# Networking and CPD

A few events coming up in the near future with opportunities for CPD and networking. I will be attending:

National Mathematics Teacher Conference (#mathsconf6) – 5th March

Mathsmeet Glyn – 19th March

Maths in the Sticks – 24th April

(Hopefully) National Mathematics Teacher Conference (#mathsconf7) – 25th June

Please let me know if there is anything else I should be trying to get along to!

# #ChristMaths15

On the 21st December 2015 Jo Morgan hosted the first ever ChristMaths party event with CPD, networking and of course alcohol! This post contains some of my reflections after reading what I wrote down during the talks.

Strategies for teaching previously ‘Grade C and beyond’ topics to Foundation students – Mel Mundowney (@Just_Maths)

Mel delivered some interesting points in her talk, particularly addressing how many students are now playing ‘catch up’ with the curriculum changes due to different demands and teaching. One of the key things I noted were that there is a need to ‘keep things fresh’ as, more recently, there has been cyclic and repetitive content being taught in a disjointed curriculum. Another was that it’s ‘all about the questions!’ In particular how these differentiate tasks and how it can help develop pupils.

Flexible maths – The Michaela Community School Maths Team (@BodilUK, @danicquinn & @naveenfrizvi)

The Maths team from Michela school delivered a session discussing their approach so far (being a new school they have only year 7 and 8). They showcased their knowledge booklets which have been used to aid lesson teaching and have a strong focus on developing mathematical vocabulary and knowledge through ‘drilling’ the basics. It was interesting to hear their approaches and the booklets that were shared at the event will probably be a valuable resource!

Developing problem solving skills – Colleen Young (@ColleenYoung)

Colleen Young’s talk had a focus on developing the problem solving classroom. She suggests that the teacher-student relationship is a key aspect of this development. Additionally our use of vocabulary and students understanding of this could develop. When tackling ‘problem solving’ questions students should not fear just trying something; there should a resistance in the urge to rely on the teacher as ‘mathematical guru’. She provided lots of resource suggestions and her whole talk can be found on her blog!

A five year GCSE – Kris Boulton (@Kris_Boulton)

Kris talked about how we can better our own teaching, in particular discussing examples where he had not explained or taught topics well and had then adapted or radically them at the next time of teaching. He also identified that there is plenty of time to teach the new curriculum, but we need to focus on teaching well in the first instance and sequencing the content better. He concluded his talk by saying “Mathematics is mathematics!” This was a suggestion that we should be teaching students maths from (at least) year 7 through to the end of (at least) year 11 and we shouldn’t ‘start teaching GCSE in year 9 or year 10’.

Closing remarks – Jo Morgan (@mathsjem)

Jo was the concluding speaker raising some of her talking points and concerns about the new GCSE. One that stood out to me was the mention of Gove claiming the new GCSE would include fundamental mathematical content – but who decided what is fundamental (e.g. trig ratios in foundation)?

Evening networking

Having recently joined the Chalkdust magazine team Jo kindly allowed me to distribute copies around the room for people to take. It was really well received and I hope everyone from #ChristMaths15 enjoys reading issue 2 as much as I did!

The evening of the event saw maths teachers talking, completing Jo’s quiz and solving puzzles from Emma Bell (@El_Timbre).

An excellent ending to a very well organised and successful event! Well done Jo!

# Mathematics in Action

On Wednesday 25th November 2015 I took 13 sixth form students from my school to the Mathematics in Action event organised by The Training Partnership. It was an excellent day out and I summarised some of my notes from the day’s lectures in a post for my students which is replicated below.

Host (Tom Evans)

The host of the day was Tom Evans. He opened up the session with two puzzling questions which the audience were asked to attempt during the breaks between speakers. The problems are below:

Happy birthday Fermat’s last theorem (Simon Singh)

The opener was Simon Singh talking about Andrew Wiles and Fermat’s last theorem. He opened up the talk with the start of the BBC Horizon episode (see here) he directed on the same topic. In the video Andrew Wiles expresses an analogy for mathematics whereby it can, for a time, feel like you are walking around a dark house stumbling into things all the time. Then, one day, the light switches on and suddenly you see. Wiles becomes very emotional when talking about Fermat’s last theorem, which as Simon explained in his talk is due to the sheer length of time and determination spent solving a problem which had become a childhood dream.

Simon gave us the problem and spent a large part of his talk discussing the back story and some of the people who tried to provide a proof for Fermat’s last theorem across some 300 years. He recommended purchasing his book for further reading (which I did!). If you are wondering the theorem states the following:

No three positive integers $x, y$ and $z$ can satisfy the equation $x^n+y^n=z^n$ for any integer value of $n$ greater than two.

There were also recommendations at the end, for further enriching mathematics, to take a look at Numberphile, Vi Hart and Martin Gardner. Do take a look at all if you haven’t yet!

How big is infinity? (Chris Good)

Chris focused a large part of his talk on infinity around the work of Georg Cantor. He opened the talk by asking a classic question; ‘Which is bigger 1 or 0.99999999999…?’ He used this to clarify that every number between 0 and 1 can be represented as a unique non-terminating decimal (due to one-to-one correspondence) which was introduced by Cantor first in 1874. As a result of much of Cantor’s work there was an implication that there are an infinite number of infinities (i.e. I can always choose a bigger infinity than the one you just chose!). Chris concluded his talk by discussing transcendental numbers.

Exam technique (optional session with Colin Beveridge)

I really liked the Venn diagram Colin used at the beginning of his short talk about exam technique to describe the ‘ideal’ experience maths A level students should have (i.e. extended subject knowledge and support with exam technique). One of the things I really liked, and have already used, is the ‘error log’ idea. This is where pupils are asked to write down their mistakes, take note of where they went wrong or got stuck and then include the steps they need/needed to take to rectify the problem. Colin had some really valuable things to say so I am glad I stayed to listen to this (even if my students didn’t!).

7 things you need to know about prime numbers (Vicky Neale)

Fact 1: 1 is not a prime number.

Fact 2: 2 is a prime number (and the only even prime!).

Fact 3: (Theorem) There are infinitely many prime numbers.

This was proved by both Euclid (c.300BC) and Euler (18th century). This theorem of the week blog post gives some detail on both.

Fact 4: (Fundamental theorem of arithmetic) Every integer greater than 1 can be expressed as a product of primes in an essentially unique way.

Fact 5: Every prime is one more or one less than a multiple of six if $p>3$.

Therefore, could you prove the following statement (imagine delivering your explanation to a year 9 student)?

If $p$ is a prime number greater than 3, then $p$ is of the form $6n \pm 1$, where $n$ is a natural number.

Fact 6: Let $\pi(x)$ denote the number of primes less than or equal to $x$. For example, $\pi(10)=4$ or $\pi(100)=25$.

(Prime number theorem) Then $\pi(x) \sim \frac{x}{\log{x}}$ where here $\log{x}$ is the number theory notation for $\ln{x}$.

Fact 7: (Twin prime conjecture) There are infinitely many primes $p$ such that $p+2$ is also prime.

This conjecture is yet to be proved, but there have been many recent developments!

Exit question:

If 3 and 5 are twin primes then let us call 3, 5 and 7 a prime triple. Are there any more prime triples?

Geometry and the art of optimisation (Richard Elwes)

Richard opened his talk by discussing how much of his work on optimisation is applicable in everyday life (e.g. traffic lights and train timetabling). He discussed an example of a toy factory where we needed to consider how to maximise the profit from the production line. The calculations made led to the consideration of the feasible set of values which we then needed to consider maximising. Richard then introduced us to the simplex algorithm found by George Dantzig in 1947. He concluded with the Hirsch conjecture to which a counter example was found in 2010.

Cryptography (Keith Martin)

Keith was a very engaging and entertaining speaker, and whilst his talk didn’t contain much ‘maths’ he was able to discuss the importance of cryptography. Some elements of security are ‘lost’ in the cyber world and we need to ensure our information holds its confidentiality, integrity and authentication. Cryptography is a tool used and built by mathematicians to help with encryption and security in cyberspace. Keith discussed ciphers, our data integrity (using ISBN codes as an example) and authentication:

On the internet no one knows if you are a dog.

Keith recommended taking a look at cryptool.org if you are interested in looking further into cryptography. His alternative suggestions were Piper and Murphy’s Introduction to Cryptography book or Simon Singh’s The Code Book.

# My favourite function…

The content of this post originally appears on Chalkdust’s ‘What’s your favourite function? Part II’ post.

Rob Beckett’s favourite is a classic:

$e^x$

My favourite function is the exponential function $f(x)=e^x$. This is primarily because $\frac{d}{dx}(f(x))=e^x$, in other words the function is growing at a rate which is equal to its current size. This is a really interesting property which comes from the fact that $e=\lim\limits_{n\rightarrow \infty}{(1+\frac{1}{n})^n}$. Just like pi is the ratio between the circumference and diameter of circles, the number $e$ is the base rate of growth and it crops up whenever things grow or decay continuously and exponentially. Our exponential function appears when considering bacterial growth rates, populations, radioactive decay and even occurs in the Black-Scholes formula which is used in the financial market.

# Quick post: Plickers cards

This week I brought Plickers cards back into the classroom. Admittedly only for a test run with my two year 7 classes, though I am excited at the prospect of including these in my lesson planning again.

A quality (free) resource for completing multiple choice quizzes, the Plickers cards provide anonymity to the pupils answers which allows you to gauge whether pupils really have ‘got’ something if you are presenting them with hinge point questions. I used these a lot during the second placement on my PGCE as I learnt more about hinge point questioning in the FutureLearn course ‘Assessment for Learning in STEM teaching‘.

I am looking forward to using them more effectively, allowing the pupil responses to help me determine how I proceed with the remainder of the lesson.

# ‘Evaluating probability statements’ Standards Unit task (S2) with year 8

Having moved on to the topic of probability with my year 8 classes this term I was reminded of my final university tutor observation of a year 8 probability lesson last year, which happened to be one of my better lessons during my PGCE. I had decided to ‘be daring’ and conducted the ‘Evaluating probability statements’ Standards Unit task (link courtesy of @mrbartonmaths) with the class. The feedback was good and I was able to get really fruitful discussions from the class.

The structure I re-used with my two year 8 classes last week, with some tweaks, which resulted in both classes being more engaged with mathematics and ‘real’ mathematical discussion than before!

The task encouraged students to, in pairs, discuss the validity of a number of probability statements. They were asked to ensure that following their discussions they wrote down their thinking in order to refer to it in a later whole class discussion. Some students found some statements difficult to interpret and these were left until the end where pairs were able to join together into a small group to discuss the leftover statements.

After the discussions I wanted to have some class feedback. Using iDoceo’s random student picker I was able to select a student to chose a statement and explain their reasoning as to why they had decided that it was true or false. This then allowed the opportunity to open up a discussion with the class as in many cases there was conflicting opinions or reasons behind pupil answers. It really helped to meet the task’s criteria of clarifying the misconceptions in the statements, and for almost every statement I was able to take a ‘back seat’ listening to my students argue their points and eventually reach an agreed conclusion through their discussion.

The Standards Unit tasks are probably some of the best classroom activities I have come across. They are challenging, promote mathematical thinking and engage all learners in the task. In addition to this they all contain a preamble with a suggested approach to the task which has been helpful on many occasions. If you haven’t used them yet, you should consider it!

You can find all of the Standards Unit tasks on mrbartonmaths.com.

# First half term as an NQT completed…

… And hasn’t it been tough?! An ‘interesting’ start to the year resulted in a number of timetabling (and therefore class) changes, which meant having to go through the introductory stage with classes again after two weeks! I have enjoyed experimenting with a number of ideas and resources I have seen this half term, and the idea of this post is to document some of these, much like my previous post ‘First two weeks as an NQT’. I shall try to ensure that these ideas are ‘new’ and that I am not repeating things which are mentioned there!

First off I want to talk about marking. Whilst I have by no means found the ‘best’ approach to marking, this sticker shared by a member of my department has helped me to share feedback clearly with students. What I really like about it is not only the ‘RAG’ style effort rating bar, but that you can invite students or peers to assess work in their books using the sticker. I am still looking for effective marking methods, so please share your strategies with me!

We have used the diagnostic questions website (@MathsDQs) this half term with year 7 to assist with placing them into ‘appropriate’ sets after half term. These were an excellent resource and I would recommend use of the website across key stages. I imagine the GCSE collections would be invaluable to assist students and teachers in becoming (more) aware of what areas still need to be addressed, and where misconceptions are most often occuring. There is also a collection focusing on the new AQA specification which would also be of benefit.

Due to our mixed ability year 7 classes there were a few occasions when the work was not sufficiently challenging for some pupils. To tackle this I looked at the ‘My Classroom’ post from @solvemymaths which I mentioned in a previous post. I had recalled seeing a section called ‘extension activities’, and when reviewing the post I found the link to resources from mathschallenge. The questions are excellent and challenging, so I printed some of these out which solved the problem of not always having sufficient material to occupy students in the lessons!

With KS5 I have been making use of MEI’s integral maths on a regular basis as well as looking at Jo Morgan’s (@mathsjem) bank of resources on resoureaholic. I am awaiting word on login details for CMEP having seen a selection of these resources at an FMSP development session at UCL earlier in October. I have also started blogging for my KS5 students (see ‘Blogging for KS5’ post) after each lesson, providing them with access to the lesson resources and some additional follow up material. After half term I am beginning a KS5 enrichment club which is starting off as training for the senior maths challenge hosted by the FMSP before developing into a less specific enrichment club. I hope to continue improving where I go to find resources so as to provide my sixth formers with engaging lessons and encourage them to see the real beauty and excitement of mathematics.

Another thing I saw via Jo Morgan is the website Create A Test (@createatest). I consequently took a look and on finding it to be free, signed the school up. It is an outstanding resource for producing assessments and exam style questions with the ability to generate variations of one particular type of question. I really like the website and have already begun to encourage other members of my department to take a look and make use of this FREE resource.

Monday 19th October saw the second maths journal club discussion on Twitter (@mathjournalclub/#mathsjournalclub). This was a nice ‘break’ from teaching, diving back into the research and taking part in an interesting discussion. This focused on Colin Foster’s paper “Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts”. There were a number of great ideas in the paper which I hope to now implement in my future teaching. Check out the storify of the discussion put together by host Tom Bennsion (@DrBennison) here. Also, next discussion is on Monday 7th December!

I am still developing my bank of resources and ideas and the maths education Twittersphere has been one of the effective places for me to do this. Thank you to everyone who freely shares their teaching ideas and resources, so many of us appreciate your hard work!