What you’re looking at is the GCSE Mathematics curriculum. Each node represents a topic, e.g. transformations, ordering decimal numbers, frequency polygons etc. There are 164 nodes in the diagram representing all topics on both the foundation and higher tier curriculum. The nodes are connected by 935 links. Each link represents a connection between two topics whereby one is the prior learning required to be able to access the other. For example, equivalent fractions is linked to adding fractions because you need to be able to do the former before you can learn how to do the later. Continue reading →
Numberphile.com is a website devoted to enrichment maths videos. The quirky, fast-paced style of the presenters is engaging and fun. Whether finding maths deliberately hidden in episodes of The Simpsons or finding the flaw in the Enigma code, Numberphile videos never fail to inspire.
A fascinating TED talk by Jean-Baptiste Michel opening our eyes to a future where maths helps us unravel the mysteries of the past. So history teachers…. look like you’ll need to be learning some stats!
Lyapunov exponents of the Mandelbrot set (Steel Beach) (Photo credit: Arenamontanus)
I got an email from a reader, Andrew Chambers drawing my attention to a website he has built for IB students studying in Thailand. The content they study is generally equivalent to A-level. His site IB Maths, ToK, IGCSE and IB Resources features lots of resources to enrich maths learning of gifted and talented pupils at KS3 and GCSE. In his own words, here are the highlights:
http://ibmathsresources.com/ibtokmaths/ (links for everything from using ESP tests to look at probability models, to using a mobuis strip to help understand extra dimensions to chaos theory or fractals…..
http://ibmathsresources.com/ – has a number of blog posts on everything that I think of that could be useful to teaching – from correlations on the latest premier league wages to league position analysis, to maths podcasts to sequence puzzles….
The Magic of Pineapples, my latest book has just gone live in paperback format on Amazon. I wrote the book to inspire kids and ‘curious-minded’ adults into appreciating the beauty of maths. It has just been reviewed by TES Maths Advisor, Craig Barton who says:
“It is impossible to claim maths is boring after reading this wonderful book. I will also never look at a pineapple in the same way again! A must read for the curious minds of students and adults alike.”
The book is available in paperback via Amazon at these links:
Since the introduction of the ‘functional’ questions on the maths GCSE last year it has become important for pupils to improve the skill of taking a ‘wordy’ question and interpret what it is requiring them to do. Many pupils find this difficult and seem to give up before they have even read the question. Through a couple of strategies obtained from an excellent INSET I attended recently, I have had some success in getting pupils to improve their interpretation of functional questions. Surprisingly, these strategies were presented by our Head of English under the umbrella of a training session based on literacy, but I have found them to work well in the functional maths part of our subject.
Two colour highlighting
After reading the question once, get pupils to read it again twice more. On the second time they should highlight all the numbers in the question (both those in digits and in words). The third time they read it they should highlight in a different colour all the ‘key maths vocabulary’ words that are important to the context of the question. For example words like: more, each, difference, total, profit etc. Through reading three times, each with a different focus it seems many pupils improve their interpretation and understanding of the questions. It is a strategy for breaking down the process of interpreting a question into a series of smaller tasks.
Highlighting numbers in one colour and key maths vocabulary in another
Cartoon story boards
Another strategy that seems to work well with some pupils is to get them to create a ‘cartoon picture’ for each sentence of the question. For example, if the question begins ‘Sue buys 24 books for £2 each’ pupils could draw a picture of a book with a £2 sign on it and a ‘X 24′ beside it. They work through the question creating a cartoon picture for each sentence. They then look at the whole cartoon story board they have drawn and it is a pictorial representation of the problem. I have found that many pupils understand the question better looking at their story board, than looking at the text. I think this may be due to them creating a mental picture of the problem in their imagination, something that is essential for solving functional problems. Here is an example of a story board one of my pupils drew today for the above question and then their solution:
Cartoon story board for the ‘Sue buys 24 books for £2 each’ question
Cartoon story board of the above problem and then the student’s solution
Another cartoon story board and solution to a similar problem by a different pupil
Do you have any other strategies that you use when teaching pupils how to tackle functional questions? If so share them with us in the comments section!
How are children’s puzzles and patterns based on infinity related? What are the similarities in the maths behind the shape of tropical storms and how pineapples grow? Why is much of internet security built on one of the great unsolved problems in mathematics?
A year ago I decided to write a book that answers these questions. The Magic of Pineapples was born. A year later, it’s ready! The aim of the book is to inspire maths-curious teenagers and adults into a life-long love of the subject. I want the readers to realise that maths is not just a set of routine steps that you blindly learn to enable you to live in our society, but a portal into a whole new way of seeing and understanding the world around you. I want them to see the beauty of the subject.
The content of The Magic of Pineapples is accessible to anyone proficient in secondary school maths. I teach 11-16 year olds and I wanted to write a book they could understand. Readers are not just spoon-fed facts however, with the book setting numerous challenges for them to tackle before the interesting results are discussed. The Magic of Pineapples is a hands-on, book that leads the reader into making some of the most famous mathematical discoveries themselves.
Combining interesting historical events with contemporary applications, the book makes links between many different real world phenomena, showing the reader how often the maths underlying the behaviours is the same. For example, the maths used by Carl Friedrich Gauss to quickly add all the numbers between 1 and 100 (1 + 2 + 3 … + 100 ) is the same as that used to calculate the number of handshakes that take place in business meetings!
The Magic of Pineapples discusses the big ideas in maths in a way 11+ year olds can understand and relate to. If it inspires some people into a love of the subject I’ll be very happy.
Numberphile.com is a website your pupils simply must know about. It describes itself as “videos about numbers and stuff” which is a pretty good summary in my opinion. The videos are not tutorial skill-based offerings, but engaging adventures into interesting mathematical concepts and problems. I really like them as they show maths at its best: interesting problems and fascinating results, rather than contrived contextual links. That’s not to say there isn’t context, but where there is it is meaningful and adds to the intrigue.
These videos are the KS3 maths curriculum we’d all love to be teaching if standardised testing and judging teachers and students on exam-based success we not the order of the day. The passion and enthusiasm of the presenters combined with the engaging subject matter definitely stoke the flames of enquiry. Pupils I have shown the Numberphile videos to did react very positively to them; many wanting to know more about the maths behind them.
There are links in the videos to topics we do teach however, and I think there are plenty of opportunities to get these videos in as starters, plenaries or interesting homeworks. I commend them to you!
This time Craig Barton and his guests from King’s College, London discuss falling standards in maths, advice on running discussion based lessons, and some festive maths ideas. In the attached Word document you will find links to all the resources, ideas and activities discussed, and a link to the Forum discussion as well.
The second TES Maths Podcast goes live! This time Alison Kiddle of NRich Maths is the special guest as Craig Barton discusses good ways of introducing algebra, rich tasks, ways of tracking pupil progress and more.
The TES Maths Panel are delighted to announce the arrival of The TES Maths Podcast! This is a brand new series hosted by Craig Barton, featuring recommended resources, discussions of best practice, conversations with leading educational professionals and more.
You can listen to the first episode by clicking here. TES are working on putting the series on iTunes shortly so they can be downloaded onto your iPhone, iPod, computer etc.
The other day, a friend of mine brought an excellent little podcast to my attention called The Math Factor. Suitable for pupils and teachers alike, the 10 minute episodes feature interesting problems and concepts within mathematics. Hilbert’s Infinity Hotel, Algebra on the Radio and Space Walkers; there is something here to engage any mathematically minded person. The show is pitched beautifully, making it accessible to people of all mathematical abilities. Highly recommended.
As a fun summer activity with the kids we decided to construct a geodesic dome! We got the instructions from cutoutfoldup.com at this link. Our first attempt was a failure as the newspaper struts were too weak and flexible and the suggested joint method of using masking tape just didn’t hold the struts in place under sustained load.
We realised that the cutoutfoldup.com design came from desertdomes.com, a superb website that gives you full designs for any size domes you want to build. We took another design from this website and changed to using bamboo skewers and a glue gun for the joints. The result was a geodesic dome of 0.85m radius that made a perfect ‘tent’ for the kids to play in… Here is a picture of the finished dome: