Mar 26 2017

Revision Time 2017

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, an annual job I have checked and made many major updates to the series of revision pages. There are two new pages, one is GCSE Questions by topic – I thought it would be useful to collect together resources which allow for revision by examination topic; the other is Chasing the highest grades?

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. 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.

On Study Strategies, note the very valuable set of resources from The Learning Scientists. See their blog for more information and note the excellent downloadable materials on study strategies including Retrieval Practice. Note the blog on meta-analysis of 217 Retrieval Practice Studies.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to research learning strategies with high utility include 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.

Mar 19 2017

Examinations, Twitter Lists…

… can be so very useful!

For example, try this list of just the UK Examination Boards Maths teams; you don’t even need to sign up to Twitter, just follow the list for updates and resources from the exam boards.

For some samples from these tweets:

From MEI, their Interactive Scheme of work
MEI noted resources from the Core Maths Support Programme
Note that Edexcel also have an Interactive Scheme of work, I have linked to this here, along with some other Edexcel A Level information and resources. (See also the series of pages on GCSE and A Level Examination reform.
OCR on 4 big changes to A Level (Will Hornby)
OCR’s Exam Builder is the new question builder platform from OCR for GCSE and A Level sciences, computer science and maths qualifications. Exam Builder, is now available. It is free for all and gives you unlimited users per centre.
Maths Puzzles from OCR
AQA on GCSE Exam preparation, Making Assessment Count
AQA noted @Ofqual on GCSE 9-1 grades, useful for sharing with parents.

For a more general examinations list which includes more organisations associated with assessment, see this list which includes all the examination boards including WJEC, who I see also have a Question Bank tool which allows teachers of Maths, Computing, Science, Electronics, Business Studies, Food & Nutrition and Physical Education to create a paper at either Entry Level, GCE or GCSE. I can confirm the Question Bank tool is very easy to use and works brilliantly; I searched for GCSE Maths filtered by Algebra and Problem and created a paper with mark schemes and examiners’ comments in minutes.

The list also includes Ofqual, the Department for Education and the Chartered Institute of Educational Assessors.

WJEC GCSE Algebra problem

Mar 12 2017

Mathematical Miscellany #10

For any of your students studying for STEP direct them to this excellent portal from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics. Advanced Problems in Mathematics is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

See also, from Cambridge University, their STEP Support Programme and from Nrich, Prepare for University.

These details are also available on Mathematics for Students.

On the subject of challenging questions for older students and with revision on our minds, perhaps a good time to remind everyone of the excellent MadAsMaths site.

MadAsMaths mark scheme example

The AQA Mathematics AS and A Level specifciations have now been accredited. Watch the AQA website for further resources on the new specification. Checking Teaching Resources we see that AQA are developing their route maps; I have always found the GCSE route maps very helpful indeed.

AQA Route Map

Something I have used a great deal with my GCSE teaching for both the current and previous specifications is AQA’s detailed and very clear teaching guidance.

AQA Teaching Guidance

An A Level Teaching Guidance extract is available.

We can also see Command Words which reminds me a little of the Exam Terminology document so useful at GCSE. There seem to be versions of this document in various places, I believe the first time I used it was back in the days when there were more Examination Boards, this may well have come from the then Southern Examining Group!

Under Assessment resources we find Specimen Papers and mark schemes; also an Assessment Guide on using a large data set. On the subject of large data sets, for information on all the Examination Boards and large data sets, read Bruce Hampton’s clear and detailed comparison.

I have added an AQA page to the A Level Reform series.

Eduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

Staying with the subject of Statistics AQA and Edexcel have accredited GCSE specifications; note that coursework is no longer a requirement of GCSE Statistics.

See more in the Mathematical Miscellany Collection.

Mar 8 2017

Women In Mathematics

March 8th 2017 is International Women’s Day.
We’ll start with an image I shared this time last year that I think still says it all! Thank you Steve Lomax who shared this wonderful response to the task ‘Describe a mathematician’ from Mansfield Green E-ACT Academy.

Capture

Some useful references on women in Mathematics:

From the American Mathematical Society: Women Doing Mathematics. Note there is much information on this site. Women@NASA caught my eye.
European Women In Mathematics
MIT highlight MIT Women in Mathematics
Follow @womeninmaths the Women in Mathematics Committee of the London Mathematical Society (@LondMathSoc).

And for some History

The excellent St Andrews site has information on female mathematicians. Look for example at Florence Nightingale, a pioneering statistician. Or Caroline Herschel perhaps less well known than brother William!
From Nrich: Women in Mathematics
From Agnes Scott College in Atlanta, Georgia, pages to illustrate the numerous achievements of women in the field of mathematics.
From Wikipedia a list of women in mathematics
Smithsonian.com: Five Historic Female Mathematicians You Should Know

Mar 5 2017

Examination Resources

With changes to examinations at both GCSE (UK examination taken at age 16) and A Level (UK examination taken at age 18) all the examination boards are offering help and support for teachers and students. Many excellent resources are available with several published very recently.

For example we have Edexcel’s very helpful resources for teaching new content. For each topic, information, examples and exercises (with answers) are given.

Edexcel – New Content Resources

More helpful Edexcel resources include the Exemplification of the New Sample Assessment Materials and the Topic Tests, note the Show More button which will take you to more resources including for example posters of formulae that students need to know.

From AQA and OCR too we have many excellent resources to support the teaching of the new specifications. Given so many new and useful resources I have separated the UK Assessment pages further and now have pages for AQA, Edexcel and OCR. Whichever board you are using it is well worth while looking at resources from all the boards, the specifications are all based on this content.

I have also been updating (this is a work in progress) the A Level pages, noteable additions to the A Level documentation are Interactive schemes of work from Edexcel and OCR MEI. From MEI – look at this excellent scheme of work for the new specification. Each of the 43 units is based on a topic and includes a commentary of the underlying mathematics, a sample resource, a use of technology, links with other topics, common errors, opportunities for proof and questions to promote mathematical thinking. The schemes of work is freely available. And from Edexcel for each unit of work you will find Specification References, Prior Knowledge including GCSE Specification References and Key Words. For each sub-unit you will find Objectives, Teaching Points, Opportunities for Reasoning / Problem Solving, Common Misconceptions / Examiner Report Quotes.