Teaching London Computing Newsletter – October 2019

Welcome to our fifth Teaching London Computing newsletter (the previous newsletters live here) and you are welcome to forward this to colleagues – new readers can sign up using the orange form on this page.

1. Save the date [1]
Please mark Wednesday 11 December 2019 in your diaries as the date for QMUL’s annual free family-friendly Christmas Computer Science lecture, aimed at a secondary school-aged audience. This year Prof Andrea Cavallaro is talking about his ‘Vision’ work in computing. I don’t have any more information yet but I’m sure the lecture will soon appear on our public events page.

2. Save the date [2]
Please mark, Saturday 29th February 2020 in your diaries. We are running our CAS London conference again at Gladesmore. A huge day of CPD for computing educators – keep it free. Booking will open soon for early bird tickets.

3. Courses: TechPathways London
Our next TechPathways London course is free, and on 1 Nov 2019 from 9.30am to 4.30pm at Manorfield Primary School, E14. “Digital Art and Design for Secondary Schools” is aimed at both computing teachers and their art and design colleagues: “We are particularly keen to see teachers from both departments so that they can support each other in introducing digital art and design in their schools.” The course is aimed at secondary school teachers and Year 6 primary teachers but anyone educating young people aged 11-24 is welcome.

This course is being run by Queen Mary University of London as part of the TechPathways programme and is supported by the National Society for Education in Art and Design (NSEAD) and the Institute of Coding (IoC).

[Book your free place via Eventbrite] [Bookmark our courses page]

4. Courses: Other
The IDEA Store in Whitechapel runs beginners’ courses in Python (we’ve not seen the course content however).

There is a five week course starting on Wednesday 30 October called Programme in Python – Beginners [IML] – 6.30pm, two hours a week (£43, £12 conc).

We also recommend keeping an eye on Computing At School where a great deal of courses are advertised on their Events page, taking place in London and beyond. It’s free to register.

5. It’s nearly Hallowe’en! – free resources from Teaching London Computing
There are some slightly spooky goings on with these algorithms aka Tudor Computational Witchcraft, ideal for getting to grips with 6, 7 and 8 times tables, and for 9 times tables we have the Cunning 9x table algorithms. For younger children we have a colour-in pumpkin pixel-puzzle and a Hallowe’en kriss-kross – download our free Hallowe’en puzzles.

Martin Gardner (whose birthday it is today, 21 October) popularised mathematical games including the hexaflexagon. It’s a simple folded strip of paper which ends up with more than two sides. Hexahexaflexagons have even more sides and you can use them to illustrate computational thinking about graphs and maps, that links contains downloadable templates for coloured hexahexaflexagons as well as blank ones for your class to create their own designs with. Here’s Prof Paul Curzon explaining how to fold one. Why not make a Hallowe’en hexaflexagon where pictures of ghosts appear and disappear as you flex it.

6. Computing and Poetry
National poetry day was on 4th October and to celebrate we created a new page of computing activities with links to poetry. Write your own odes inspired by an Ancient Greek poem about a town of automata, use rhymes to teach loops, uncompress poems to learn about compression algorithms, write programs to shape programs or go the whole hog and write a program that writes love poems for you.

7. Prof Peter McOwan and the next issue of CS4FN
Prof Peter McOwan, who sadly died in July this year after an illness, co-founded CS4FN with Prof Paul Curzon in 2005. He and Paul shared an enthusiasm for communicating computer science in fun and engaging ways, particularly using unplugged methods and magic shows. We will miss him greatly and our next issue of CS4FN will celebrate him and his research interests.

8. Royal Institution Masterclasses in Computer Science at QMUL
For the last five years we have been delivering a series of Masterclasses in Computer Science with the Royal Institution (Ri). The QMUL / Ri Masterclasses are for young people aged 13-14 and involve a series of six weekly Saturday morning workshops on a variety of topics, with sessions run by different researchers in the Computer Science department here at QMUL. The Ri Masterclasses are a UK-wide program with several running in London (not just in Computer Science but also in Maths and Engineering). You can find out more about our own sessions here and about the program as a whole (and how to sign up your students for next year) at the Ri’s masterclass portal. They’re free! You can also see what people tweet out on the #RiMasterclasses hashtag on Twitter.

9. New computing hubs coming to London
Six new computing hubs are getting ready to start to support teachers in London. There are Langley Grammar,  Newstead Wood, Saffron Walden, Sandringham, Westcliff High School for Girls (@cs_essex, c.anderson@setsa.info) and Dartford Grammar. Each of them will be contacting schools in the boroughs that they have been allocated to support in the very near future. Dartford Grammar is holding a launch event on the 15th November [we will publicise the link / update this page when we have it].

10. Isaacs Computer Science for A level students
If you teach A level Computer Science then check out the new Isaacs Computing Science online learning Centre run by the NCCE for both students and teachers. Use it in the classroom, for homework and for revision. It is a great resource to support your students in doing well at A level.

11. Lesson plans for teaching primary and secondary computing
The NCCE has launched its new Teach Computing resource repository. It contains a series of units, each containing 6 lesson plans giving coherent programmes matching the national curriculum. The units range across many topics for primary and secondary computing. It gives you off the shelf lessons with the resources to deliver them. It aims to reduce your workload whilst also supporting you to increase your subject knowledge and have a greater understanding of effective pedagogy. More units are being added all the time.

12. Miscellaneous
Techy / hacking / music stuff in London(ish)” is a curated list of organisations (mostly in London) where people can go along to learn or create or watch what other makers have produced. There’s a fairly wide range including the Barbican and V&A as well as Maker / Hack / Music hackspaces, Dorkbot London, and the Restart Project which encourages people to fix their tech where possible, rather than simply replace it.

TUDOR COMPUTATIONAL WITCHCRAFT

  • 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.

TudorMultiplication.jpg

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

TuderMultiplicationAlgebraProof.jpg

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.