Communicating Educational Research

Ahead of Thursday’s (27th July, 8.30 – 9.00pm)  on communicating educational research I thought I would check and update my Reading series of pages which includes some very useful educational research summaries.

PorterThe various pages on free books have also been checked and updated. With the new A Level Specifcations coming perhaps some of those old textbooks might come in handy and will take older readers on a trip down memory lane – anyone for Porter’s Further Elementary Analysis?!

Several books are available – answers included.

On research, note in particular the pages Research – Learning & Teaching and Research – Mathematics Learning and Teaching.

From Harvard Graduate School of Education, see Communicating Research with readings, tips and strategies for clear expression. There are many good points here for communication generally not just in communicating research. Excellent examples of such clear communication are:


Research in 100 Words – Chris Moyse

Research in 100 Words from Chris Moyse who descibes this series as “Simple summaries for busy teachers”. Also from Chris, his favourite research articles in one collection.

Cambridge MathsEasy to digest research on Mathematics education from Cambridge Mathematics, see their Espresso page where in their words, “Each month we bring you an Espresso – a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading.”


Games & Other Mathematical Activities

What to do for those last lessons?

Some of these activities would be great for any lessons, not just at the end of term. The complete collection can always be found on the End of term activities page. For readers familar with this collection all links have been checked and there there have been several updates.

You might want something other than a video, though perhaps consider a Numberphile video or I could make an exception for the counting chimps, a video I was introduced to by Alex Bellos at the SSAT conference which he included in his session and shows the astonishing recall of a chimp – compare the human!

Try some UKMT team challenges, their crossnumber puzzles make a great end of term activity. The junior materials can be found here and senior here.


Relays from Chris Smith. These are excellent, note there is a complete set; I used his Valentine relay very successfully this year! Featured in Mathematical Miscellany#2.

JM Quiz & Matchstick PuzzlesFrom JustMaths a great end of year pub quiz. I do like the way this ends with a round on Matchstick puzzles, this will keep our students happily busy! Note the very useful recommendation for Matchstick Puzzles from Dawie van Heerden.

Get your students thinking with some resources from Underground Mathematics. Try Equation Sodukuor perhaps LCM Sudoku.
Equation Sudoku
Another possibility frm Underground Maths, try the Division Game.

UGM Division Game

Let your students get their phones out to play Factris, a new App published in July 2017 developed by Richard Lissaman, of MEI.

Bingo always works really well.


A team game? Try Workers of Zen.

Workers of Zen

(ATM publish books of team games).

I must mention A Little Problem for the Holidays!

Some Mathematical games and puzzles perhaps? There are plenty to choose from.

The Set Game  which is a daily puzzle is set in The New York TimesHow many sets can you find? Click ‘How to play’ in the menu on the left for the rules.

Or try some pencil and paper games such as Sproutsdescribed very clearly here by the Iowa State Math Department.

Countdown - Nrich
Always popular with students is the game of  Countdown. Exellent programs for both games can be downloaded free from Chris Farmer’s CSF software site. For a new challenge why not try Coundown with Fractions from Nrich or another variation – see this Countdown collection.

Make 24
On a similar theme try  Make 24 a game where four numbers in the range of the natural numbers 1 to 9 are chosen randomly; these must be combined to obtain the result 24  –  but you may only use the four basic arithmetical operations and brackets. This online version optionally shows solutions as well as presenting random problems. The program will also show solutions for any given set of four numbers.

Learn the syntax for WolframAlpha, perhaps a chance for students to explore WolframAlpha, using the various slideshows, note the questions on the worksheetNote the last slideshow on a little fun with WolframAlpha!

Explore the Desmos Graphing Calculator (and note the further reference to Desmos below, use Desmos to create some art work!)

For a main activity a Tarsia puzzle provides an engaging activity. I intend to use one to see how many of the formulae needed for the part of the course which my Year 10 students (age 14-15) will be studying next year are already known.

Darth Vader curve

We could of course have some fun with WolframAlpha. Did you know you can plot Darth-Vader?  There are in fact a whole family of Star Wars curves! Or maybe you prefer Dr Who?!

Have you seen Wolfram fun facts? (You can view these on Twitter whether or not you have a Twitter account). Why not try modifying these queries? Note the different cookies you can try in the cookie query shown below. You could perhaps invent similar problems! How many pizzas would it take to fill the moon? OrJupiter?

fun facts

Art Elements

If those WolframAlpha equations are a bit much for younger students they could try something simpler using the Desmos graphing calculator; look at Alec Schultz’s PacMan for example, you could just show your students how to restrict the domain for straight lines, maybe show them the equation of a circle and see what they can produce! See this post on Graph Art on Mathematics for Students.


To generate some more pretty curves why not try Spirograph?! Students could experiment with these online versions to see the various curves that can be generated.

These logic puzzles from John Pratt should keep students happily and usefully occupied. (I have added these to the Puzzles page on Mathematics Games.) Or we could try another Kakuro Puzzlestudents were fascinated by these when introduced to the puzzles by a member of the class. At the end of the year we often ask students to do a presentation to their peers which works well.

Try (or write a new) Sporkle Quiz.

Sporkle: Find the missing primes in two minutes

Still thinking about games, from Nrich these Strategy games are for Primary teachers; but could also be useful for lower secondary.

For more ideas check Jo Morgan’s Resouceaholic.

We could finish with a song or two!

Wishing teachers everywhere a happy holiday (only WolframAlpha would give you the Scrabble score as well as the definition!)

Underground Mathematics – Save & Organise Favourite Resources

A new page in the series of pages on Underground Mathematics …

If you create an account (all free) on Underground Mathematics you can easily save and organise your favourite resources.


Select User from the menu at the top right, then New User to create an account. Note that you also use the User menu to log in.

When you are logged in you can add any resource to your collection by selecting the star to the right of the title. And note this resource Pick a card, which I highly recommend, think about multiple representations for Quadratic Functions. This could be used with younger students too.
Save resource

See also: Tutorials – Saving favourite resources – a video from Underground Maths
To see your resource collection, select ‘Your resource collection from the User menu.
User Menu

You can also use subcollections to help organise your resources. Subcollection1

When you display your resource collection, note the options for each resource, the first of which is the ability to add the resource to a subcollection.

Note the choice to add to one of your existing subcollections or the option to create a new one.

Note that when you display your resource collection you can select a subcollection if you wish:

See for example Building Blocks resources I personally like; I created a subcollection and downloaded as a csv file. The ability to add notes is really useful too.

For reference, this is one of a series of pages on Underground Mathematics. With so many outstanding resources on the site, this is a continuing work in progress.

Mathematics Resources (Age 16+)

As mentioned in my previous post I am continuing to develop the series of A Level pages, for students aged 16-18 which will be a major ongoing project during this Summer and beyond. With a growing collection of resources, I have now split the Resources section into a series of pages and also added a tab to the top level of this blog for I hope easier navigation.

Having just returned from an inspirational MEI Conference I have much to reflect on and will be returning to many ideas from this in future. For now I must highlight MEI’s Problem Solving – Examples and Solutions which has just been published. 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).

MEI Problem Solving

Underground Mathematics, STEM Learning and Nrich have all mapped resources to subject content which makes it simpler to look for good resources for learning which means we can concentrate on teaching well and just how our students will learn. With MEI’s Interactive Scheme of work we have a suggested resource for each unit as well as ideas for using Technology and of course crucially very helpful commentary on learning and teaching. Jonny Griffiths RISPS collection has a very clear resource listing by topic. The list goes on. All the examination boards too have very clear and helpful documentation.

I have also added pages for Vocabulary and Formulae for easy reference.

Learning & Teaching A Level (Post 16) Mathematics

IndexI have made several updates to every page in the A Level series of pages recently. The A Level Resources page has had many new additions. I am currently reorganising this as the collection has grown rather and I wish to add more resources and commentary, but all links will still work, the main page will simply become a resource index page for easier navigation. The series is very much a work in progress, I will continue to develop these as I teach both A Level Maths and Further Maths next year.

All three examination boards are developing really helpful resources to support teachers in delivering the new specifications. For A Level Mathematics, like GCSE we now have common content which means that it is well worth exploring resources from all the examination boards, something I have been doing for the new GCSE specification.

For some images to ilustrate these resources, see the Slides here. A summary slide has been included to aid navigation. You can view the slides on slideshare but as slide to slide links do not work on slideshare you may wish to download the PowerPoint file or the pdf version for easier navigation.

For Maths Conference 10 delegates, these are the slides used in my presentation on 24th June 2017. I have added a small number of slides which I hope aid navigation and help you find A Level resources on this blog. It was lovely to meet and talk to so many enthusiastic and dedicated teachers. Please do not hesitate to get in touch using the comment facility here or drop me an email.


A Level – Free MEI samples

Looking at the samples for MEI’s Integral resources we see several outstanding resources for the new specification; these should give you some good ideas on high quality teaching resources. Note also the free resources for teaching the 2017 specifications where you will find a lovely collection. These can be used with MEI’s with MEI’s scheme of work which can be used with any of the 2017 A level specifications.

You can sample resources here for AS Mathematics. These samples are for four topics including Problem Solving. The level 1 exercise may well give you ideas for Higher abaility GCSE students.

MEI Sample Problems Level 1 Exercise

Note that schools and colleges can register with the Further Maths Support Network which has many benefits including a free single-user teacher access account to extensive online resources to support the teaching and learning of Further Mathematics, and also enrichment materials for A level and GCSE mathematics students; access to all the Large Data Set materials will be available free. You can find the correct form here, Note that the form makes the terms and conditions very clear: the resources can be used to support teaching and learning within your mathematics department, including displaying resources to students and distributing hard copies of formative assessments to students. They cannot however be made available to students by any other means, a VLE for example.

MEI Exponential FunctionsLooking at Integral Maths on Twitter, (you do not need a Twitter account to access this link) we see that for subscribers to Integral, Summary Sheets for the new A Level Specification will be provided. Summaries like this used at intervals throughout a linear course will provide very useful reviews of previous learning for students. A very useful free sample is provided on Exponentials and Logarithms. Looking at this document, we see a 5 page very clear summary of what students need to know. I do like this explanation, it is exactly what I find useful to say to students: “What power do I need to raise the base to….?”

MEI Exponential Functions 2

For a further taste of these summaries, see these extracts from Graphs and Transformations and Coordinate Geometry.
Graphs & Transformations

Coordiante Geometry

SumazeAlso from MEI, some free apps including a free resource to help your students make the Transition to post GCSE work, try Bridge It!, a quiz game. Note that Bridge It! will only run on devices with a Flash player. This version is best played on a laptop or desktop computer using a mouse or finger pad. Sumaze! and Sumaze! 2, puzzle games are available on IoS and Android. And watch this space as more free apps are on the way!
Bridge It



Mathematical Miscellany #14

Years 7 and 8 (UK ages 11-12 and 12-13) Summer Assessments

WR 7 & 8 Assesments

From the White Rose Maths Hub, (@WRMathsHub on Twitter) Year 7 and 8 Summer assessments.  I have mentioned the White Rose team before, recall their excellent Problem Solving resource.White Rose Maths Hub problems

The GCSE Problem Solving Questions of the Day – Compilation  available free on TES Resources. The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided.

GeoBoard Activities
Answering a question from a reader on unique triangles on a 4×4 GeoBoard, I have updated GeoBoard Activities to include the solution to this and also added several new activities, including the use of GeoGebra.
GeoGebra GeoBoardGeoGebra isometric dot paper

Staying with the subject of GeoGebra, I discovered some very nice resources by Tom Carpenter,  I do like his Line Graph worksheet which demonstrate how to draw a line graph and/or how to interpret a line graph.
Line Graph, Tom Carpenter
As I mentioned in last week’s post on GeoGebra, even if you are not familiar with GeoGebra, there are so many resources already available ready to use.

I have mentioned the excellent PhET simulations before. This on Least Squares Regression provides a very easy to use demonstration. Try and find the line of best fit then see how closely your line matches the actual line.
PhET Residuals
On this subject you can also very easily use GeoGebra, Desmos, or WolframAlpha for regression, full details with examples are provided here.
GeoGebra Regression

See more posts in the Mathematical Miscellany series. Collections of mathematical goodies!



GeoGebra is astonishingly powerful and seems to keep just getting better. It works brilliantly on my phone and my tablet as well as on a desktop. I will be using it a great deal more in future with all the students I teach.

Time for some new pages on GeoGebra, this collection will grow, but I wanted to bookmark the tutorials and note also how to very simply use the Data Analysis tools. Sophisticated analysis is possible of course but in moments one can copy data from a spreadsheet application to GeoGebra’s spreadsheet view and see some charts.

GeoGebraThese Tutorials are an excellent place to start learning how to use GeoGebra. GeoGebra works not only on desktops but on phones and tablets as well.

The Manual is comprehensive and note the Quick Start tutorials which are very clear. You will also find manuals and much helpful documentation on the same page. The great thing about GeoGebra is that so much has already been written you can probably find what you need already online!

You can also use GeoGebra’s YouTube channel to watch demonstrations.

GeoGeoGebra is not just for Geometry, as mentioned above note how good it is for Statistics too, copy in those large data sets and get analysing! (GeoGebra Data Analysis as a pdf file or  PowerPoint: GeoGebra Data Analysis.)

The slides show the Classic application first which perhaps experienced users are most familiar with, followed by the newer Maths Calculators interface. If you are new to GeoGebra I would recommend using the Calculators which of course have the same functionality and more and will give consistency across the various platforms.
GeoGebra classic & Maths Calculators

So much is already written for GeoGebra you can use material already written. For example thinking try MEI’s very helpful advice on the Use of Technology, also on Integrating Technology into schemes of work for older students (UK A Level  age16-18). Note that tasks are also given by type of software including GeoGebra.
MEI Tasks AS

Another source where you will find GeoGebra used to help students understand and explore Mathematics is Underground Maths where many tasks have associated GeoGebra resources. An Underground Mathematics search on GeoGebra reveals the extent to which it has been made use of!

Note also some excellent examples from the ATM Conference 2017.

See also Use of Technology and Statistics in the A Level series of pages.

I would like to thank MEI for an inspirational (and free) conference recently. So many good sessions including the use of GeoGebra for statistical analysis.  A highlight had to be looking at the GeoGebra 3D graphics view with our 3D glasses!

Advanced Level Mathematics

The new UK A Level Mathematics specifications require students to demonstrate overarching knowledge and skills specified as follows:

Overarching Themes:

  • OT1 Mathematical argument, language and proof
  • OT2 Mathematical problem solving
  • OT3 Mathematical modelling

Also required, we have the use of technology and the use of data in statistics.
These links are for pages in the A Level Reform series where information and resources are added and updated regularly. There have been several updates recently and this will be an ongoing project. I am very much looking forward to teaching the new specifications in both Mathematics and Further Mathematics.
A Level Reform Index

Note that all A level specifications are accredited and for Further Maths most specifications are now accredited.

MEI Postcards

MEI’s pstcards illustrate these principles very clearly. Note that solutions are also provided for each postcard with further suggestions. The Large Data Set postcard for example links to the data used. Looking at the Technology and Modelling postcards, we can of course use Technology! I thought I’d have a play with Desmos!
MEI postcard technology

I also had a look at the Modelling problem on Desmos.