To a school in Bristol to share and learn with plenty of nerdy Maths teachers. Who knew – not all teachers are under 35! School 21 is a bit of a bubble…

We did speed-dating with people around us, to share ideas and make friends. Here is my favourite:

- Type a random 3 digit number into your calculator
- Divide it by 7. Hands up who got a whole number?
- Divide it by 11. Hands up who got a whole number?
- Divide it by 13. Hands up who got a whole number?
- Now, get you 3 digit number and type it in twice (for example becomes 456456). Divide this by 7, then 11, then 13. Hands up who got a whole number?! What number did you get?!

7 x 11 x 13 is 1,001. How could you extend this problem? 101 is prime, 10,001 factorises to 73 x 137, 100,001 factorises to 11 x 9091. Hmm.

**Talk 1: From Abacus to Zero**

By Ed Southall (who shares excellent problems on twitter)

We explored trivia about the etymology of mathematical language. Fun, and sometimes useful to hang meaning on, but not much maths. Here are some titbits:

- Calculus derives from a word for pebbles (maths used to be done by counting pebbles). You can have calculus on your teeth – a term used in dentistry to describe tiny pebbles of plaque.
- Which words connected to one?
- Atone
- Reunion
- Alone
- Only
- None
- Condone
- Onion
- All, apart from condone. Onion means “the big one”. Pearls used to be called onions.

- If only eleven and twelve were oneteen and twoteen are rules for naming numbers would be almost sane. We are lucky – in Danish the word for 54 translates as “two-and-a-half-of-twenty-and-four”
- Factor and factory have common root – they both build products (two puns in that sentence).
- Linear and lingerie have common root – they both derive from the word for thread.
- Average is an abbreviation of “averie damage”. When a boat gets broken, how do you work out how much each investor has to pay? You share the total equally between the number of investors, obviously.

Enjoyable, but unsure of how I will use this to motivate students who drag their feet when entering the maths classroom.

**Talk 2: Two A-Level Topics**

Geogebra links:

- Differentiation from First Principles
- Approximating the Derivative
- Newton-Raphson 1 (Cobwebbing)
- Newton-Raphson 2 (Convergence)

Two friends who did their PHDs together are now writing a textbook for A level, chock-full of proof and links to applications, both at university and in industry. We explored geogebra apps to visualise differentiation from first principles and Newton-Raphson Method for solving messy equations (most equations are horribly messy).

Why do we care about Newton-Raphson method? Because it is used in Formula 1 car design, in Google searches, in weather forecasting… This argument left me dissatisfied – either show me explicitly how it is used (although this is presumably horribly complicated) or I won’t believe you.

One thing that got me excited was thinking about when the Newton Raphson method would fail (for example if you get stuck in a loop) – for me that is more mathematically profound than tenuous links to the weather.

**Talk 3: Algebra Tiles!**

Mark McCourt, Chief Excec of La Salle Education, ran an excellent session on the use of algebra tiles, from early primary right up to A level. Key thesis: we jump straight to abstract representations of mathematical concepts far too quickly in a topic, at far too young an age.

Claim: they are all the same question.

Bus-stop notation tells you exactly what you are doing. Given the area of a rectangle and its height, what is its length?

Bus-stop division is exactly as hard as dividing algebraic polynomials – you just shift from base 10 to base x. If you understand this deeply enough using algebra tiles then all will be well.

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