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:

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 Algebra problem

WJEC GCSE Algebra problem

 

 

 

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 MathematicsAdvanced 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.


Royal Statistical Society Problem Solving

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.

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

 

 

edexcel-iteration

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.

MEI Interactive Scheme of Work

MEI Interactive Scheme of Work

Note also the addition of a Use of Technology page.

MEI on Integrating Technology

MEI on Integrating Technology

Diagnostic Questions – Quizzes

venn-example

To use the links in this post you will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

quiz-libraryI wrote earlier on the brilliant collections of Diagnostic examination questions available. As well as the various Collections, there is an extensive library of quizzes are available ready for you to use.

It is very simple to create a quiz of your own using the Instant Quiz Facility. The following slideshow shows how I created a quiz on logs and exponentials. To create a new quiz I make sure that the Instant Quiz has no questions currently in it so have got into the habit of clearing it out once I have created a new quiz. The instructions for doing so are included here.

To see the pdf version choose this file: Logs & Exponentials Diagnostic Questions and to view the quiz online then follow this link. I have created several quizzes, some simply to gather question types together; see for example the many questions on Probability and Venn Diagrams.included in this Venn Diagrams collection. I created a quiz of all these questions so I could download the pdf for reference. Included in the Further Resources section on Iterative Methods for Numerical Solution of Equations I have included the whole collection of Trial and Improvement and Iterative Methods diagnostic questions; the complete quiz is here.

Checking Insights for my Year 11 class I can see that students have completed many of the diagnostic examination questions. Two students in particular have been rather busy completing 253 and 484 questions, they both got 9s in their mock examinations! (We used AQA Practice Papers set 3).

There is also a mobile app which students can use to complete quizzes assigned to them by their teacher. Testing this recently it works on both my Android tablet and phone.

Extensive help on Diganostic Questions is available on the site. Clear step by step instructions are given.

GCSE Mathematics – Marking Mock Examinations

Further posts are also available on this theme.
See also GCSE Mathematics and Heading for High GCSE Grades.


For this first post – just some initial notes having marked the mock examination papers for my Year 11 class (UK age 15-16). This class is studying for AQA GCSE Mathematics and also the AQA Level 2 Further Mathematics qualification; they have completed the AQA specification and have taken a complete set of Practice Papers (Set 3) for their mock examination. (Teachers who offer, or are considering offering AQA maths qualifications can register for AQA’s All About Maths). AQA  recommend the use of these papers as mock exams as they reflect the balance and expected standard of their new assessment. The papers have been trialled with over 6000 students. Detailed mark schemes and  further marker training material is available to support teachers. Many of the points here apply for any specification.

ao123

Assessment Objectives

It is time consuming but provides a really valuable analysis and I feel time well spent on this new specification – For each paper, I am entering the marks for each question or part of a question into an Excel spreadsheet. I have used AQA’s Higher Papers AO grid so I and my students can see a breakdown of marks for AO1, AO2 and AO3. The grid is available with the Practice Papers.

AQA Higher Papers AO Grid

AQA Higher Papers AO Grid

 

 

This type of analysis clearly shows which topics and/or question types were more problematic for individual students as well as for the class as a whole. Using Excel with conditional formatting makes the information easy to interpret.

excel


Some AO1 marks have been lost simply because students have forgotten material or misread a question, perhaps reading too quickly and not noticing key words. Continuing to use mini-tests should help with this. It also strikes me that we can sometimes display some flashcards as a starter. We can also use starters for GCSE revision. Links to Flashcards from Tanner Maths and other high quality GCSE revision questions are in this post on Mathematics for Students. Last time I taught a year 11 class having done a similar analysis I made sure that questions on the most problematic areas from their mock examination featured regularly in our mini tests. We used Corbettmaths 5-a-day regularly which they found very helpful.

5-a-day


An understanding of graphs is crucial, it seems to me we should take every opportunity to provide a graphical representation where possible for all year groups. Multiple choice questions where students have to identify a graph could be used in KS3; students simply need a common sense approach: for example “if x is 0 what is y?” They need us to help them be confident that they can work it out – work it out, not everything is a memory test. Many students who were successful in identifying an exponential graph simply took a moment to work out a small number of coordinates. Encourage graph sketching in Key Stage 3.


On notation – something I have often seen before – students confuse notation for inverse functions with a reciprocal.


Naming angles and sides, it is so much clearer when students use what use what is given in the question – if an unknown side is BD then call it BD – certainly don’t call it c when there is a C elsewhere in the diagram! Encourage students to mark angles on diagrams – it provides very clear evidence.


Whilst the laws of indices may be understood, students can be thrown with algebraic examples, (32x)3 for example.


Constructions – one of my favourite quotes from a Principal Examiner, “No arcs, no marks!”


Some facts turn up so often, for example: 2 is the only even prime number, if you square a number it’s always a positive result – watch out for these – they turn up is so many different questions!


The value of a sketch: eg reflect a quadratic with a negative coefficient of xin the y axis and you’ll get another quadratic – also with a negative coefficient of x2.


I train my students in the ways of marking! They all understand isw – ignore subsequent working. So a harmless extra bit on the end of their answer may not matter. However there are times when extra information will lose you marks – for a question specifically asking about the spread of marks – don’t mention the median!


On my To Do list for my Year 11s and I’ll comment further on these in blog posts to come:

  • What are the most common things they have struggled to remember?
  • Plan the flashcards to display
  • Providing some model answers – annotating the questions, highlighting key words, clear explanations
  • Using the analysis of the papers, with other assessments to write helpful reports for Year 11 this term

See also GCSE Mathematics and Heading for High GCSE Grades.


 

Diagnostic Questions

To use the links in this post you will need to be logged in to the brilliant Diagnostic Questions site. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free. If you scroll down the page you’ll see that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

Diagnostic Questions provide a way of assessing your students’ knowledge and understanding, they are excellent for identifying misconceptions. Try for example the collections of GCSE 2017 examination questions from AQA, OCR and Pearson Edexcel.(scroll down each of the pages linked to for numerous quizzes on different topics on the GCSE syllabus).

Diagnostic Questions GCSE 2017 Collections

Diagnostic Questions GCSE 2017 Collections

Diagnostic Questions - GCSE examples

Diagnostic Questions – GCSE examples

You will find excellent coverage of topics new to the GCSE specification. You can also search all questions for a topic of your choice, for example a search on iteration will lead you to the whole collection of Trial and Improvement and Iterative Methods questions.

For bitesize revision assign your class a stream – just two questions a day in the run up to the exam.

When you are logged in to Diagnostic Questions, you can easily return to the menu using the menu icon on the left.
menu2
Returning to the collections, there are many – scroll down the page and you will see collections such as GCSE Maths Takeaway – 111 mini topic-specific quizzes covering all the content on Higher and Foundation GCSE (keep scrolling down the page for all the quizzes). These quizzes are ideal to use as baseline assessment before revising a topic, or as a measure of progress following the teaching of a topic.

For schools teaching AQA’s Level 2 Further Maths specification, the AQA Level 2 in Further Maths collection has 12 sections of very useful questions for this specification.

You will see choices for each quiz including the very useful option to download the questions as a pdf.
quiz-options

quiz-pdf
For example I created a quiz on Circles and Tangents, downloading this as a pdf creates this file. See the guide mentioned below for instructions on creating quizzes.

Extensive help is available to help you learn how to use the site. The Getting Started with Diagnostic Questions Frequently asked questions guide is very helpful for new users.

This post has looked at some of the questions available but note all the other features – start exploring!


 

 

 

Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.
Problem Solving

Note this page for a large collection of free Mathematics books.


Tools for Maths Teachers J HallJonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.
JHall site


The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

Sumaze Integral


In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.
Mathisfun Algebra Balance


tickUK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)


Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.

Low Stakes Testing in the Mathematics Classroom

To download:
Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)

Low Stakes Testing in the Mathematics Classroom (pdf)

Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016

There are many hyperlinks provided in the presentation, for ease of access these are also provided below:

Further Reading

Colourful Chi Squared!

Updating a presentation –  Colour in Mathematics led to a happy find!
Chi Squared examplw

When teaching the Chi Squared test I have often found that students sre not always clear on ttheir interpretation of the contributions to the test statistic. A worked example with a little colour to help where we look at the observed data. the expected probabilities and the chi squared contributions seems to work well . This exercise made me realise that a chi squared calculator I had previously recommended did not seem to be working, so fortunately I found a better one!

From Social Science Statistics this Chi Squared Calculator is for a contingency table with up to 5 rows and columns. It is very simple to use, enter the group and category names, then the data, choose the significance level and calculate.
Chi Squared Calculator 1
Chi Squared Calculator 2

A clear conclusion is then given:
The chi-square statistic is 10.2061. The p-value is .037096.
The result is significant at p < .05.

The calculator is included on the Statistics 16+ page of Calculators & Tools.

Note the many other calculators  for statistical tests  available on Social Science Statistics.

Looking at the new A Level Specifications – I can see that on the OCR MEI course the Chi Squared test for association is an option in the Further Mathematics A Level. The Chi Squared goodness of fit test has also been introduced. MEI have comprehensive information on the Mathematics specifications here including vey clear videos such as this on the Statistics strand. For further information on A Level Mathematics reform see A Level Reform and Resources.

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.


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.
MEI Sample Resources

OCR A Level Check In Test

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).


Royal Statistical Society Problem SolvingEduqas 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!