The eagle-eyed amongst you will have noticed a new link in the Great Maths Teaching Ideas’ menu: GMTI Scoop.it.
I follow a lot of bloggers and like to share lots of wonderful things with my readers, but don’t want to put everything I see on the GMTI blog. Whilst I do share other people’s work on here I do like to keep a decent proportion of it my own contributions, rather than just being an aggregator.
I have been sharing links to interesting articles and resources a lot through my Twitter account @Maths_Master, but wanted to make them available to more of our readers. To do this I created the Scoop.it page. This is an aggregation of interesting maths teaching articles, ideas and resources that I find elsewhere on the net. Bookmark the site and add to the comments if you’d like.
The best will still appear on the GMTI blog, but I thought you might be interested in the rest too…
“Surely 3.12 is a lot bigger than 3.2 because 12 is bigger than 2…!” said one of my students the other day. I do see where students are coming from with this misconception and you can dive into place value and talk about hundredths being smaller than tenths, but another model that I’ve found successful is the “zooming in on the numberline” approach:
This approach gets them to realise that when we need a number between 3.1 and 3.2 that we break the numberline down into ten more increments by putting another digit on the end.
I found this approach useful when it comes to rounding to decimal places and you’re trying to get them to spot which two numbers the number could round to, for example 3.453 could round to 3.4 or 3.5 to 1 d.p. They then know that 3.45 is half way between the two so it rounds up to 3.5 …
Generally I have found this approach to be more successful than talking in terms of tenths and hundredths with pupils who don’t find maths easy. Do you know any others? If so share them in the comments!
Click this link to open a remarkable infographic summarising the main academic theories behind how learning happens. I’d heard of many of these, but I think it is wonderful to see how they are connected.
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!
I’ve been putting some thought recently to what to do to refresh the displays in my department when the time comes. Wordle.net is a superb tool for creating ‘word clouds’ like the one above. You just paste in some text, (I took mine from a maths vocabulary website) and Wordle does the rest! You can choose the font, colours and layout after creating your word cloud to fine tune it to your visual preferences.
Combine your Wordle output with Posterazor which allows you to take a pdf and convert it to a multiple-page document (for enlarging it), and you have some stunning maths literacy displays!
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….
Here is a worksheet to give pupils lots of practice on identifying particular types of number. Perfect for a consolidation lesson. If they do it correctly the coloured boxes spell out the word FACTORS, which makes it easier to mark for you
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:
Lungs diagram with internal details (Photo credit: Wikipedia)
Just a quick idea here… To make a lesson on calculating the volume of a sphere contextually meaningful how about using a balloon to calculate the capacity of your lungs? Get a pupil to take a deep breath and then fully exhale into a balloon. Then measure the radius of the balloon and calculate the volume. You’ll need too get balloons that form spherical shapes for it to work well.
An interesting chat about the accuracy of the results could follow. Is the surface tension of the balloon similar to that of your lungs? Is it an over estimate or under estimate and why? Etc…
As an extension, how about relating the volume of a sphere to that of a cylinder? Archimedes’ famous cylinder and circumscribed sphere discovery states the volume of a sphere circumscribed inside a cylinder is 2/3 the volume of the cylinder. Compare the formulae; can you prove it!?
Archimedes sphere and cylinder. The sphere has 2/3 the volume and surface area of the circumscribing cylinder. (Photo credit: Wikipedia)
The TES Maths Podcast episode 6 is now live at this link. This was recorded during Craig Barton’s recent visit to Bangkok where he was the keynote speaker at the South East Asian Maths Competition. In this episode Craig discovers what it’s like to teach in international schools and interviews the well know Canadian mathematician, Ron Lancaster. A more in-depth interview with Ron can be found at this link.
As always, the podcast including previous episodes can be downloaded from iTunes at this link.
Episode 7 will be discussing the Flipped Classroom model and the Singapore model of maths teaching and learning. If you would like to contribute to the discussion please leave comments in this TES forum thread.
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.
I’ve got a small year 10 class that struggle with number work. We had good lesson looking at writing numbers as a product of prime factors, but they had a significant learning block in not being able to quickly find two factors of numbers when constructing their factor trees.
I’ve made the following multiplication table that is adapted specifically for writing numbers in prime factor form. Say pupils are trying to find two factors of 28, they find it in the grid then read up and across to find the two factors, 2 and 14 or 4 and 7 etc. They then continue constructing their factor trees with these new factors, using the grid to find two more etc.
Quite often pupils need to go beyond the 10 X 10 times tables in this task, for example spotting that 26 = 2 X 13, so I have extended one side of it up to 30. The primes are shaded and I have removed all the 1 X y where y is a composite number so they don’t start putting 1s and ys into their prime factor trees.
Using the grid effectively will certainly require some demonstrations first. I’m going to give it a go tomorrow and see how they get on. Ultimately it would be nice if it led to conversations about strategies for finding the factors without the grid, but that can be another lesson rather than trying to tackle both things at once…