Jun 25 2016

Review Questions – Underground Mathematics

I wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications I believe this site will provide us with rich resources for these new specifications.

Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.

Alternatively you can browse all the Review questions.

An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.

See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.

Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.

I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.

I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.

Jun 18 2016

Mathematical Miscellany #4

A compilation post this week…
(More collections of mathematical goodies.)

For Problem Solving – a wonderful find, GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Team available on TES Resources. The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided.

From AQA comes an outstanding resource, GCSE Mathematics: GCSE Mathematics 90 maths problem solving questions.

Em @EJmaths has a brilliant PowerPoint with all the questions and answers – see it here.

And finally, 28th June is a Perfect Day to enjoy some Mathematics!
28 is also a happy number!
It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)

Jun 12 2016

A Level – Draft Specifications & a Statistics Qualification

The A Level Draft Specifications have now been published, including specimen papers.
Use this Twitter List to see updates from all the exam boards. As you can see @Ofqual are making announcements about accredited specifications.

For the specifications use the following links.

AQA
Edexcel
OCR AS accredited
OCR MEI AS accredited, see OCR (MEI) for supporting information and videos on the new specification.

Further resources:
AQA Resources including a very useful Specification Summary. AQA have several very clear resources, see: Planning Teaching and Assessment which includes the Specimen Papers and mark schemes.

Edexcel Specification & Sample Assessment Materials note the inclusion of a data set for AS and A Level.

Edexcel – Assessment support including mapping documents.

From OCR, specifications, specimen papers and other resources can all be downloaded here.
Note the option to download a zip file with the specifications and sample assessment materials.

OCR have individual subject pages with further resources:

MEI have helpfully compared Further Mathematics Specifications so you can compare the content and structure from each board.

OCR have also linked to some new sample MEI resources. These include some very nice “problem shorts” and also the use of technology to analyse large data sets.

OCR A Level Check In Test

I do like OCR’s check in tests for GCSE and I see a small number check in tests and lesson elements on the A Level subject pages; I assume this collection will grow.

From MEI, see this short video presentation on the new specification including the new work on large data sets.

For further reference documents and some suggested resources see A Level Reform.

For easy access to announcements regarding Maths from the examination boards, use this twitter list. (You do not have to use Twitter to access the list).

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.”

This discovery led me to a treasure trove of resources from Educas for Mathematics at all levels, including GCSE – this definitely needs further exploration!

Jun 5 2016

Assessment and Feedback in Mathematics

Some further notes and additional resources on Assessment and Feedback…

The first few slides (slides 1-15) introduce Assessment and Feedback, looking at definitions. To summarise:

Assessment and feedback is something we do every day in our classrooms. It’s a two way process, students and teachers working together. The feedback needs to be helpful to the students in that they can do something with it to improve their learning.

Some further useful reading:

Quality Improvement Agency – Quick Start Guide on Assessment for Learning
Quality Improvement Agency – Assessment for learning guide
The Educational Endowment Foundation Toolkit includes Feedback
Dylan Wiliam – Is the Feedback You’re Giving Students Helping or Hindering?
Daisy Christodoulou has written a Guide to her posts on Assessment
A really useful read from Dylan Wiliam – The Secret of Effective Feedback
What makes great teaching? Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major

The next section of the presentation (slides 16-23) concerns teacher – student relationships, so important and something which comes up continually in my own conversations with students, note section 3 on Classroom Climate and also these comments from younger (age 11-12) students. This is all about knowing our students well and creating a climate where it is OK to be stuck, there is trust between teacher and students and the students know that their teacher has their best interests at heart. To quote Dylan Wiliam:

Without that relationship, all the research in the world won’t matter.

Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

Slides 32-38 illustrate some learning activities such as matching exercises which have built in feedback. For some useful resources for this type of activity try the following:

Tarsia for making your own matching activities – or you can find many Tarsia resources on TES Resources for example.
Spot the Mistake these activities can be a good alternative to peer marking
Treasure hunts and loop activities
Code Breakers on TeachitMaths

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free.
I have found many high quality resources here for all ages. Look at this activity on quadratic functionsfor example – this should really help understanding.

The next section (slides 39-45) is on questioning. Used wisely, well planned for questions can help us work out just what our students know.
Recommended reading and resources:

Questions worth asking – the Brighton & Hove Assessment for Learning Project
Assessment without Levels, note Daisy Christodoulou on using multiple choice questions
Multiple Choice Questions
Diagnostic Questions
Rich Questions in Mathematics
Here’s the diagram, what’s the question?

Retrieval Practice (Slides 46-49) looks at low stakes testing to help students recall information. Something I have found valuable throughout my teaching career and an area I am currently working on and will write further on in the near future. See:

Homework ideas are given on slides 50 to 53.

The next section is on marking (slides 54 to 63). See:

Consider a question by question analysis on tests; this can be very revealing as to which topics a class has found harder.
Look at examiners’ reports to give advice to students about what examiners are looking for.
A very interesting read from the University of Oxford and the Education Endowment Foundation is A marked improvement? (April 2016)
Plan for marking, what are you looking for in a particular piece of work. Consider Ross Morrison McGill’s (@teachertoolkit) 5 Minute Marking Plan
For simple day to day marking, ask your students to assess themselves using RAG123.

Further Resources