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!

The Mathematics of History

Rita Pierson: Every kid needs a champion

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/maths-videos/ - a large number of embedded Youtube videos looking at speed of light travel, Mandelbrot sets, synathesia, the golden ratio in nature and more…..

and the homepage:

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….

There’s also a load of maths dingbats that I’ve created  http://ibmathsresources.com/mathsdingbats/ - which work really well as lesson starters and in quizzes…

I have taken a look at think it is just the thing my super-keen year 8s would love to explore. Enjoy!

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

Click here to download the worksheet

UPDATE: @StudyMaths has created a brilliant interactive online version of the extension task here.

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:

UK: http://www.amazon.co.uk/The-Magic-Pineapples-Adventure-Mathematics/dp/1482545306/

US: http://www.amazon.com/The-Magic-Pineapples-Adventure-Mathematics/dp/1482545306/

It is also available in the Kindle Store. Just search for The Magic of Pineapples.

Here are some video trailers for the book that I’d really appreciate if you could share via your social networks:

Pattern in the Primes- The Magic of Pineapples: http://www.youtube.com/watch?v=YHVAg6FciAE

Cherry in Matchstick Glass- The Magic of Pineapples: http://www.youtube.com/watch?v=E3N2aexY7PQ

Addition and Handshakes- The Magic of Pineapples: http://www.youtube.com/watch?v=OROmYIY8MvU

Think of a Number- The Magic of Pineapples: http://www.youtube.com/watch?v=mEX0QlOFQHE

I hope you enjoy the book and a big thanks for your support

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.

Available in the Kindle Store now:

The Magic of Pineapples in the UK Kindle Store

The Magic of Pineapples in the US Kindle Store

Coming also in paperback via Amazon soon!

Here is a video trailer about the book:

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…

Click here to download the product of prime factors multiplication grid

Check out this wonderful animated visualisation for the prime factor form of numbers: click here to view.

This super animation was made by the Data Pointed blog.

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.

Here is an example of one their videos called Dragon Curve:

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!

Enjoy!

This post may not surprise experienced maths teachers, those used to working with kids who find maths difficult, or our primary colleagues. However, whilst none of this is revolutionary in the slightest, it has been a new world for me and something I’d like to share.

I have a small year 10 class who find maths challenging. They show many signs of discalculia and many have a phobia of numbers. I have recently had to teach them the topic of ‘types of number’ (squares, cubes, factors, multiples, primes etc) and have had a few breakthroughs by trying to make it as kinaesthetic as possible. When I thought about it, I realised that multi-link cubes can be used for so many parts of this topic:

Square numbers-Make squares out of a single layer of multi-link cubes with side lengths of 1, 2, 3 and 4 cubes etc. Pupils soon realised in my class that when calculating the number of cubes they needed that they just had to multiply the side lengths of the square. They understood where the square numbers came from and have a mental image of what the pattern looked like out of multi-link cubes, rather than it being an abstract concept.

Cube numbers- Same as above, but get them building cubes. They realised a large cube with sides of length 3 was made up of 3 X 3 X 3 = 27 multi-link cubes.

Multiples- If we want multiples of 6 then pupils group cubes into piles of six and count the total in all groups as they go.

Factors- If pupils need to find the factors of 12 they get 12 cubes then see what rectangles they can make by rearranging the cubes. They realise they can make a 1 X 12, a 2 X 6 or a 3 X 4 rectangle, and they have found the factors…

Primes- Primes are those rectangles which could only be 1 row high.

I do think there is mileage in trying to make links to tangible concrete things that pupils can remember, particularly for kids who find taking in abstract concepts difficult. By my own self admission I need to improve my own practice in this area. I thoroughly enjoy breakthroughs like this as it is something I shall look forward to in the future when I have a similar class. Little victories! I’m still learning every day…

I have always found converting between fractions, decimals and percentages a challenging topic to teach when you’ve got pupils who have difficulty with mental and written arithmetic. Quite often you seem to get bogged down in the arithmetic of the calculation, and the pupils lose sight of why we are doing it in the first place.

Rather than plod on with numerical calculations: ‘divide by 100′, ‘divide numerator by denominator’, ‘use equivalent fractions to make denominator 100 then read off numerator’ etc I’ve been trying to think of alternative ways into the topic. Sometimes pupils who struggle with numerical calculations are good at spotting patterns and so I thought if I could create some kind of diagram that pupils could do FDP conversions with and look for patterns within it that it might be another way in to develop their understanding.

I’m a big fan of fraction walls for introducing the idea of equivalent fractions; the idea being that a pupil puts their ruler vertically on the fraction wall and can read off equivalent fractions.  It occurred to me, why couldn’t we just put a decimal and percentage number line above the fraction wall? That way, when pupils put their ruler down on 3/4, not only can they see this is equivalent to 6/8, but also 0.75 and 75%?

Here’s the completed FDP converter:

To use it pupils place their ruler vertically at the appropriate point on the page and can read off the other scales.

I wonder, if over time and with plenty of practice using the diagram and identifying links and patterns within it, if some pupils will be able to make the step of not needing the diagram? Could they visualise it in their heads, even if just from a conceptual point of view? I’m going to give it a go with some of my classes to find out! If you have a go I’d love to hear your feedback in the comments section.

Click here to download the FDP converter file.

Andreas Schleicher gives an insightful, data-led talk about what the PISA (Program of International Student Assessment) tests tell us about what successful education systems look like. For some time I’ve been aware of the PISA tests, which rank countries based on the literacy and numeracy ability of their youngsters, but I did not realise that they used the data to go a step further and identify common features and principles of successful education systems. A must-watch talk for anyone working in education:

Use data to build better schools

The TES Maths Podcast episode 5 is now live! I was fortunate enough to be asked by Craig Barton to be the special guest on this episode. We discussed two ‘show and tell’ topics: differentiation in the maths classroom and teaching maths in context. I would love to hear your thoughts on the episode and the ideas we discussed.

Click here to listen to the TES Maths Podcast 5.

You can also subscribe to the TES Maths Podcast on iTunes at this link.

Four Fours

Can you make statements equal to all the numbers 0 to 20 by using just four fours? Brackets, multiplication, division, addition and subtraction are allowed for starters. When they start getting stuck you can introduce other operators such as square roots, factorial etc. Can you make all the numbers up to 100?

My year 7s had a good go at it this week, writing their answers collectively on the board:

Four Fours investigation- the class really got into this and refused to go to break at the end of the lesson because we hadn’t got one for 19!

I made a worksheet for the investigation that you can download here (Microsoft Word).

BIDMAS Bodge Ups

To get pupils evaluating answers to BIDMAS statements you can give them some incorrect ones based on common misconceptions and get them to identify the mistakes and correcting them. Here is a booklet I made (in Microsoft Word) that covers 5 common BIDMAS misconceptions. The last one is to get across the importance of showing workings otherwise nobody knows what you have done wrong…

BIDMAS Quiz Quiz Swap

This is a nice activity to promote focussed learning discussion in a BIDMAS lesson. Download the Microsoft Word file here and print and cut out the cards. Give each pupil one of the cards. They then quiz each other with the questions on their cards, making sure they cover the answer at the bottom of their card with their hand when they ask the question. The answers are included so they can then know if they need to have discussion if they get it wrong. The idea is that if they got the answer wrong they have a discussion between the two of them to understand why it was wrong. This leads on nicely from the BIDMAS Bodge Ups activity where they spent time identifying and correcting errors. After they have answered the questions on each other’s cards and had a learning conversation if they got them wrong, they swap cards and go find another person to quiz quiz swap with. The idea is that learning travels around the room from pupil to pupil.

Tangram Wolf (Photo credit: Evelyn Saenz)

A colleague of mine, Claire Nealon wanted to adapt a resource I made a while ago of a triangle constructions tangram (see previous post). She wanted to make it more accessible for lower attaining students. Claire simplified the constructions so that the triangles are all right angled with side lengths that are Pythagorean Triples. This made the activity more accessible for her pupils who struggle reading and measuring lengths that are decimal numbers.

Click here to download the resource (Microsoft Word)

The idea is that pupils accurately construct a collection of triangles and then have to fit them together, like a Tangram to form a rectangle.

Claire is working wonders with some level 2/3 pupils this year, adapting and creating resources like these that makes the maths accessible to them. I’m learning a lot from her myself! Thanks Claire!

England cricket team (Photo credit: Wikipedia)

A deputy head at my school is trying is hand at teaching some maths this year after a career teaching PE. He’s doing an excellent job and recently came up with a great lesson idea and resource for an averages lesson.

Click here to download the resource (Microsoft Word)

The idea is that small groups of pupils are selectors for the England cricket team. They need to choose the best batsmen to take to the next Ashes series. They look at four batsmen’s scores over the last season and calculate the averages and range for each one. They then have to use these to justify their final team selection. This is a nice way into looking at strengths and weaknesses of different types of average as it provides a contextual setting to do so.

He reported that his pupils loved the activity and has been kind enough to let me share it with you. Enjoy!

Today I visited BETT 2013 at the ExCel Centre in London. The yearly event showcases the current developments and market for ICT in education. In addition to many exhibitors, there are numerous talks by practitioners explaining how they use ICT to support learning in their schools. Professor Brian Cox was the headline guest speaker this year.

Augmented Reality-Samsung

Short Range Projectors- SMART

Any Surface IWB- GloView

3D Visualisation- Reach Out Interactives Ltd

We can buy 3D TVs, now we can buy 3D projectors.. Seeing the pulsating heart throbbing on the IWB whilst wearing some 3D glasses was engaging. However, whilst I loved the experience, I have doubts about this technology as all the exhibitors who demonstrated it had a very limited collection of resources. To convince schools to invest in expensive 3D projectors, the resource collections will have to become much more comprehensive. One to watch over the next few years. 

 

Cloud Apps- Google Apps and Microsoft Office 365

Both Google and Microsoft put on impressive displays and demonstrations of their cloud based applications. With Microsoft Office 365 you can run all of the familiar Office applications like Word, PowerPoint and Excel within your web browser. Launching the program is done by logging into a website rather than needing to have it installed on your computer harddrive. If you give pupils access to this service they can login on any computer at home or at school and access Office programs. The SkyDrive cloud storage solution from Microsoft is also integrated into Office 365 meaning pupils’ work is stored in the cloud so they can access their files from any computer. No more lost USB memory sticks!

 

Google Apps is a similar suite of free Office-style programs from the Cupertino giant. These have been made available to schools for free for a few years now with excellent administrator software that allows managing student accounts, security and privacy controls straightforward. I personally am a big fan of Google Apps which is clearly maturing as a product now. Google also presented their Chromebooks, an affordable laptop computer solution that they say is ideal for schools wishing to give pupils their own computing devices. I’ve personally not used Chromebooks before but have spoken with schools who do use them and the feedback has been positive. 

 

E Books Everywhere- RM Books

There was no shortage of companies offering to support you moving away from hardcopy textbooks and towards e book versions. If your pupils have their own mobile computing devices, e books are an attractive technology as it puts the textbook in their pockets 24/7. 

 

RM Books was a platform that particularly caught my eye with a decent collection of digital textbooks from the main publishers. Furthermore, they had two purchase options, buy outright or rent, which means you can decide which option is most cost effective for your school. From the pupils’ perspective, they just visit the RM Books website, and after logging in see a digital bookshelf of their textbooks. The user interface from the pupil point of view was the thing that particularly impressed me about this product, being simple, intuitive and clean.

 

The Star of the Show- Life After VLEs- RM Unify

RM surprised me today. I have never had much respect for them as my previous experiences with their products have been perpetually frustrating and disappointing. I have always thought that they had the right ideas, just not the skill to implement them. Today they were showing off their post-VLE era product that launches in March this year and it was an absolute stunner: RM Unify. 

 

Before Apple got too big and corporate they used to design products that exuded quality. Their products just worked, were intuitive and had longevity. The way they integrated everything so that different programs all interacted together in harmony created a magical experience. The disappointing iPhone 5, or as my pupils call it “the iPhone 4 that’s been put under a rolling pin”, and the terrible Apple Maps wouldn’t have happened in the Steve Jobs era. The thing that used to make Apple products so special was the design and thought that went into the end-user experience. You never knew what complex computing was happening under the bonnet as you the user just saw a simple, intuitive interface that worked. Whilst Apple have made a few slip ups recently, the fact that the iPad doesn’t come with an instruction manual, because it is so intuitive, says a lot.

 

RM Unify has the design flair of an Apple product in the good old days. They have taken the time to sit down and create something that is beautifully simple to use, takes the best parts of the cloud revolution, is flexible, future proof and are going to sell it at a price that is quite frankly, unbelievable. Their strategy is just so right and it’s clear in the product.

 

Their strategy is simple: the cloud apps that are out there are brilliant, so rather than trying to create something better and failing, lets be a curator of the best that the internet has to offer. Speaking with one of the RM exhibitors, I learned that during their design process they thought about problems with this model and then designed around them including:

1. If you use lots of different cloud services (Prezi, Office 365, Google Apps etc) you currently need to set up logins for each pupil on each different website. In RM Unify the pupils have a single login and password and from that point on they never need to login again. They go to the RM Unify site, enter their login details once and then see a collection of tile icons that directs them to different web apps or websites. RM Unify creates logins and passwords for the pupils on all the different cloud apps and automatically logs the pupils in when they launch it. The pupils never even need to know their logins for all the different sites! For example, they just launch the Prezi app by clicking on the tile in the RM Unify launchpad window and it automatically logs them into Prezi where they can access all the Prezis they’ve made before! If they launch Office 365 Word, it automatically logs them into SkyDrive so they can access all their previous Word files. They just login to RM Unify then from that point on they are logged in to everything!
2. Cloud based web apps are growing quickly. How can you keep pace with knowing which are the best? In RM Unify there is an App Library. This is constantly updated and so when a great new web app comes out in the future, the pupils will be able to get it right from their launchpad window. It’s future proof.
3. How do you deal with the many different computing devices pupils have and their limitations? Make it device agnostic! Today I saw RM Unify running on a Windows PC, a Mac, an Android tablet and an iPad simultaneously. I saw Microsoft Office running in the web browsers on all the devices. Finally, this is a product that truly works if you adopt a ‘bring a browser’ approach where pupils can bring any type of mobile computing device and connect to what you want them to.

If your school is using Google Apps, rather than Microsoft Office 365 with your pupils, RM Unify can integrate with that instead. 

RM Unify is free to schools for all the functionality, except the integration with Microsoft Office 365 or Google Apps. If you want that integration they are going to charge just £495 per year for any school with more than 500 pupils. Compare that to your old VLE cost!

RM are calling this a ‘single sign-on revolution’. Never did I think I’d come away today saying that I think I’ve seen the future of IT software in schools in a post-VLE era from RM, but I think I have. They’ve managed to create a beautiful, simple to use product that combines the best that web developers around the world have created. I haven’t seen anything so well polished in quite some time.

Well done RM. 

Here is a video preview of RM Unify:

The TES Maths Podcast 4 is now live! This month Craig has special guest Celia Hoyles, the outgoing Director of the NCETM. They discuss a wide range of issues including Numeracy Across the Curriculum, the midfield of misconceptions that is Fractions, and the use of technology in maths lessons.

Click here to listen to the TES Maths Podcast 4

A typical representation of the forgetting curve. (Photo credit: Wikipedia)

How many times have you heard teachers complain that students couldn’t remember what they learned yesterday, let alone last week or last month? Retention of learning is a big issue and one that must be addressed. This year my department is trialling some key stage 3 homeworks that directly tackle the issue of pupil retention of learning and I thought you may like to take a look at our practice.

We shouldn’t get frustrated when pupils do not retain learning from one day to the next. They are human and some experiments carried out by the German psychologist Herman Ebbinghaus show that all humans forget things at an exponential rate. His famous Forgetting Curve illustrates the idea nicely and demonstrates that if you are only going to learn something once, you might as well not learn it at all. I have written at length about the Forgetting Curve and what it should mean for our own practice in my book, 100 Things Awesome Teachers Do, but the main point is that if you periodically relearn things, the rate at which you forget them again decreases rapidly.

Taking this idea, we decided that the most appropriate time for pupils to relearn topics was during their homework. The challenge then was to create homeworks that stayed in sync with the scheme of work and repeatedly revisited topics from earlier in the year. At the beginning of the year the first homework covers what you learned in the first week, but they build up as the year progresses so by week 10 you cover topics that you learned in class from weeks 10, 9, 8, 7, 6… etc.

Click here to see an example of our Forgetting Curve Homeworks. As you progress through the homeworks you can see that the number of topics they cover grows too. Any objective they learn in class gets periodically revised on subsequent homeworks all year. The whole years homeworks are in a single pdf file that we get the pupils to download at the start of the year from our revision website, avoiding the need for homework textbooks or endless amounts of photocopying.

Example of one of our Forgetting Curve Homeworks. Topics taught earlier in the year are regularly revisited on the homeworks. The ‘L’ column tells the pupil what level the question is and the ‘C’ column informs them whether they are allowed to use their calculator for that question

The homeworks are differentiated by level and so it is the teacher’s responsibility to choose the questions that are most appropriate to the level the pupils are working at. For example, a low-attaining class may do questions 1 to 20 where a high-attaining class may do questions 20 to 40. We decided to put all the questions ranging from level 3 to 7 on each homework so it gives pupils an opportunity to try some from a higher level that they had been prescribed if they would like to. Many pupils are choosing to do the 20 questions set then some extra ones to see what the next level up is like.

We are alternating these Forgetting Curve Homeworks with MyMaths homeworks for a bit of variety.

It’s not perfect and we are having some niggles as you would expect. For example, there are a few pupils who we need to print out the worksheets for as they do not have access to computers at home. Nonetheless, pupils are expressing positive opinions about the homeworks and our feeling as teachers is that they are providing real opportunities for pupils to relearn topics they covered earlier in the year. Given time in lessons to review and reflect on their performance on the homeworks it is helping pupils identify areas they need to work on, providing good AFL.

We will look both at exam performance and our professional judgement as teachers at the end of the academic year to see if we feel they have had a positive impact on learning retention. Please feel free to ask further questions or give us some constructive feedback in the comments section.

I have recently read The Elephant in the Classroom: Helping Children Learn and Love Maths by Jo Boaler. The book summarises the extensive research that Professor Boaler has conducted studying what successful maths classrooms look like both in the UK and the USA. Based upon a significant wealth of her own research and other significant contributions, the book is frank about what teaching styles promote the fastest progress in maths learners. The book goes further, describing the current state of maths education within the UK and makes recommendations that both parents and teachers can embrace to improve both the rate of progress and the enjoyment maths students have in their learning.

Jo Boaler’s research is worth considerable attention. She has spent significant periods of time conducting longitudinal studies, following pupils through most of their school careers and within a large variety of educational contexts. The book made for fascinating reading as it challenged what I thought I knew about learning environments that promote rapid and sustained progress. In short, her work shows with considerable research evidence that setting is counterproductive for learning. Mixed ability classes that have a problem-solving focus through the use of Rich Tasks lead to faster rates of progress, high levels of motivation and engagement. Whilst my own prejudices have always steered me away from mixed-ability teaching, believing that you can’t stretch the top and support the bottom as well as you can in a set class, she explains the research says that high attainers achieve just as highly in a mixed ability class, but the lower attainers achieve much higher in a mixed ability environment.

She goes on to explain common learning blocks and negative beliefs that pupils have and what you can do to overcome them. For example, she encourages activities such as Number Talk, where you set the class a mental arithmetic calculation to do. Then you ask them how they solved it, writing all the different methods that pupils used to ‘pull the numbers apart to make the calculations easier and then reassemble them’. Through pupils seeing different strategies for mental arithmetic they learn more efficient methods and understand that we should see numbers as flexible things that can be decomposed and reassembled to our convenience. She explains that these kinds of activities are so important because in a study of low attainers they found the vast majority still count on their fingers and didn’t know any alternative strategies such as number bonds etc. Another worksheet with 100 questions on column addition won’t move them forwards with their maths at all if they count on their fingers for all of them…

I must say that there were portions of this book where Jo described a state of education that I have not seen myself. She talks in depth about Assessment For Learning and how schools are not using it. This is not my own experience as I see effective AFL practice around my own and other schools all the time. Perhaps the national picture is different, but it did come across very doom and gloom in places.

An interesting read, politically controversial in places, but always thought provoking. With such a deep and comprehensive collection of research behind here findings and recommendations, this book is a must read for maths teachers.

This year I am going to cycle over 2000 miles in UK Cycling Events Sportives to raise money for The British Heart Foundation. This challenge evolved from an original plan to cycle from Land’s End to John O’Groats. For various reasons I have decided to change to doing the Sportives which are 100 mile rides in over 20 different locations around the country. The distance is twice as far as Land’s End to John O’Groats and I will complete this between March and November this year.

The British Heart foundation support amazing work into the research and treatment of heart problems, changing people’s lives every day.

Please support me in this challenge by donating some money to this worthwhile cause. You can donate via my JustGiving Page, or by texting the code:

JGLE83 and the amount £1, £2, £3, £4, £5 or £10 to 70070

Thank you for your support

(Photo credit: Wikipedia)

I was thinking of how to jazz up the topic of estimating the answers to calculations (by rounding first) for a KS3 class when it occurred to me that a bit of physics could provide just the opportunity. The lesson is about pendulums and calculating the speed at which they swing.

Start by giving the class mini-whiteboards and tell them they are not, under any circumstances to use their calculator in the lesson today.

Hang a mug, or similar weight from a piece of string from the ceiling such that it nearly touches the floor, forming a long pendulum.

The period of oscillation (time for one complete swing forward and back), T seconds for a pendulum of length L metres is:

T = 2 X pi X square root (L/g)

g is the gravitational acceleration and equal to 9.81 m/s/s.

Get a pupil up to the front of the class to measure the length of the pendulum and then ask the class to estimate what they think the period of time, T, for one oscillation will be. To do this they need to round the values in the equation to 1 sig fig and then calculate T. For example, 2 X pi becomes 6, g becomes 10 and a pendulum of length 2.8m is entered as 3m long. They estimate T = 6 X square root (0.3) = 6 X 0.5 = 3 seconds. (Assuming square root of 0.3 is 0.5 as 0.5 squared is 0.25 which is very close). Then swing your mug pendulum and get them to time the period for one oscillation with the stopwatches on their phones. When I did it with a class, the time of the real life oscillation matched the estimation very well and the class were delighted.

Then you ask the question, how long does the pendulum need to be to have an oscillation of 2 seconds? A bit of changing the subject of the formula and some more estimation later they can give you an estimate of the pendulum length required. We found this to be approximately 1m and when we built and tested it the oscillation was 2 seconds bang on.

Pupils seemed to be really engaged with the lesson and the learning was good too. They told me they got a real sense of why estimation by rounding is important and were surprised we they could predict the movement of the pendulum so accurately without using a calculator.

Definitely one to try out. Do you have any ideas of other science links that we could bring into our maths classrooms?

A colleague of mine recently stumbled across the website of Peter Bland, a maths tutor. It contains some excellent GCSE revision resources in the form on booklets of exam questions on particular topic. They are all available form his website here, but for your convenience I have also linked to his hosted resources by topic below:

Algebra for Foundation

Bounds

Box Plots

Circle Theorems

Cumulative Frequency

Fractions

Frequency

Histograms

Locus and Constructions

Number

Percentages

Probability Tree

Pythagoras

Quadratic Equations

Quadratic Graphs

Questionnaires

Scatter Graphs

Sequences, nth Term

Simultaneous Equations

Surds and Indices

Transformation of Curves

Transformation and Symmetry

Trigonometry

Trial and Improvement

Vectors