I have made several updates to the organisation of this blog recently, always attempting to make things easier to find!

This includes the creation of some new pages.

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Note the Lesson Planning series which includes pages on Technology also some useful reading. Note the excellent post from Peps Mccrea, The 7 habits of highly effective lesson plans (on the Lesson Planning Reference page). Much food for thought here with the author’s emphasis quite rightly on learning and making the material memorable.

The post includes some rather thoughtful comments on sins of planning!

With Technology in mind I have the Tools & Calculators and Use of Technology pages and also a new series of GeoGebra pages. Note the wealth of resources available from MEI; MEI as a GeoGebra Institute provides us with many excellent classroom resources. The Calculators page includes instructions and examples on various calculators including the new Casio FX991EX-Classwiz.

For more on Statistics data sets and teaching activities resources from the examination boards please see the Statistics page in the Advanced Level series. Edexcel have very useful guide to teaching Statistics including examples and calculator instructions.

All checked and updated – many of these songs have gone down well for a considerable time. A more recent discovery was the One Direction quadratic formula song which makes my student smile (and sing a long!) (A reminder of GCSE Formulae)

The following songs have all gone down very well with students, particularly the Circle Song!

This on the Quadratic Formula makes my students smile – and they sing along! The One Direction Quadratic Formula song!

The Klein Four are a bit beyond school Mathematics you may appreciate this if you are studying a Mathematics degree!

….and of course, ‘Katie’s bad science’. I love this!
Original and re-edited version of Katie Melua’s song nine million bicycles proposed by Simon Singh and presented on Ted talks by Michael Shermer.

A resource miscellany this week, a reminder of where to find excellent teaching resources provided by the examination boards and also from MEI.

MEI, AQA, Edexcel and OCR (also Eduqas, part of WJEC) provide excellent support for teachers. With GCSE and A Level subject content now the same for all the examination boards we have an excellent library of resources to use irrespective of the specification chosen for public examinations.

MEI have produced such a valuable collection for teachers with the latest addition to their work on Problem Solving. See their Problem Solving examples and solutions. As well as all the problems and solutions with very valuable suggestions and commentary, MEI have provided a guide to support teachers with the problem solving content of GCSE (14-16) and A Level (16-18).

At A level MEI’s Interactive Scheme of work includes a resource for each section of the course. See also, MEI on integrating technology into your scheme of work which includes many calculator, Desmos and GeoGebra tasks.

AQA All About Maths – many excellent resources for teachers who offer, or are considering offering AQA maths qualifications. There are many excellent resources including KS3 (11-14) tests, many resources for GCSE and a new section for the new A Level specification where topic tests are being developed for the new course.

GCSE Teacher Support includes new content resources, a worksheet collection for Foundation and Higher, teaching low attainers and formulae posters.

Edexcel Worksheets

Teaching and Learning Materials includes an extensive collection from baseline tests for younger (KS3, age 11-14) students to demanding GCSE (age 14-16) Problem Solving questions. The Problem Solving questions with full mark schemes are excellent as are the Practice Papers and topic tests.

Signing up to the wonderful Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you use. Register for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number. In the GCE AS/A Level Mathematics cabinet you will find documents for GCE 2017 including baseline tests and unit tests, also Transiton materials for GCSE to A Level. More will be added to these collections.

Reading Jo Morgan’s latest Gems post led me to the very happy discovery of Graspable Math. Graspable Math offers a highly innovative interface for mathematical notation. You can read the Graspable Math story here.

You can learn a great deal about Graspable Math simply by experimenting, selecting Explore Algebra takes you to the interface which is intuitive; you can also find plenty of help and tutorials on the Learn section of the site, note the Gesture Library as well as the video tutorial collection. There is a YouTube channel here.

Graspable Math is very easy to use, I decided I would solve an equation and wanted to show all the steps. I have used the method of selecting and holding the = sign to start as you can see illustrated in the video above; I was then able to enter an operation to apply to both sides of the equation.

We can also illustrate the solution graphically by inserting a graph to open a GeoGebra window.

Each expression has a circle at the end – simply drag that to the GeoGebra window. You will sometimes see more than one circle at the end of an expression, select to separate expressions hence showing all steps clearly.

I can see this becoming a regular part of lessons, a go to resource.

From Colin Foster on Nrich we have Mathematical Etudes where he discusses lovely rich tasks and tedious exercises!

Colin Foster – Mathematical Etudes

An important read as we begin another school year I feel, the more our students have to think about a task, the more they will learn. I agree with Colin liking the factors task, I have used this approach successfully in class too. In fact we can extend the task and look at finding numbers with varying numbers of factors.

How many Factors – nzmaths

How Many Factors on nzmaths requires students to find ways to group numbers, which numbers have only two factors and which have only three factors?

For more from Colin Foster his KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. Colin Fosteris an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham.

I have mentioned Dr Jamie Frost and his plans for the new A Level specifications. Dr Frost has been very busy producing a complete set of resources for Pure Mathematics 1, I do like the fact that Dr Frost has included extension questions for each chapter. These resources reference an Edexcel text but of course the content is common to all qualifications so all the explanations and worked examples for A Level. I have included a page for Dr Frost’s resources as part of the A Level series. Note the collection of extension questions mapped to the new specification.

For more A Level (UK 16+) resources, Danielle Moosajee has a growing collection of A Level resources on her site PixiMaths, Check her KS5 Teaching Resources Index. The resources include very clear PowerPoints, associated questions and student self-assessments.

A consistently popular post on this blog is one on online whiteboards. All resources / links have been checked and I have removed resources which have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

An important read I feel on such Statistics from Cambridge Mathematics, Examining our own statistical literacy on results day. which makes such important points about the size of the dataset required for it to be explored in context.

With the new school year fast approaching, I have reorganised some pages and resources in the never ending quest to make things easy to find! This is an ongoing project.

A new series on Tools and Calculators includes for example GeoBoard Activities with GeoBoard resources.

There are many excellent PhET simulations from The University of Colorado Boulder. Look at Trig Tour for example. Note that this is HTML5 so available across platforms.

You will also see on the same page this calculator from Math Warehouse which shows the solution to any quadratic equation with full working using the formula.

Math Warehouse

The Problems and Activities page has had updates including the addition of Transum, a site I like a great deal as do many students. From Transum, we have the very wel known Maths Starter of the Day. Note that there is a complete index of starters including the topic of the starter. The Transum site is easy to navigate, there is a clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning. The example shown here is one of the Algebra Activities found on this page.

Transum – Algebra Activities

An essential part of every lesson is of course that we check that students are indeed learning, hence my reminder on Study Strategies on the Lesson Activities page.

From OCR (MEI) their Foundations of Advanced Mathematics level 2 qualification covers arithmetic, algebra, graphs, trigonometry and statistics. Assessment is by a two hour examination which consists of 40 multiple choice questions. As OCR suggest these questions could be used for diagnostic tests.

Choose Past Papers, mark schemes and reports. Papers and mark schemes from June 2007 are freely available (access to the most recent papers is available for schools only via OCR Interchange).

The UKMT Maths Challenge questions are excellent for students of all ages. This post includes a selection of links and resources to access the Maths Challenges.

For superb resources for the Oxford Admissions test multiple choice questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.

At the start of my teaching career I really liked the first paper of the Mathematics A level from the University of London School Examinations Board – thirty multiple choice questions to complete in one hour, 15 minutes.

For questions 1 to 20, candidates had to select one answer from 5 and for questions 21-30 the instructions were as follows.

The pdf file here has the paper, followed by the exam board answers followed by notes from the 1986 version of me! These days I would illustrate with Desmos and/or WolframAlpha for example as well where appropriate.

Note the comment from Graham Cummings below, there are further papers available in the Edexcel’s Emporium:

The Emporium has some 17 multiple-choice question papers from the period 1988-1992 – by no means a complete set, but they range across the Mathematics, Further Mathematics, Pure Mathematics and Applied Mathematics syllabuses. You can find them in the “Pre-C2000” cabinet within GCE AS/A Level.

Signing up to Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you use. Register for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number.

So – back to school again and I thought I would make a final and rather important update to Resolutions for (Mathematics) Teachers. Reading John Hattie’s Visible Learning for Teachers is such an important reminder that we should really be looking at the impact of all we do on our students. We might think a particular method or resource is amazing, but do we think so because we have considered very carefully how it will help our students learn? For a summary of the book,read this from The Main Idea.

The five dimensions of Expert Teachers Hattie identified were based on a review of the literature.
In summary:

Expert teachers identify the most important ways to represent the subjects they teach

Expert teachers create an optimal classroom climate for learning

Expert teachers monitor learning and provide feedback

Expert teachers believe all students can reach the success criteria

Expert teachers influence a wide range of student outcomes not solely limited to test scores

I have sometimes listened to audio books as I do like to hear authors read their own work, I believe it helps understanding. You can hear John Hattie himself on the principles discussed in Visible Learning in these two videos: Visible Learning Part 1: Disasters and below average methods and Visible Learning Part 2: effective methods. If you are in a hurry you might want to skip straight to the last part of the second video! For anyone who can’t get enough of Hattie, he was interviewed as part of Radio 4’s series The Educators.

I have written various posts on the available tools online for writing Mathematics and this is a topic which remains consistently popular. Time for yet another revisit and update as new possibilities are now available – all resources / links here have been checked. I have removed resources where blogs / twitter have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

Something I use a lot. I should explain my requirements – I want tools to communicate Mathematics online, for example I may wish to provide some model solutions or answer students’ questions. Writing mathematics can be a pain (and yes I know about LaTeX). Note that there are various possibilities – sometimes just a static picture is required, sometimes you may want to display how to solve a problem in stages, or perhaps you require a collaborative space. You will also need to consider if you want the examples to be permanent or whether you just want a collaborative space for discussion. A graphics tablet is essential.

My favourite method for illustrating Mathematics online (and in fact the one I use most often) when I just need a series of static displays is to turn an interactive whiteboard flipchart (or a PowerPoint) into a pdf file; the pdf file can then be sent to students or uploaded to whatever virtual learning environment or online storage your school uses. If you do not have access to interactive whiteboard software there are alternatives, one could use Windows Paint for example; there are also various free online tools available; see some of the resources below.

flipchart to pdf example

For sharing resources, it is possible to upload a PowerPoint or pdf file to Slideshare. There are many examples on this blog of my SlideShare slideshows – see this for example

I should mention that I find Slideshare excellent – I use the free version which offers me everything I need – it works every time – I use it a lot!
I created the PowerPoint for the slideshow above by writing on the interactive whiteboard software using my graphics tablet and taking a picture of each page using the Windows snipping tool (it’s in Accessories) – this takes seconds – the snipping tool is something I use every day! (Alternatively I could have saved the interactive whiteboard flipchart as a pdf).

There are as always several options:

Screencastomatic

If you wish to record a screencast of the moving pen / step by step solution variety and save your work, Screencast-o-matic is an excellent option. It is very easy to use to capture the screen and your recording can then be uploaded to YouTube if you wish.

Illustrating how to simplify an algebraic fraction :

Screencast-o-maticoffers everything I want in this category. It is very easy to use indeed – I can write very smoothly whilst recording.

Further resources offering various solutions for writing Mathematics online:

Twiddla

For a collaborative board, try twiddla which seems excellent for collaboration – voice as well if you want. Twiddla offers some very sophisticated features including the ability to use mathematical formulae and upload files and images. Use of the board with all it’s features is free but you cannot save any of your work (possible with a subscription). This would be good for working online with a group of students.

Doodle.ly

Doodle.ly offers a very easy way to have a quick scribble and then share your thoughts! See quadratic example(and note that I created that just to test Doode.ly years ago – a good sign that it’s still there!) Select Doodle Now, doodle, then if you want to publish you will need to sign in. You can sign in with Twitter or Facebook. I like the different pen tools available, the full screen option and the ease of publishing. Apps are available for Android and iOS.

Finally – your students may find this amusing – the Writing Repeaterfrom ICT Games – write something and play it back – now this is a lovely tool for little ones learning to write but I’m sure we can think of some uses!