Here is something a bit special. It’s an amazing Geogebra applet that shows where the formula for the area of a circle comes from. I’ve had pupils cutting circles into sectors before to perform the same proof, but this interactive applet it first class in showing the concept in a visually stunning way and quickly. Top stuff!
The Standards Unit are a collection of resources produced in response to the Smith Report by the Department for Education and Skills. They use ‘active learning’ strategies that were originally planned for use post-16 but have now been introduced into the secondary sector. The well known Dr Malcom Swann of Nottingham University played a big role in the development of the resources that span the whole secondary maths curriculum.
I personally use these resources a lot and consider them to promote high levels of mathematical thought and making connections between topics. In addition to the paper-based resources, the Standards Unit also features software applets. I have added as many of these that I can find to the list below, but there are more out there. If you find a link to a piece of software discussed in the Standards Unit and it isn’t included below could you please send me the link so I can make it available to everyone.
If you would like to purchase a hard copy of the Standards Unit you can from the NCETM website.
The Standards Unit Resources
Mostly Shape and Space
Here’s another classic mind boggling video from Vi Hart about a very amazing number…
At a more basic level this idea could be used to introduce the idea of identities. Great stuff Vi!
Thanks to @SamGWebster for bringing this to my attention.
Allow me to introduce The Ultimate Maths Faculty. This is a project created by Dave Gale (@reflectivemaths). Dave is a maths AST and founder of the Reflective Maths Teacher’s Posterous blog. The idea is simple, but the impact could be a paradigm shift in the way we look at CPD. I believe getting involved with this project could be the best CPD you’ve ever had, and it’s totally free.
The Ultimate Maths Faculty is an attempt to share best practice by connecting brilliant teachers around the world using social networking. These teachers then work in their free time using collaborative-technologies to share ideas and produce guidance on high quality pedagogy for teaching specific topics.
The social network of choice is Twitter and the Ultimate Maths Faculty’s actions can be followed at this hashtag: #UMFac. Dave also posts progress updates through his blog.
The first project worked on by the Ultimate Maths Faculty was to produce best practice guidance on how to teach surds. A GoogleDoc document was made available that anyone could edit to contribute their own ideas of how to teach this topic. Click here to view the document. You will see a melting pot of ideas with teachers recommending their own suggestions then sharing their views on those of others. Dave is going to collate the ideas expressed in the GoogleDoc document and then produce a’ model lesson’ and teacher guidance from it.
The project is still new but other topics are now being explored such as:
Please feel free to join the Ultimate Maths Faculty yourself by contributing to the GoogleDoc documents above. Share your suggestions on best practice for teaching these topics. Follow the Twitter group at #UMFac and also Dave’s blog. Make sure you add your name to the Ultimate Maths Faculty list as it will allow you to connect with brilliant maths teachers around the world.
I am personally very excited about this project as it blends the power of ICT to connect people, with the collective will of teachers to improve their own practice through sharing their expertise. Isn’t this project the pure essence of what CPD should be?
Regular readers of Great Maths Teaching Ideas will know what a fan of TED.com I am. TED has changed the way that I look at the world on countless occasions. Their videos are never anything but inspiring and thought-provoking. They remind us of what the best and worst parts of the human condition are about.
TED-Ed have recently launched a new initiative to bring awesome educational videos to the world for free. Think Khan Academy, but with professional levels of production and teaching. I could say more but this video says just about everything you need to know:
The Khan Academy has just released a free app for the iPad. For people unfamiliar with the Khan Academy, it is a website featuring over 2500 free educational videos about a variety of topics including maths, science, art and much more. Salman Khan, the site’s author delivered a superb TED talk last year explaining his vision. Many people who are trying out a Flipped Classroom teaching style are using the Khan videos for homeworks.
The app is good. It is easy to navigate to any video in the Khan collection and logging in with your Khan account details allows you to save your progress. Overall the user interface is well designed and intuitive.
Laura Rees-Hughes and Sharon Derbyshire are teaching resource megastars! Many of their wonderful resources have been available from Craig Barton’s site (www.mrbartonmaths.com) for a while, but they have now created a resources website to share all of their amazing creations. Please allow me to introduce: www.numberloving.co.uk.
The resources are a long way from ’10 questions about ….’ worksheets. On the Number Loving site you will find Top Trump card games, treasure hunt activities, QR code activities, matchup cards, quiz-quiz-trade activities, collective memory sheets, online investigations, revise and draw activities and much more. The resources will have your pupils doing ‘hands-on’ maths in engaging, active ways.
Laura has kindly agreed that I can feature some of her and Sharon’s resources on Great Maths Teaching Ideas. Here is a sample of some of their ideas:
I can’t recommend www.numberloving.co.uk highly enough! Definitely have a look when you get a moment.
Conrad Wolfram, founder of the amazing Wolfram Alpha site discussed on Great Maths Teaching Ideas previously, spoke recently about his concerns about the way maths education is delivered right across the world. In an engaging and persuasive talk, Wolfram argues that there is more to maths than calculating, yet this is what we are teaching pupils to do by hand 90% of the time. He believes that computers should be used for calculating and the maths curriculum should embrace the other areas of maths that computers cannot yet do such as formulating a problem, deciding what information you need to know and how you are going to use it and then interpreting the results.
I’ll go on the record saying that I believe Wolfram is right here. The current approach of trying to make pupils ‘more functional’ in their maths is an add-on to the current curriculum. Wolfram’s vision is where the ‘functionality’ pupils need to develop is the curriculum and we let the computers handle the solving of the quadratic equation.
This year I discovered Wolfram Alpha and how it can solve just about any question on the maths syllabus I teach. It can complete the square, factorise, calculate the sum of interior angles in polygons and solve cubic equations (without trial and improvement!) and pretty much anything else you’ll ever need. I was so energised when I discovered it as I thought it was going to be a tool pupils could really use to help them with their learning. In reality I could never see a way to get pupils as excited about it as they all realised they are investing large amounts of time learning how to solve things by hand that a computer can do faster, for free and without making mistakes.
You’re right Conrad.
Learning Without Frontiers Talk by Conrad Wolfram
What do you think?
I’d like to tell you a bit about a new project that I’m running with a top set year 7 class at the moment. The project is called Information Is Beautiful and is based around techniques for data representation and visualisation. We have done a few lessons on the basics such as how to draw comparative or multiple bar charts, frequency diagrams, pie charts etc and now the pupils are using these skills in the context of infographics.
If you don’t know what and infographic is, it is a poster that uses different graphs and charts to communicate a message, but in a visually attractive, beautiful way. Quite often traditional graphs or charts are adapted to make them more visually appealing and relevant for the topic. Good websites to find infographics are InformationIsBeautiful.net and Good.Is.
Pupils started off by looking at this fantastic infographic about who is likely to buy the iPad 3:
Pupils looked at how traditional graphs and charts had been changed. For example, notice how the pie chart that shows the proportion of different sizes of memory in iPads in circulation is also divided into 3G vs Wifi connectivity too. The authors are showing two types of data on one pie chart!
Next, pupils watched this excellent TED talk by David McCandless that shows many examples of how he makes information beautiful.
Pupils are researching infographics for homework this week with a focus on answering the question ‘how have they changed traditional maths graphs and charts to make them more relevant to the topic and gorgeous to look at?’ In future weeks pupils are going to start researching their own chosen topic and getting their own primary or secondary data for it. An excellent source of free public data is the Google Public Data Explorer website that features wonderful interactive charts for real world data from greenhouse gas emissions to the proportion of seats held by women in parliaments. Here is an example of one of the interactive charts:
The pupils seem to be very engaged in the project so far. I’ll make sure to update this post with their own infographic productions once they complete them!
Here is a superb plenary for a lesson about multiplying and dividing by 10, 100 and 1000. This resource consists of two files. The first is a PowerPoint presentation that runs a game of Who Wants To Be A Millionaire. The Second is an Excel Document that gives pupils a worksheet to record their successes and failures on. A nice alteration to the traditional format of the game is to not eliminate players once they get a question wrong. Instead, encourage pupils to use the worksheet to record the winnings they get from each question and then to total up their prize money at the end. A super resource and thanks to Ceri Reece for bringing this to my attention.
MathsNet have a wonderful collection of 3D shape resources at this webpage. There are a variety of interactive applets that cover 3D shape topics including nets and 2D views of 3D shapes.
My particular favourite is ‘Building Houses 2′ where pupils have to build the 3D shape by using the 2D views given. They score maximum points by using the minimum number of blocks possible. By clicking and dragging on the 3D view pupils can spin their construction around in real time to help them with the task.
NRich Maths have a superb and challenging activity based on 2D views of 3D shapes called The Perforated Cube. Pupils can use the Building Houses 2 applet to help them with the investigation which is based around a cube made from 125 smaller cubes in a 5x5x5 arrangement. The cube has ‘mini-cubes’ removed to cause perforations. Pupils are given 3 2D views of the shape and have to calculate what is the maximum and minimum number of mini-cubes required to give those views. Highly recommended.
UPDATE: MathsNet seems to be history, but the same links are available from this site: http://mathandmultimedia.com/2012/03/02/3d-math-applets/
The Mathematical Palette is a new blog from the fantastic Guillermo Bautista. To add to his already prolific blog collection, including Mathematics and Multimedia, Geogebra Applet Central, School of Freebies and Blogineering, this new blog is aimed at enriching maths for your pupils by finding maths in everyday situations and presenting it in an interesting and light hearted way.
Already featuring the maths of crisps and donuts, and looking at the artistic genre of pointillism, The Mathematical Palette is certainly a blog you could encourage your students to subscribe to if they want to find interesting uses of maths in the real world.
How one man can maintain so many high-quality blogs I’ll never know, but Guillermo Bautista has potentially done it again with this one. Early signs are good. Certainly one to watch…
Cary Huang has created a fantastic website that shows how relevant standard form is to our lives. You can start at the 10^0 m scale and zoom in or out seeing significant objects that vary in size from the width of the universe to a Plank Length. Very engaging and interactive. Highly recommended.
Today Apple announced iBooks Author, a brand new free app that makes creating textbooks as easy as drag and drop. I’m going to stick my neck out and say that what Apple have planned for textbooks is going to change everything. I think this could be a defining moment when the way we deliver content at school could change forever.
The software allows you to easily create interactive textbooks that run on the iPad which include endless multi-touch interactive features such as videos, interactive images, multiple choice questions, web-based widgets, 3D images that allow the user to spin things around and much more.
I think Apple have done it again. With big publishers on board like Pearson, there’s going to be a goldrush starting today to generate this kind of content. I can’t wait to see what the first maths textbook looks like when it’s available soon.
2011 has been a busy year in education. Emerging technologies are making computing more ubiquitous and communication easier. By following the feeds of many wonderful educational blogs, I have seen a real mind shift happening in education with many teachers embracing technologies to change the way that learning happens in their classrooms for the better. I feel confident in saying that I will look back at 2011 as a year when many learning mini-revolutions began, when education systems around the world started thinking about moving on from the lecture-style model of learning they have used for the last 120 years. Maybe these emerging trends will pass as edu-fashion and fads or perhaps they will make a lasting positive impact as their proponents suggest. As 2011 comes to a close I’m going to take this opportunity to reflect on key innovations and events of the last year and to stargaze into the future with my predictions for 2012.
2011- Looking Back
Three big trends in education in 2011.
The Flipped Classroom Takes Hold
Turning the learning model 180 degrees is becoming increasingly popular, particularly in classrooms in the USA. The idea of the Flipped Classroom is that pupils learn new concepts at home, rather than at school through watching educational videos (quite often made by their teachers). They then work in class collaboratively on problems that they would have traditionally done for homework. Teachers who have tried the flip successfully say it’s a better model for learning as pupils learn concepts without the distraction of their peers and then when it comes to practising applying their new knowledge they do it in an environment surrounded by people to support them. See this link for a fuller description of the Flipped Classroom.
I have followed the blogs of teachers who use the Flipped Classroom model for a while now and am convinced in its benefits and plan to trial the approach with one of my classes next academic year.
Particularly towards the second half of this year I really noticed much more chatter about the Flipped Classroom approach within the blogging community. I believe the excellent work of Salman Khan through his Khan Academy website, which has now received funding from Bill Gates, and his TED talk (see below) raised the profile significantly to a whole new audience.
With the efforts of people like Salman Khan, MyMaths and the excellent CGP MathsTutor (click here to see my review), and with video creation becoming simple through apps like Educreations on the iPad (click here for my review), the resources and the necessary ease of use in the technology is now available to realistically support teachers who want to use the Flipped Classroom approach.
iDevices make quality technology for education available to the pupils
This year I was fortunate enough to attend an ‘iPads in Action’ conference at Longfield Academy, Kent where every pupil has their own iPad with them in every lesson at school. My thoughts and comments can be found at this link along with an excellent write up of the day by Rob Harrison on his blog. I left Longfield in no doubt that 1-2-1 iPad schemes can be implemented successfully with a real benefit to pupils’ learning. The pupils were fully engaged in their lessons and were using their iPads for quality learning, not just fun.
I ran a student survey at my own school and discovered that 50% of pupils own an iPod Touch. There are enough for one-between-two in nearly all my lessons and I have started making use of them for learning. For example, Quick Graph is a superb free graph plotting app that makes graphics calculators look like dinosaurs. The intuitive, simple, colourful user interface is so good you literally do not have to teach pupils how to use it. Click here to read my review of Quick Graph.
2011 is the year where lots of teachers realised the potential that iPods/iPads/iPhones have for learning. I think that potential is in its infancy at present and I hope that the blogging community continues to share ideas for teaching with these devices so we can all benefit.
Using Social Networks and Blogs for learning becomes more widespread
For years the education system fought the introduction of the calculator for fear that pupils will lose all their mental calculation skills. Mobile phones must be ‘turned off and in the bottom of your bag’ in most schools at present, although that view is certainly wavering in many schools. The educational benefits of mobile phones and iPod Touchs etc are now being realised, particularly over this last year. Social networks and blogging are also on the education system conveyor belt of being banned originally and then realised as great tools for improving learning. As using mobile phones and other mobile computing devices in lessons has become more ‘socially acceptable’ over the last year, the early adopters who have the mandate to experiment with social media and blogging have found them another good tool to support learning. I have myself run a blog for my pupils this year, which in the first 14 weeks of the academic year has been visited 4747 times by the 200 or so pupils that I teach. I am convinced by the comments I receive from pupils that blogging is an excellent way to engage pupils in your subject and make them realise that it is bigger and more wide-ranging than what you cover in class. I would thoroughly recommend blogging in particular to fellow teachers as I have not found any other technology medium yet that seems to engage so much student interest.
I could not finish off this section of looking back over 2011 without mentioning that this is the year that Google+ was born. In only a handful of months I have built up a social network of 545 like-minded teaching people with whom I share ideas, resources and laughs. Google+ will be the demise of Facebook, I am certain of it. Not only is it less cluttered, yet more functional, you can also do free video chats with up to 10 people simultaneously, called Hangouts, which are great fun. The Hangout video of the Dalai Lama chatting to Archbishop Desmond Tutu has now definitely entered the YouTube viral-video archives as a truly unforgettable moment. Google+ allows you to control which of your followers see which of your posts in a very easy to use way, handling your online privacy much better than its rivals. Go Google, Go!
2012- Looking Forward
And now for my predictions for 2012. Don’t hold me to these (unless they are right!) ;-)
Twitter supports collaborative learning in the classroom
How do you get all pupils in your class to engage with your questions, ask ones of their own and continue this outside of the classroom as well? How do you get knowledge that is learned shared around your classroom without needing to stop the class whilst they are on task? How do you get quality feedback from all the pupils in your class without needing to speak to them individually?
Check out this wonderful article which forms part of series of pieces written by a South African teacher who is using Twitter in the classroom to answer these questions and more. I believe, done right, this could take assessment for learning to a whole new level and promote quality discussion of learning between pupils in our classrooms. I have experienced this style of learning and communication myself at conferences and really seen the benefit. I think this could be very big and am certainly going to give it a go myself. I will of course keep you up to date with the results of my experimentation on Great Maths Teaching Ideas.
The Flip It movement grows supported by more technology and resources
The Khan Academy has really supported the Flipped Classroom movement, providing resources to allow teachers to try the new model. I am big fan of the Khan Academy but I do think there is room for improvement. Taking a UK maths teacher’s perspective, I often find that the Khan videos contain language differences which confuse my pupils. For example, Khan talks about ‘Greatest Common Divisor’ rather than ‘Highest Common Factor’. Whilst you could argue that the language should not be a problem, my pupils tell me it confuses them.
Early into this academic year I discovered the CGP MathsTutor product. It is like the Khan videos but more professionally produced by a maths-specialist teacher and designed for the UK maths curriculum. Click here to see the demo website. I am very excited about using these with my pupils to take independent learning to the next level.
YouTube has this month released ‘YouTube for Education’ which features filtering to ensure content is appropriate for pupils and no related video links at the end of videos. Early impressions are good and this may be another channel that supports independent learning.
My second prediction for 2012 is that the Flipped Classroom model of learning will become more popular as the increase in quality independent learning resources makes it practical for teachers to plan and deliver this model of learning. To truly embrace the model I think pupils will need their own mobile computing device in school which is a trend I predict will continue to rise throughout 2012.
Project-based and enquiry-based learning methods become more widespread
Presuming my first two predictions about 2012 are correct, what our pupils do in class will be different to what they do at the moment. Teachers who Flip say that it frees up a lot of class time for practice in applying knowledge through project-based and enquiry-based learning activities. Both of these approaches promote Higher Order Thinking Skills on the upper-reaches of Bloom’s Taxonomy and are desirable if you can ever fit them in, which the Flipped method allegedly gives you time to. Proponents argue that this teaching style is more like real life in the world of work and also makes learners much more active in ‘constructing their learning’ rather than ‘passively receiving it’ from the teacher. A move in this direction might even please the government who have recently introduced the ‘functional skills’ focus on the maths GCSE. The problem solving skills promoted by these teaching methods would support the focus on functional skills type questions.
One well-known apostle of enquiry-based learning is Dan Meyer who writes Dy/Dan, his blog that promotes teachers being less helpful with the purpose of getting the pupils to think more for themselves. Dan is not a fan of traditional textbooks which break a problem down into its solution steps and then makes them ‘part a, part b, part c’ sub-questions. He argues pupils should be deciding what the sub-steps are themselves. Dan got huge recognition of his cause on the back of his TED talk (see below) where he articulates his views in a clear and humorous fashion.
My third prediction for 2012 is that project-based and enquiry-based learning styles will become more prevalent. Dan’s blog, his ‘three acts activities‘ and projects on sites like YummyMath and Real World Math will become more popular and important.
I hope you enjoyed reading this blog post and please feel free to leave your own thoughts and comments either in the comments section here or get in touch with me via my Google+ profile. I wish you all the very best for a happy 2012 with lots of exciting teaching and learning developments!