Having returned from the 350 mile round trip from Bristol to the wonderful Manchester Enterprise Academy Central, I thought I’d note down and share some of my thoughts and findings from the most recent MathsConf15.

I’d like to start by saying how grateful I am for the The Complete Mathematics Conferences, organised by LaSalle Education, that have garnered such critical acclaim over the last few years. It is so inspiring to see so many maths teachers using their free time so eager to learn, share ideas and network on a Saturday morning. Such is the pull of the events, teachers travel from all over the United Kingdom to attend and no doubt take much of what they have learnt to affect the lives of the pupils whom they teach.

**Jo Morgan @MathsJem– Indices in depth**

- Pupils will see indices for the first time in Year 5 (Using squared and cube numbers only).
- Descartes (1637) popularised index notation and exploring some of the mathematical history has helped some of her pupils previously to understand the rationale behind the notation.
- Clarity of explanation can be important when first introducing the multiplication law: “The base is the same, we are multiplying them, we can add the indices.” This leads into talking through non-examples too “The bases are not the same…, The bases are the same but we are not multiplying them…”
- With the division law, pupils should see problems using the obelus (÷) and a vinculum (-). For example, pupils should see problems as written division and in fraction form to help pupils understand the similarities in both.
- The Victorians had a great phrase… “When the index is unity, it is omitted.” I love the clarity and conciseness of this explanation.
- Finally, the zero index can be shown in many ways, including showing the pattern of reducing the powers of 10 each time. 10^4, = 10,000, 10^3 = 1,000, 10^2 = 100, 10^1 = 10. By showing that each time you are dividing by 10, one can see that 10^0 = 1. This method of showing a pattern can also be used to introduce negative powers too.
- Alternatively, one could write 2^3 / 2^3 as a fraction and write them in expanded form as 2 x 2 x 2 / 2 x 2 x 2 and show that this was result in 8/8 or 1.

**Philipp Legner @MathigonProject – Mathematical storytelling**

- Maths can be explored and made more interesting through the power of stories.
- If there is an opportunity to use stories in maths, they should be used.
- Trigonomtery is often illustrated in maths textbooks for problems that would never use trigonometry in real life. Instead, Philipp spoke about how trigonometry was actually used in the Great Trigonometric Survey of India to work out the height of Mount Everest.
- Numerous examples of real-life mathematics were used, including the replication of the Cicada population in a prime number of years to avoid predation, the unrealistic human bias in recording random data from experiments of roulette wheels in Monaco, to the calculus involved in rollercoaster production, to the orange properties being the most likely to be landed on in Monopoly.
- Stories, if known, can aid mathematical insight and inspire pupils to go on and study maths a higher level.

**Richard Tock @TickTockMaths – Making Statistics (even more) interesting**

- “Statistics without context is just number work.”
- Regardless of the debate between statistics and maths, Richard argued that we should incorporate real-life examples and contexts as much as possible when discussing statistics.
- Finding correlations in datasets is far more interesting and memorable when discussing real life examples, such as income per capita and life expectancy. Pupils are likely to have more awareness of why the statistics is relevant too.
- Gapminder (https://www.gapminder.org) is a tremendous resource for using statistics in the classroom. It’s free and can be downloaded to work online and offline. It has good functionality and can be used to show various different statistical techniques.
- The idea of confidence intervals can be used for real life examples, such as Donald Trump winning the elections. It was rarely predicted but it was within a confidence interval.

**Dan Rogan @AQAMaths – AQA Large Data Sets – Food for Thought**

- An interesting session looking at the use of the Large Data Sets in the new A-Level
- Although marks are given for “material advantage” within the exam, this doesn’t involve a wide background knowledge of the topics in question. It is simply an understanding of the maths.
- There are far too many variables and permutations for pupils to know correlations and relationships between different variables and time periods so this is not required. Pupils should understand the maths behind the data set (rounding errors, differing measurements etc) but an actual in depth knowledge of why a particular picee of data peaked one year is not required.

**Close**

Once again, I’d just like to thank Mark McCourt and the team at LaSalle Education for hosting these wonderful events. It really is such a great day to learn, share ideas and meet new people which can enhance mathematics education in this country and beyond. They have become a staple calendar item for me over the past few years and I have really taken some of the ideas from these events to help continually share my practice. I have already booked my ticket and flight for the next one in Glasgow. Roll on #MathsConf16 on the 8^{th} September!