country, it appears that most now use some form of Virtual Learning Environment (VLE) or Learning Management System (LMS). These two forms of technology do have subtle differences but for the purposes of this assignment they will be treated as equivalent and may be used interchangeably. It is not immediately obvious how important integration with these systems may be for digital resources obtained outside schools, so some of the questions in the survey were designed to clarify this.

Figure 4: Pie chart - Does your school use a VLE or LMS?

Figure 5: Pie chart - Are any of your resources integrated via SCORM or LTI?

Figure 4 shows that roughly two thirds of respondents’ schools use a VLE or LMS, but figure 5 illustrates that almost 70% of those in this group do not know whether any of their resources are integrated via SCORM or LTI. These are two common standards for technologies that integrate digital resources into educational systems so that (for example) results of quizzes within a resource can be recorded against a learner’s account within the VLE. Most teachers spoken to informally were responsible for choosing and implementing the resources they use in the classroom, so the fact that so many do not know about SCORM and LTI integration implies that these are not widely used by classroom teachers.

Figure 6: Bar chart - How closely are the digital resources you currently use integrated with the VLE/LMS used at your school?

Figure 6 corroborates that, with most respondents stating that the digital resources that they currently use are entirely separate from their school’s VLE, and nobody stating that they are completely integrated. These results all suggest that VLE integration is not important (to teachers) for the time being.

In Figure 7 it can be seen that respondents were overwhelmingly geared towards resources that could be used on a laptop or desktop computer, with relatively few looking for something to use on mobile devices. This may indicate that a majority of the teachers are expecting something that can be presented to learners rather than interacted with directly by learners. The surprising number who chose “print onto paper” may be related to the observation earlier that most digital resources encountered in the initial research were printable pdfs.

Figure 7: Bar chart - How would you prefer to use digital resources?


Resource features

School teachers have a large amount of subject matter to cover in a relatively short amount of time so it seems clear that any resources produced by museums must contribute to this in some way. Figure 8 supports this idea, but suggests that links to taught curricula may not need to be completely explicit. Figure 9 may go some way to explaining this as cross-curricular links are ascribed some importance in these data.

Figure 8: Bar chart - How closely must a digital resource be linked to an aspect of the taught mathematics curriculum?


Figure 9: Bar chart - How important is it to you that a digital resource from a museum shows links with the curricula of other subjects?


In terms of the focus and scope of resources a large majority of respondents indicated a preference for lesson-based activities, although a little more than a quarter expressed an interest in resources intended for use at other times (Figure 10).

Figure 10: Pie chart - In which situations would you be most likely to consider using a digital museum resource?

It can be seen in Figure 11 that short activities lasting a few minutes would generally be preferred, but that there is also an appetite for resources suitable in a range of situations.

Figure 11: Stacked bar chart - Please rank the following digital resource types in order of preference.


Conclusions

From the research detailed above it appears that there is certainly a place for digital resources produced by museums in the mathematics classroom, but this research makes it clear that to be successful they must be planned and designed appropriately. Bringing together Lin, Fernández and Gregor (2010) with the findings from the teacher survey they must be novel yet accessible and straightforward; multisensory and story-based yet fit within a tight educational structure restricted by short timescales. They must also be curriculum-linked, but with some flexibility; the opportunity to explore cross-curricular links as well as introducing students to extracurricular “real world” and historical uses of mathematics is of great value and something which museums are uniquely placed to exploit. This harks back to Martin (2004)’s “straddle the ‘formal’ and ‘informal’.” Some of the survey responses indicate that a breadth of resources are what is called for, which may be difficult given budgetary and other constraints that museums are subject to.

The research findings also prompt further questions, such as:

  • The expectation from teachers appears to be for resources explicitly delivered by teachers rather than experienced independently by students. Is this what teachers genuinely want, or is it what museums have taught them to expect?
  • There is currently a lack of interest in VLE integrated resources, but is this something that will change as more schools adopt their use and more teachers gain experience?

This topic represents an interesting opportunity to explore a direction that isn’t the subject of much prior research. Further study is evidently required which, although fairly niche, has the potential to prompt positive change and development in two disciplines that are often thought of as being quite distinct.

References

De Freitas, E. and Bentley, S.J., 2012. Material encounters with mathematics: The case for museum based cross-curricular integration. International Journal of Educational Research, 55, pp.36-47.

Harrell, M.H. and Kotecki, E., 2015. The Flipped Museum: Leveraging Technology to Deepen Learning. Journal of Museum Education, 40(2), pp.119-130.

Jisc, 2018. Fourth Industrial Revolution inquiry. [pdf] Jisc. Available at: <http://repository.jisc.ac.uk/7152/1/fourth_industrial_revolution_inquiry_.pdf> [Accessed 15 August 2019].

Lin, A., Fernandez, W. & Gregor, S. (2010). Designing for enjoyment and informal YouTube as the art commons? 407 learning: a study in a museum context. Proceedings of the 14th International Pacific Asia Conference on Information Systems (PACIS 2010), 904-915.

Martin, L.M., 2004. An emerging research framework for studying informal learning and schools. Science Education, 88(S1), pp.S71-S82.

National Council of Teachers of Mathematics, 2015. Strategic Use of Technology in Teaching and Learning Mathematics A Position of the National Council of Teachers of Mathematics. [pdf] NCTM Available at <http://www.nctm.org/Standards-andPositions/Position-Statements/Strategic-Use-of-Technology-inTeaching-and-Learning-Mathematics/> [Accessed 16 August 2019].

Parry, R., Eikhof, D.R., Barnes, S.A. and Kispeter, E., 2018. Mapping the Museum Digital Skills Ecosystem-Phase One Report.

Rowlett, P.J., 2013. Developing a healthy scepticism about technology in mathematics teaching. Journal of Humanistic Mathematics, 3(1), pp.136-149.

Welsh Government, 2018. Digital Competence Framework Guide. [pdf] Welsh Government. Available at: <https://s3-eu-west-1.amazonaws.com/hwb-live-storage/6e/7f/33/19/c3494e069deaeab755d4c156/digital-competence-framework-guidance-2018.pdf> [Accessed 16 August 2019].

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