Slides from my session on Assessment and Feedback in Mathematics session at the Forum on Education, held at St Albans School on Saturday 28th May. Many of these slides are intended as discussion prompts and/or reference for later.
Category Assessment
Diagnostic Examination Questions
Just a short post to capture the links to Craig Barton’s and Simon Woodhead’s excellent question collections of examination questions on their Diagnostic questions site. Note that you will need to create a (free) account to follow these links. 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.
I found the AQA taster quizzes useful with my students.
And now we have their latest addition, a GCSE Mathematics collection for the new GCSE specification from Cambridge University Press which include worked answers at the end of the quiz. These are suitable for Foundation students and provide useful revision for higher students too.
..and hot of the press, Craig has added a quiz on his predictions for the higher calculator paper!
I created this Circles & tangents – Diagnostic Questions Quiz for use with my GCSE Year 10 class.
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
- National Curriculum UK
- Assessment Without Levels KS3 (11-14)
- GCSE Reform
- GCSE New Content
- GCSE New Content – Resources
- A Level Reform
- Results 2015
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!
Further references and reading
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
Multiple Choice Questions
Daisy Christodoulou on Life After Levels – conclusion
Daisy Christodoulou on Multiple Choice Questions
From researchEd 2015 and highly recommended, Daisy Christodoulou discussed the removal of National Curriculum Levels. Read Daisy’s post and see her slides on her blog you can also watch the presentation.
In that presentation, Daisy discussed the use of Multiple Choice Questions, something I have always liked using in my teaching. Daisy’s discussion of making questions harder by changing the number of correct answers reminded me of the, in my opinion excellent, Multiple Choice A Level papers which the then London board included in their A Level Mathematics examinations (London Syllabus B) (see an example below).
In the meantime, happily we do have access to some Multiple Choice questions online and I thought it would be useful to bring them together in one place.
Diagnostic Questions
I have written several posts on the excellent Diagnostic Questions site which hosts thousands of multiple choice questions written by teachers designed to address student misconceptions. I have found it worthwhile to discuss the wrong answers with students so we are all aware of the kinds of mistakes it is easy to make. It is a site I use regularly, teaching Year 10 about the equation of a tangent to a circle at a given point for example, I created a Desmos page and a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent).
Note the various collections on the site.
Some Advanced Level Pure topics are also covered on Diagnostic Questions; see for example this quiz I created on Logarithms and Exponentials.
Phil Bruce – Multiple Choice Starter Questions
On TES resources, author pbrucemaths has a brilliant collection of clearly indexed multiple choice starter questions, Phil Bruce has aimed to cover every objective on the GCSE syllabus.
Colin Billet – GCSE Multiple Choice Questions
Also on TES, Colin Billet has created multiple choice questions from old GCSE papers, one set is for the higher tier and another for foundation.
Mega Maths Quiz from Ben Cooper
For a superb collection of Multiple Choice questions, great for starters, plenaries or any time, head for Ben Cooper’s resources; see for example Mega Revision from Ben Cooper and 30 Number Starters. Resources by Ben can also be found on TES.
Don Steward – Rearrangement Steps
Don Steward has so many outstanding resources on his Median blog, including multiple choice quizzes, see this on rearrangement for example. Note that he also has a separate blog for GCSE practice resources. many of these quizzes are multiple choice.
From UKMT, the UK Maths Challenges provide a wonderful library of multiple choice problems; note the past papers where you will find questions and full solutions. Check also the Individual Challenges pages where you will find details of the challenge and see sample materials. Check the Junior Challenge for example. Note the addition for 2015 of extended solutions.
American Mathematics Competitions
Another brilliant set of multiple choice questions comes from another Mathematics Challenge, the American Mathematics Competitions (AMC). There are several competitions which increase in difficulty by student age. Problems and solutions are available. I do like this problem, a good one to use when teaching Systematic Listing Strategies perhaps.
Mathisfun has an extensive library of very clear diagrams and explanations and also multiple choice questions for most topics. Use the Index to find the topic you want and note that for most topics you will see some questions at the end.
mathisfun – Simplifying Square Roots – select image
As you can see from the Index all ages are catered for including older students; I have used the clear explanations and questions on finding the inverse of a 3×3 matrix with Further Mathematicians for example. Once you have selected an answer a complete solution is provided. Note the Question Database – some exploring to do I think!
The Who Wants To Be A Millionaire format can provide a fun way to present Multiple Choice quizzes. A Google search returns various resources and of course, provides you with PowerPoint Millionnaire templates you can adapt for your own use. Some highlights from that search, the Primary Resources files use a simple and clear format and William Enemy has described a resource on Great Maths Teaching Ideas which also uses that template; such a good idea to have all students answer all questions and add up their winnings! Another example – Algebra on TES.
For older students the old London A Level Multiple Choice papers could be very useful, I have scanned one of my old collection and will add more.
Oxford Maths Admissions Test
F
or an extensive collection of Challenging questions for Advanced Level students, we can turn to the Oxford Maths Admissions Test, note the menu on the right-hand side of the page, many papers and also solutions are available. I can never resist a quick graph on Desmos but note the very comprehensive solutions provided. For more Oxford MAT questions see this extensive collection on Underground Mathematics. These Underground Mathematics resources will provide so much more than the question in each case. Note the suggestions and solutions.
There are various options for creating your own multiple choice questions. That Quiz is simple but effective – all free and no adverts. There are many quizzes already available on a variety of topics, it is also possible to create your own quizzes. Teachers can register and add classes if they wish. You can search the many quizzes available, searching for Fractions, for example, led me to this quiz.
Testmoz
For an alternative way to set up a simple quiz try Testmoz. No registration is required. This has been written by Matt Johnson, an undergraduate student – the instructions are all very clear and you can check out the FAQ! (I love those FAQ! For example: I lost my quiz URL can you retrieve it for me? Answer: No). Try this test on Directed Numbers – log in as a student, the passcode is cy090610
More to Explore!
In Daisy’s talk mentioned at the beginning of this post she mentioned British Columbia questions in her discussion of multiple choice questions, a quick search led me to this Pre-Calculus paper for example...
If you want to write your own questions, you may find the references in Learning Scientists‘ post on Multiple Choice Questions useful (Smith, 2016).
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Bibliography:Smith, M. (2016) Weekly digest #4: How to write good multiple-choice questions. Available at: http://www.learningscientists.org/blog/2016/4/3/weekly-digest-4 (Accessed: 4 April 2016).
RAG 123
At Maths Conference 4 recently I attended a session on marking, Martin Noon’s “Marking for the Reluctant Marker”. you can find Martin’s resources from the session here.
The session was a reminder to me that I really wanted to try the RAG 123 idea, something I had already read about from Kev Lister.
I decided I wanted a very simple version without the word level anywhere and created my version as follows: Marking Guide (Word) Marking Guide (pdf). (We assess students on their “Engagement with Learning”, criteria they are familiar with.)
I also created a version for students to stick in their books for reference.
Student version RAG 123 student books (Word) RAG 123 student books (pdf)
Having tried this with my Year 9 class this week I am convinced this is something I want to try next academic year. Talking to a student later she said she thought it would be useful in other subjects too.
I explained the idea at the beginning of the lesson and let them know that I would ask them for their assessments at the end of the lesson, stressing that a 3 for understanding was a note to me that they needed help
Having collected the set of books it took a very short time to go through the set and see their I believe very honest RAG 123 assessment on the work on Functions we have been studying. I signed my agreement of their assessment. Some students also made additional comments to clarify / justify the reasons for their assessment.