Digital Mathematics Resources from Museums

If you've been here before you may remember that I recently began to work towards a Postgraduate Certificate in Digital Leadership*. For my first assessment I need to produce a reflective e-portfolio on a digital literacy theme, and I have decided upon a research question for that.

Whilst researching various themes around digital literacy and education, I discovered that there is very little literature that concentrates on a particularly relevant subset of that genre - digital provision in museum education - and even less focusing on the nexus of my two career themes to date: museums and mathematics.

The question I have settled on, therefore, is:

"What do secondary mathematics teachers want from digital museum resources?"

More specifically, I'm looking at digital resources served remotely rather than on the museum site, and the following questions in the hope that I will discover the features that will make digital museum resources truly useful to mathematics teachers:

• Do they want LMS integration?
• Do they want individual activities or full lessons?
• Do they want resources to be explicitly curriculum linked, generally subject-relevant, or cross-curricular?

With related considerations:

• What do they think about museums as a source for digital resources at the moment?
• Are there any really good resources out there already that we (as museum educators) can learn from?

I have some insight into these questions from my own experience as a secondary mathematics teacher, but it's been a while since I was explicitly employed as one and am well aware that the sector changes, as does technology.

With this in mind, I would be incredibly grateful to any secondary mathematics teachers who were kind enough to:

1. Submit a response to the following survey.
2. Share with any other maths teachers (or people who might know any maths teachers) in their network.

It shouldn't take more than 5 - 10 minutes of your time, and after analysing the results I will be posting outcomes on this blog. More general comments and discussion on the theme are more than welcome, and probably best conducted over on twitter. I'm @TeaKayB: if we're not already connected do say hi!

Here's the survey (and thanks again for taking part):

* See my other posts related to this course here.

Digital Literacy: What Does it Mean?

An early task in the Digital Leadership course that I'm following was to think about a "definition of what digital literacy means to [me]". You might want to skip to the bottom if you're looking for a quick answer.

What do other people think?

First stop: Twitter, naturally, to see what some of my followers thought. Click on the tweet I posted (below) to see what the raw responses were, and I'll summarise underneath it. Any more responses (either in reply to this tweet or using the included hashtag) would be very welcome.

What does "digital literacy" mean to you?#digitalliteracymeans pic.twitter.com/VRpL0xMpgB

— Tommaths (@TeaKayB) June 15, 2019

Some common themes from these responses (and from chatting to people about it elsewhere):

• Digital literacy isn't necessarily about knowing how to do things with technology, but knowing how to find out how to do things when you want to (paraphrased from @CantabKitty).
• Part of this is being able to navigate technology (whether an app, website, or device) by recognising common features such as icons and menu structures (paraphrased from @RJS2212).
• On a similar theme to these is @neilnjae's suggestion that digital literacy is the ability to use computer-based tools to do the things you're actually interested in.
• @Loumeracy summed things up nicely with the idea that it's all about "understanding the digital environment and how to navigate it competently and effectively."
• A number of responses were along the lines of "not believing everything you read online," which I hadn't considered before asking this question of others.

How about the literature?

There's a wealth of writing and research out there, and we were given some links to browse as part of this task. Some of these include:

The Welsh Digital Competence Framework

Find it here: https://hwb.gov.wales/curriculum-for-wales-2008/digital-competence-framework/framework/

This is a full framework covering all stages of school education in Wales (which is practically the same as for the rest of the UK) and has been structured to be familiar to anyone who has seen the National Literacy and Numeracy Framework. It's massive, and the whole thing can be viewed in parts online or downloaded as a spreadsheet from the link above, but in summary it splits key skills into four strands with elements summarised as follows (table reproduced from https://s3-eu-west-1.amazonaws.com/hwb-live-storage/6e/7f/33/19/c3494e069deaeab755d4c156/digital-competence-framework-guidance-2018.pdf):

Citizenship	Interacting & collaborating	Producing	Data & Computational Thinking
- Identity - Wellbeing - Digital rights - Online behaviour	- Communication - Collaboration - Storing - Sharing	- Planning & sourcing - Creating - Evaluating & improving	- Problem solving - Modelling - Data and information literacy

In case you're interested, there's a draft available for an updated framework due to begin implementation in 2022. It's here: https://hwb.gov.wales/draft-curriculum-for-wales-2022/digital-competence-framework-draft-curriculum-for-wales-2022-version/

The European Digital Competence Framework

Find it here: https://ec.europa.eu/jrc/en/digcomp/digital-competence-framework

A similar idea to the Welsh framework, I've summarised the information at the link above into the table below ordering the columns to facilitate comparison between the two:

Safety	Communication & Collaboration	Digital Content Creation	Information and Data Literacy	Problem Solving
- Protecting devices, content personal data & privacy - Physical & psychological health - Social well-being & inclusion - Environmental impact of digital technologies	- Interaction - Communication - Collaboration - Awareness of cultural & generational diversity - Citizenship - Identity & reputation	- Creating & editing - Improving & integrating content into an existing body of knowledge - Understanding copyright & licensing - Giving understandable instructions for a computer system	- Articulate information needs - Sourcing information, data & content - Storing, managing & organising	- Identify needs & problems - Resolve conceptual problems - Use digital tools to innovate - Keep up to date with the digital evolution

The main difference is that the European framework splits its elements into five categories, with the final two columns in this table being the final column from the table summarising the Welsh framework split into two. The other headings match up quite well, with a few elements appearing under different columns. An important difference is that "use digital tools to innovate" and "keep up to date with the digital evolution" from this framework don't appear to have an analogue in the Welsh one. They may well be covered in the detail of the Welsh framework, but I think they're important enough that they should be a "top level" skill.

Jisc Fourth Industrial Revolution Response

Find it here: https://www.jisc.ac.uk/news/digital-skills-crucial-to-the-success-of-fourth-industrial-revolution-28-jun-2018

Jisc, formally JISC (which stood for the Joint Information Systems Committee) is a not-for-profit organisation providing digital services and solutions to the UK Higher and Further education sectors. They do a lot of research and development work into educational technologies, and have a number of interesting things to say about what they're calling "Education 4.0", the educational aspect of "Industry 4.0", or the Fourth Industrial Revolution.

Industry 1.0	Industry 2.0	Industry 3.0	Industry 4.0
Much greater mechanisation; steam and water power	Mass production on assembly lines; widespread use of electricity	Modern computers and automation	Robotiocs & biotechnology; ubiquitous use of digital networks; artificial intelligence; the Internet of Things & "smart" technologies; 3D printing

This document starts off by quoting the UK Government: "within two decades, 90% of jobs will require some digital proficiency, yet 23% of adults lack basic digital skills." Jisc believes that digital skills are "non-negotiable" for future generations of students to be successful. They argue that strategies must be put in place alongside staff (and leaders) with appropriate skills. A digital capabilities framework is proposed, with lifelong learning an important part of updating the skills of the current workforce.

They contributed to the development of the Welsh Digital Competence Framework discussed earlier and seem to be advocating that the UK Government develops something similar. As it stands, the UK Government's Essential Digital Skills Framework is much less comprehensive.

There's not much here about what Jisc means by "digital literacy" but they do list a few benefits to increasing it generally. Jisc.ac.uk has a wealth of information

What does "digital literacy" mean to me?

The idea of "digital literacy" clearly spans a vast array of skills, but which are the most important? If I had to list just a handful of prerequisite skills to master before being confident that one is digitally literate, I'd probably pick:

• Ability to recognise problems which may be solved using digital technologies;
• Ability to seek out digital tools which may help to solve these problems;
• Ability to develop personal skills in using these tools, through a mixture of experimentation, research and the experience of others;
• An awareness of the potential risks associated with using digital tools, and steps to take to reduce them.

Whilst clearly of paramount importance, the "not believing everything you read on the internet" skill is not, to me, a specific requirement of digital literacy, but part of a broader and crucial life skill. In many situations this would be covered in specifically "digital" situations by my final bullet point.

What do you think? Comment/ tweet away!

I'm Learning About Digital Technologies and Could Really Do With Your Help

My last foray into the world of academia was way back in the heady days of '06 - '07 when I completed my PGCE in Mathematics (with A-Level Accreditation, dontcha know). This was at the tail end of those dark times when PGCEs didn't come with any Masters credits. I've always been interested in continuing my own education. For the past decade or so, it's been self-directed studying, reading the odd paper and half-completing Futurelearn courses. I've also built up a network of astonishingly accomplished friends and acquaintances in the worlds of mathematics, education, museums and heritage, and all conceivable intersections of them, and I'm never quite sure how they keep up the pretence of being pleased to bump into me at conferences.

Back in the Ring

Now, though, I have started on an actual accredited course! Last week I attended my first online session for the distance learning Postgraduate Certificate in Digital Leadership with the University of Northampton (kindly funded by my employer). It was mostly an orientation session, with introductions to the course leader (the fantastic Helen Caldwell) and the other coursemembers.

The course, in short, "will give you professional recognition and equip you with the subject knowledge, teaching skills and critical understanding you need to lead positive change as a digital leader in your setting" and includes two modules: Developing Digital Literacy, which will involve research into digital technologies and practices with a view to bringing my own understanding of the sector up to scratch; and Developing Digital Leadership, which will empower me to take what I've learnt so far and pass skills, knowledge and understanding on to peers and colleagues.

I'm going to be blogging as I go along and I'd really appreciate not only support and encouragement but also the benefit of your experience.

My first task is to come up with a key research question, so I'm going to be thinking about how digital literacy could impact upon my own job role and those of others, both within my organisation and related roles outside it. That'll probably be the subject of my next post on this subject.

Help!

For now, though, I'd really like your help! Either in the comments below, via twitter, or any other method of communication you may have for me, I'd very much appreciate some answers to the following questions. If you could provide some idea of your own job role or other reason for being interested in the topic that'd be really useful too:

• Everyone:
• What does "digital literacy" mean to you? (Please respond to this tweet!)
• Is there anyone I should be following (blogs, podcasts, twitter, etc) who's really doing this stuff right (or provoking thought)?
• Teachers (thinking about museums, but thoughts from other angles welcome):
• What do you want/need from digital resources? What gets in the way? What's the dream?
• Do you already use digital resources from museums? Which ones/ where/ what?
• Please post links to anything that's getting it right!
• Museum educators:
• What digital resources do you provide?
• What are your main barriers to producing them?
• What digital resources do you want?

What are the Chances: Lucky Tourist Cracks Safe Code

I've been trying to figure out the forgotten combination
for this lock for months. Maybe Mr Mills can help?

A friend sent me a link to this article on the BBC's website about a lucky tourist who opened a combination-locked safe for the first time since the 1970s.

The article briefly goes into the chances of guessing the combination correctly with one attempt, but doesn't really say how they were worked out. I thought I'd post with my thoughts on that as it may make a nice puzzle.

Just the Facts

The safe has a dial with the numbers from 0 - 60. Turn it three times clockwise to get to the first number; twice anticlockwise to get to the second; and once more clockwise to choose the third.

My initial thought was that the second number couldn't be the same as the first because the dial has to turn (ditto for the third number compared to the second), but then it goes all the way round anyway so I don't think it matters.

What are the chances?

If we assume that the numbers were chosen randomly in the first place, then there are 61 possibilities for each one (the numbers 1 - 60 inclusive, and also zero), and they're all equally likely to be chosen.

The First Number

There are 61 options for the first number. That's easy.

The Second Number

There are 61 options for the second number. Easy! However, looking at the first two numbers together, there are 61 options for the first, and then 61 options for the second for each of the possible choices for the first number. That makes 61 * 61 = 3,721 possible options.

The Third Number

There are 61 options for the third number, but extending the reasoning in the previous paragraph, we have 61 * 61 * 61 = 226,981.

Altogether now!

So, 226,981 different possible combinations. My tiny mind can't really comprehend that, however, so I like to come up with a spurious context to help it along a bit:

If you employed someone to systematically work through all of these possibilities, assuming they were pretty quick and could try one per second it would take them just over 63 hours. That's about two weeks of working full-time hours*.

But wait!

Award-winning statistician Professor Jeff Rosenthal (mentioned in the BBC article) says that these sort of locks have a certain amount of "wiggle room". Using the suggestion in the article that there might actually be a "three digit leeway" (I'm taking that to mean that the "correct" number and the one either side of it will work), that means there's not just one combination that will work to open the safe.

How many are there, then?

Using similar reasoning as I did earlier in this post, there are 3 "correct" positions for the dial for each of the three numbers in the code, so there are 3 * 3 * 3 = 27 solutions that will unlock the safe. That means that 27 out of the 226,981 possible combinations will work, or about 1 in every 8,406 ish. Or 1 in 8,000 even-more-ish, as quoted in the article.

But wait a bit more!

The winning combination was actually 20-40-60. It's entirely possible that was chosen randomly, but think about your own "random" passwords, padlock combinations and the like. How many of them are really random? Humans are rubbish at random, so often use patterns and personal information to set passcodes that they can remember easily.

I alluded to a similar situation in a recent puzzle I set for the Today Programme on the theme of Enigma machines and their settings. Essentially, Bletchley Park's Codebreakers were trying to "guess" the settings that their enemies were using to set up their cipher machines. The underlying maths behind figuring out the scale of the problem is exactly what we've used here, and the considerations in the previous paragraph are equally applicable to the World War 2 cryptanalytic operation.

* Or about 4 days if you're a teacher.

Film Review: Mile 22

Friday night's cinema trip saw Mark Wahlberg monologuing his little socks off through this espionage-action-thriller. Catch up on the trailer below:

After some character introduction, scene-setting and plot exposition the movie eventually gets to the crux: an asset needs transporting twenty two miles (ah, right) to an extraction point. This (probably not a spoiler) doesn't go entirely to plan. John Malkovich tells them they need to get there quickly; no delays. There are plenty of delays and they, naturally, get there just in time.

It's a pretty violent film with guns, explosions, blood, death and some pretty impressive martial arts scenes courtsey of Iko Uwais (fans of The Raid movies will recognise this name). There's a decent core story delivered by some famous names (Lauren Cohen will be a lot more famous in my head once I've finally got around to watching The Walking Dead), and on the whole I enjoyed the experience.

That said, there's a lot of padding for such a short movie (94 minutes). There's a sort of narrative device which sees Wahlberg popping up every so often part-way through an interview which is evidently a post-balls-up inquiry. This goes nowhere. His character's super-intelligence and the fact that he's somewhere on the autistic spectrum is regularly mentioned, though this has no bearing on the plot other than to be occasionally used by the other characters to explain away him being an arsehole at points. There's a nuclear weapons/ terrorism backdrop which also doesn't really come to anything and appears to be a bit of a red herring to draw viewers away from the plot twist, which really isn't groundbreaking enough to require being drawn away from.

Also, it's pretty derivative. There's a street shootout that isn't quite Heat. Uwais runs around an apartment block decking people with cool moves, but it isn't The Raid. There's even a little Ronin in there somewhere.

Ignore all that, though, and it's not a terrible way to spend 94 minutes if you're into action movies and like a bit of Wahlberg. It's forgettable, a bit confusing at points, and probably has some enormous plot holes if you think too deeply about it, but if a bit of Friday night violence is your thing, it's better than heading into town and baiting the big guy at the bar, and you get a thick smear of psuedo-plot thrown into the bargain.