At the beginning of the year, time to contemplate some resolutions perhaps – an annual update – all links checked and some new ones added:

Firstly, remember the ~~ten~~ eleven commandments!

Also available as a poster: **11-commandments-mathematics**

To elaborate a little more on some of these and provide some further links:

1 – reading and understanding the problem

See this document from The University of California, Berkeley for a succinct guide to Polya’s problem-solving strategy and for a more detailed guide with examples try **this excellent publication** from Arizona State University which is exceptionally clear.

2 – on Algebra, you will find many examples to help – see **Notes**. See also this post on **Transition Time** which includes some very helpful documents with lots of examples.

See for example this brilliant guide for students from OCR – **Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide**.

5 – looking it up – there are several excellent resources online for you to **look up definitions** or find **extra examples**. Never rely on just one source if you are finding a topic tricky, it can be helpful to see explanations written by different authors.

6 – **To learn Mathematics you need to ***do*** Mathematics**. You can never do enough examples! There are plenty of questions **here** (with answers included). Have you looked at the problems on **Brilliant**?

9 – on Arithmetic, many **tests for University Admissions** require competence with estimation and mental arithmetic. Put your calculator away sometimes – perhaps have a look at this **Open Learn (free) course on Rounding and Estimation.**

If you want to practise your arithmetic you could **play some games**!

10 – on writing the language of mathematics correctly – see this clear **guide to writing Mathematics** from Dr Kevin P Lee and from John Kerl some excellent **tips for mathematical handwriting****,** many of these tips these apply to students of all ages – do you distinguish carefully between a 1 and a 7 for example? Perhaps it is hard to tell whether you have written a 2 or a z or perhaps your 5s look a bit like a letter s?

Have a look at Peter Alfeld’s guide to **Understanding Mathematics** which he wrote for his students at Utah University.

Are you familiar with all the excellent (free) resources online to help your studies? Have you tried the brilliant **Desmos graphing calculator** for example, or used **WolframAlpha** to check your work?

Some more thoughts for you.

- Are you guilty of making any of the
**classic mistakes**? - How are your problem-solving skills? There is plenty of good advice available – see
**this publication**from Arizona State University for example - If you are studying at university then have a look at Kevin Houston’s ‘
**How not to get a good mathematics degree**‘ and ‘**How to get a good mathematics degree**‘. He also has provided a pdf file you can download:**10 Ways to Think Like a Mathematician**. Kevin Houston works at the University of Leeds in the UK.

If you are trying to get organised generally then some of the resources on **this page** might be useful. I recommend Evernote highly (it’s free).

Wishing you all a very happy and productive 2019!