# Mathematical Miscellany #3

Mr Westwater – TES Resources

With revision still in mind, for some excellent PowerPoint resources with A Level questions and mark schemes by topic try Mr Westwater’s resources on TES. (Twitter @westiesworkshop). Though Edexcel questions these are clearly useful for other examination boards also. There are six of these PowerPoint files available:
Core 1   Core 2
Statistics 1  Mechanics 1
Core 3
Core 4

Diagnostic Questions

Craig Barton’s and Simon Woodhead’s Diagnostic questions site includes some excellent question collections for revision; as well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.

From AQA this set of revision tests and mark schemes is very useful and from Oxford University Press a lovely set of free revision resources is available. Under Mathematics Revision Guides, choose the ZIP file Worksheets. Note that these are headed New GCSE – this is the old new specification, not the new new specification! These are clearly perfect for UK students taking exams this year but still excellent for future years.

For many more revision resources note the Revision Activities series of pages.

GCSE Problem Solving: Steve Blades’ site www.m4ths.com has many excellent resources; on the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book.

For more Problem Solving Resources, see Problem Solving and Problem Solving 16-19.

Alec McEachran’s Furbles – a large data set!

Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s ptolemy.co.uk. Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.

Alec McEachran’s Furbles

Visual Patterns – Fawn Nguyen

From Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.

By Colleen Young

# Top 100 Tools For Learning – 10th Anniversary

Jane Hart is the Founder of the Centre for Learning & Performance Technologies and as you can see from her blog, 2016 marks the 10th year of her annual Top 100 Tools for Learning list.

Jane has put together all the presentation slidesets as well as an alphabetical list of ALL the tools which have appeared on any of the lists.

The 2015 slideset is shown here.

Voting is now open for the Top 200 Tools for Learning 2016 and will close on Friday 30 September 2016, and the 10th annual list will be released on Monday 3 October 2016. You can find all the voting guidance and forms here. Note the 200, not 100; as you can see from Jane’s description she is making some changes to celebrate the anniversary.

From the voting guidance you can see that there are three methods of voting, my choice is:

So these are my own 2016 choices as top tools for learning because these are tools I use all the time in my job, both in my teaching and in my role as a senior leader. Note that we are not discussing subject specialist resource sites here (that’s another whole (updated) story), but tools for education generally; I think it is very useful to remind ourselves of Jane Hart’s own definition:

### “Any software or online tool or service that can be used for your own personal learning or for teaching or training”.

 CY 2016 votes Education Personal Learning & Productivity Place in Top 100 2015 Evernote x x 10 WordPress x x 8 Google (search) x x 3 Twitter x x 1 Slideshare x 20 PowerPoint x 5 Excel x x 56 Moodle x 15 WolframAlpha x – Desmos x –

Looking at Jane’s alphabetical list of ALL the tools which have appeared on any of the lists, I thought it would be interesting to see which tools have been on all nine lists to date and also at popular tools from the last 5 lists, 2011-2015. I used a favourite tool, Excel to create these, the file is available if of interest: Jane Hart Top 100 Tools – Colleen Young analysis Note the tabs at the bottom, the first three worksheets show the tools which have been in every list, 2007-2015, the last two look at the longer list of tools which have been in the list for the last 5 years. You can read Jane’s fascinating analysis of trends for work place learning.

Tools on the list every year since 2007

Average Rank 2011-2015

To elaborate further on my choices
Evernote
– an outstanding note-taking tool and something I use every day. I have a notebook for each of my classes to which I upload any resources I want for that class; I also jot down any ideas I have for each class. I can use it on any PC, tablet or my phone. It is also a good way to share for example a list of websites with students – using a shared notebook. I have many notebooks both for my job and life generally; the search facility in Evernote is awesome and the ability to link from one note to another, very powerful. (Blog post on Evernote).

WordPress  – obviously – you are reading a WordPress blog right now! I have several other blogs, GamesStarters and for students I have created Mathematics for Students and something I am very pleased with is a blog I use to give the details of homework for each of my classes. I created ‘What was that homework?’ as a result of a survey of students across several schools where many students said that they would like homework details online. No student can ever say to me that they didn’t know what their homework was! I also have blogs on useful tools for students and teachers generally. (The very first post on this WordPress blog – which includes some useful WordPress links).

Twitter  – great for professional development – I have contacts in education all over the globe and have been led to many useful resources by my virtual colleagues! See Mathematics Conversations. and this post on Twitter.

Slideshare  – it is very easy to upload presentations to this (free) presentation sharing site; the two shows above are examples. Presentations for teachers or students could be uploaded for example.

PowerPoint I can’t really have Slideshare without including PowerPoint in my list because that’s where I start with my presentations, often with a little help from the interactive whiteboard software. It is interesting to see how popular PowerPoint was last year at number 5, other presentation software such as Prezi is also useful, but it’s so important to remember that it’s the content that matters! See this post, Presentations for some reading and resources on presentations.

Excel is something I use everyday in my job to analyse and present data; I also use many spreadsheets for teaching. Of all the applications in the Office suite this stands out for me, the changes from Excel 2003 to 2007 with the massive improvements to conditional formatting for example make this one outstanding application. There are also many Excel spreadsheets out there too to help in Maths lessons – see Maths Files for example.

Moodle We have a Moodle course for each year group in school; each course has links to any websites that we use in class so students can investigate further themselves if they wish. VLEs are sometimes criticised for being no more than ‘filing cabinets’; I would argue what useful filing cabinets they are – containing resources chosen by teachers for their students all in one organised place. For example we see that in the run up to examinations the relevant Moodle courses receive hundreds of hits as everything students need was available, not only syllabus information and papers but worked examples that we have uploaded. It is also of course possible to use forums and quizzes on a VLE and being a secure site for the school we can include information intended for our students only.

WolframAlpha.  WolframAlpha is not just all about Maths, it covers so many subjects and even though they would love us to pay for WolframAlpha pro, the free model still offers unlimited queries everyday!

Desmos, the outstanding graphical calculator deserves a vote in my opinion, it is wonderful for learning mathematics, accessible for young students yet has the sophistication required for university students. Brilliant. It is entirely free, very simple to use even for young students and brilliant for projecting in lessons. There are also free apps for both Android and iOS.

So that concludes the voting from Colleen as 10 tools are needed for a valid voting entry!

# UK A Level Reform

I thought it would be useful to collect the information on A Level reform in one place so have reorganized the existing pages under UK Assessment which will provide, I hope, easier access to information. The various pages, which you can see on tabs near the top of the page have been developed from areas which have proved popular.

The series of pages includes the following

From MEI comes this excellent presentation relevant for any new specification whichever examination board is being used. A strength of this presentation is its clarity. Simple statements of fact are given in very clear language and as well as stating what we know we also have a very important reminder of what we don’t know!

Note that the documents mentioned in the presentation above are included here.

From the Further Mathematics Support Programme:
2017 A Level Mathematics and Further Mathematics
This is really helpful – clear and simple statements. Note the link to the very helpful document on changes to AS/A Level Mathematics & Further Mathematics.

A Level Subject Content for teaching from 2017

GCE Subject Level Guidance from DfE, this guidance is intended to help awarding organisations understand how to comply with the GCE subject-level conditions and requirements for mathematics. The guidance includes further information on the use of Technology and large Data sets. Making Statistics Vital from Jonny Griffiths has some tasks which could be excellent, look at the this task on World Wide Statistics for example which includes the task with answers and a spreadsheet with data for 191 countries. Census at School is an excellent source of data and you can generate data for your own school too.

Making Statistics Vital – Jonny Griffiths

How demanding are questions in the new A level maths? Ofqual is planning to conduct a research study to support the accreditation process for new A level maths qualifications. Taking place in July this year, the research aims to compare the level of difficulty of exam boards’ sample assessment materials by having judges compare pairs of exam questions. An interesting method of comparison and something I have come across before – see No More Marking on Comparative Judgement.

The A level mathematics working group report is a very valuable document and one I referred to in a presentation on GCSE Problem Solving – I do believe we should always look both backwards and forwards to inform our teaching; where have our students been and where are they going? I have also created a new version of the problem solving presentation: Problem Solving 16:19.

The Cambridge Mathematics Education project (CMEP) mentioned in the presentation has now been rebranded as Underground Maths, a superb site which will I feel be very important in our work with our Mathematicians students.

Timelines

For each current school year group (2015-2016) – changes to GCSEs, AS and A Levels

New GCSE and AS & A2 courses for teaching September 2016

New A Level Maths courses – revised start date               BBC News Story

# Is That A BIG NUMBER?

Twitter (quite rightly!) suggested I might like to follow IsThatABigNumber. The aims of the site are as follows:

• Put numbers in context
• Promote numeracy
• Share number facts
• Develop Number Sense

Exploring the menu at the top, note as well as the home page, we have other options, we could ask for example how big is 5km? The question returns a very comprehensive answer with comparisons to many other numbers! I do like the various quotes that appear randomly, as I was exploring I saw (very appropriate for someone responsible for Assessment) from Charles Babbage: “Errors using inadequate data are much less than those using no data at all”.

Other options as you can see include conversion, we could convert 1cm to 1 m (though I can already do that with WolframAlpha which returns rather more comparisons, and can also do it myself, I hasten to add!). Alternatively look at some random Number Facts or an interesting option – try a quiz

On the home page we can the site is in its early stages, (the authors welcome feedback). Numbers in the News is a good idea. I wish the authors well – promoting numeracy just has to be a good thing!

On the subject of big numbers, I have recently completely checked and made major updates to my post on Standard Form resources.

# Revision Time

That quote from Robert Collier seems so appropriate when it comes to revision. Once again, this academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

Once again we are in the final run up to examinations, so I have checked and made many major updates to the series of revision pages. Before mentioning the resources though we should think about how best to use them.

The first page in the series ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ or ‘mini tests’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. Earlier this academic year when I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to the report the two learning strategies with the highest utility are distributed study sessions (last minute cramming is not effective) and practice testing.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

For students, I have added the revision and examination questions to Mathematics for Students.

Resources in the collections allow for a mix it up approach but also provide questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources. All resources are free.

Wishing your students everywhere success in their examinations.