This is the full text of the 8th newsletter which I (Jo B) send to all London-based teachers on our Teaching London Computing subscription list. Teachers outside London usually get a shorter version with anything geographically irrelevant (ie things happening in London) removed, however during lockdown this is less clear. I also send an occasional version to our international subscribers. Details in the text below on how you can sign up if you’re reading this for the first time and would like to get the emailed version in future.

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Dear colleagues

Welcome to November 2020’s Newsletter 8 (previous newsletters live here), which is full of online events and courses (mostly free) and some additional resources on the Teaching London Computing website.

We are currently working on the next issue of CS4FN  magazine, which should be arriving in the Spring 2021,changes to working practices during coronavirus had made it impossible to publish an issue this year although all of our previous issues are free to download as PDFs.

As always please feel free to share this newsletter by forwarding it to colleagues in case they’d like to sign up too – new readers can sign up using the orange form on this page. You are receiving this email because you’ve previously signed up to the ‘TLC mailing list’ to hear about new courses and resources etc but if you no longer want to hear from us please let me know (j.brodie@qmul.ac.uk) and I’ll remove you.

TechPathways London – announcment
QMUL are very excited to announce that we are working with London Connected Learning Centre again on the TechPathways London programme. Funded by the Mayor of London we are supporting educators who teach young people from the age of 11 to 25 about computing. To find out more about the programme look here. We won an award the last time we worked on this programme… so it must be good. TechPathways London also has a newsletter, scroll to the end of their website and subscribe.

Best wishes Jo
Follow us on Twitter @cas_london_crc or @cs4fn.

 

COURSES
1. Teaching programming – for IT professionals who teach in schools or work
2. Other CPD courses for teachers
3. The Skills Toolkit
RESOURCES
4. Vignettes of how computing and tech are used in the real world (good and bad!)
EVENTS
5. Alan Turing Institute events
6. “Anyone can code? Power, inclusion and the coding fetish”
OTHER NEWS
7. New book – with chapters from Paul Curzon and Jane Waite
8. Home Learning – most resources don’t need a printer
9. Lockdown Lectures – Teaching London Computing’s YouTube channel
10. UK National Data Strategy consultation

1. Teaching programming – for IT professionals who teach in schools or work
FREE: This course is aimed at IT professionals, adapted from our teachers’ course. Please pass this on to friends and colleagues in industry. It’s suitable for IT people who are helping to run code clubs etc for schools, or for those who are just training new colleagues.

This is a long course, over four sessions on Wednesdays, 6-7.30pm from 25 Nov to 16 December.
[More info on our blog post][Eventbrite tickets][PDF flyer]

2. Other CPD courses for teachers
AQA – Computing CPD courses [GCSE] [A-level]
NCCE Computing courses
– see also How teachers train in Computing with our free online courses blogpost from Raspberry Pi (whose courses are part-supported by NCCE)
OCR – Computer Science and ICT courses
STEM – CPD in Computing (bursaries are available)

3. The Skills Toolkit – general IT / programming courses collated and linked from a Government portal
https://theskillstoolkit.campaign.gov.uk/
The Gov’t has created a new Skills Toolkit page to highlight free online digital courses including programming (but also a wide range including maths, business, finance, digital marketing, graphic design). Course providers include Microsoft and Google. All are free and most are self-paced. There are 19 courses on Computing (including cybersecurity, computer networks, artificial intelligence (AI) and cloud computing) and 10 on programming (including HTML, CSS, Python, C, C++).

4. Vignettes of how computing and tech are used in the real world (good and bad!)
We hope that these pages will help spark some interesting discussion and debate in classrooms.

Computing and Society highlights problems such as biases in algorithms and other technology, ethical concerns about data use and privacy problems that arise from not having considered how tech might be used.

In more cheering news a school hired a 10 year old Nigerian computer whiz to help them teach children to code, we’ve added that to our new page about Positive Stories in Computing.

5. Alan Turing Institute – free events
The Alan Turing Institute runs free public events (as well as conferences for a technical audience).

• Data Debates: Bots in the polling booth – Tue 10 Nov, 5.30-7.30pm
• Modern cryptography in the context of electric vehicles – Wed 11 Nov, 4-5pm
• Data Debates: Talking about my generation – Thu 10 Dec, 5.30-7pm

6. Anyone Can Code? Power, Inclusion, and the Coding Fetish – FREE EVENT
Dr Kate Miltner, Centre for Research in Digital Education, Edinburgh
1-2pm, Wednesday 11 November 2020 [tickets]
Drawing on a case study from an American coding school, this seminar will interrogate common coding-related claims.

“Over the course of the past decade, learning to code has been positioned as a silver-bullet solution to a variety of structural social concerns, including social mobility for the economically marginalized and the underrepresentation of women and BAME individuals within the tech industry. In response to this discourse, a growing industry of coding ‘academies’ has developed across the globe, insisting that “anyone can code” and get a well-paid tech job with a few months’ intensive instruction. Drawing on a case study from an American coding school, this seminar will interrogate common coding-related claims and illustrate how subtle gatekeeping mechanisms at play within these schools end up subverting the well-intentioned goals they set out to achieve.”

7. New book – with chapters from Paul Curzon and Jane Waite
Shuchi Grover’s new book ‘Computer Science in K-12: an A-Z handbook of teaching computing’ features contributions from Paul and Jane. Paul’s chapter, co-written with Shuchi, is called “Guided Exploration Through Unplugged Activities” and Jane’s chapter, co-written with Shuchi, is called “Worked Examples and Other Scaffolding Strategies” and you can find out more about the book and see/hear Paul and Jane give a tiny YouTube introduction to their chapters on our blog post.

8. Home Learning – most resources don’t need a printer
During lockdown earlier this year we went through our resources and picked out ones that can be done without a printer and adapted others so that they can be done on-screen. All our ‘Computing At Home’ resources are free, and divided into primary and secondary age groups https://teachinglondoncomputing.org/computingathome/

9. Lockdown Lectures – Teaching London Computing’s YouTube channel
We recorded Paul Curzon’s free Lockdown Lectures over the summer and will be adding the edited versions to our YouTube channel here – the first one “The Chocolate Turing Machine” is already there, along with previously added videos.

10. UK National Data Strategy consultation
Relevant documents: https://www.gov.uk/government/publications/uk-national-data-strategy
Closes 11:45pm 2 December 2020
Your class might be interested in the information and commentary about data and how it’s used, but also about how Government consultations work.

• Learn a Tudor Algorithm to do hard times tables
• See a simple (and useful) example of what algorithms are.
• Understand why algebra is really useful – for proving algorithms ALWAYS work

Algorithms are magic. Even simple algorithms can sometimes look like witchcraft. My favourite is one of the ways the Tudors did multiplication. It is all down to Welsh Tudor polymath Robert Recorde. As well as being a mathematician, who wrote the first arithmetic text book, he was also the physician to two Tudor Monarchs: Edward VI and Mary. Not only that, but along the way he also invented the equal sign using it for the first time as a shorthand for the phrase “ is equalle to” when doing maths (he would have liked the C programming language!). He was particularly good at algorithms and his book contained a cunning way to make the times tables easier.

Learning times tables is a rite of passage of primary school students. Those up to 5 are not too difficult but the 6, 7, 8 and 9 times table are particularly hard to remember (though of course the 9 times table does have a cunning pattern that makes it easier). Robert Recorde had a solution. In his book he gave an algorithm that made those larger times tables easy. If you know your tables up to the 5 times table (the easy ones), then the rest become simple too. It is just a matter of knowing the algorithm and doing some simple subtractions combined with the multiplications you do know. That the algorithm works is barely believable though, it is so odd.

The Algorithm

Here is how it goes. Suppose you have two of those nasty higher numbers to multiply like 8×7.

1. Draw 7 boxes labelled A, B, C, D, E, F and G. Write one of the numbers you want to multiply in box A and the other in box B.
   • eg if you want to calculate 8 x 7, put 8 in box A and 7 in box B.
2. Subtract the number in box A from 10 and put the answer in box C.
   • 10-8 = 2, so put 2 in box C.
3. Subtract the number in box B from 10 and put the answer in box D.
   • 10-7 = 3 , so put 3 in box D.
4. Multiply the two numbers in box C and D together. Put the answer in box E.
   • 2 x 3 = 6 so we write 6 in box E
   • Because your original two numbers in A and B were above 5, the new ones you must multiply instead are both below 5 so its a nice easy multiplication.
5. Now subtract the number in box C from Box B (ie the diagonal numbers) and multiply the answer by 10 (stick a 0 on the end) writing the answer in box F.
   • 7-2 = 5, so multiplying by 10 means you put 50 in box F.
6. Construct the final answer in box G by adding the number in box F to the number in box E.
   • E holds 50 and F holds 6 so 50+6 = 56 is the answer to the original multiplication of 8×7.

Try the algorithm yourself on some more examples, like 6×9, 7×6 and 8×9. It seems a bizarre way to do multiplication – were the Tudors slightly bonkers? Well possibly, but Robert Recorde was just very clever. At a stroke his clever algorithm gives a way to do all those hard multiplications using only a few much simpler calculations.

Does it always work?

This little computational ‘spell’ seems like witchcraft! Surely it doesn’t really always work? Actually it does. The point of an algorithm is that it always guarantees you get the right answer. We can prove this one does with a bit of algebra.  Of course, as long as you trust Recorde, you don’t have to understand the proof for the algorithm to work for you. It is good to do the proof though (or at least have a rigorous argument) to be sure the algorithm really is fool proof.

The Proof

STEP 1: Let’s call the number in box A, a, the number in box B, b and so on. So we are trying to work out the answer to:

ab (thats just another way to write: a x b)

Now (see the diagram below) instead of doing the multiplication directly we work out

STEP 2: c = 10-a and

STEP 3: d = 10-b

We multiply these together e = c x d so to get the number in box E, replacing c and d by the terms they are equal to, we do

STEP 4:  e = (10-a)(10-b).

We also subtract 10-a from b, and multiply it by 10 to get the number in box F, so

STEP 5: f = 10(b-(10-a))

The final answer is then just g = e + f. This means the calculation we ultimately do is

STEP 6: g = 10(b-(10-a)) + (10-a)(10-b)

We need to show this value g is the same as a x b.  It looks a bit unlikely but let’s simplify it all.

g = 10(b-(10-a)) + (10-a)(10-b)

Expanding the brackets for the part that came from f gives:

= 10(b -10 + a) + (10-a)(10-b)

= 10b -100 + 10a + (10-a)(10-b)

Similarly, multiplying out the brackets from e’s part gives:

= 10b -100 + 10a + 100 -10a -10b + ab

Now having expanded everything, we simplify: the terms +100 and -100 cancel out

= 10b + 10a -10a -10b + ab

The +10b and -10b cancel out too.

= 10a -10a + ab

The +10a and -10a also cancel out, leaving just a single term.

= ab

So what this says is that following the algorithm leaves the answer of calculating a x b in box G which is just what we wanted.

Algorithms

Algorithms are just sequences of steps to follow that guarantee a result (whether you understand why it works or not). Here the result is to multiply two numbers doing only simpler calculations. Of course, computers don’t know what they are doing. They can only follow rules blindly. While perhaps not using exactly this algorithm, they do use lots of clever algorithms to allow them to do arithmetic quickly.

This bit of witchcraft also shows why algebra is such a useful thing. It is a great way of proving useful algorithms really do always work.

The Tudors may still mistakenly have believed in witchcraft, and may not have had computers, but their computational witchcraft was still a really useful thing.

This one is for Peter,  the only person I imagine ever to get spontaneous applause from a class of teenagers for algebra… and a wonderful computational magician. 

He also loved hiding Easter Eggs in our work.