Underground Maths: Prepare for the new A Level

This will be so helpful for our preparation for the new A Level, I particularly like the Resource suggestions.

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

These of course are suggestions. There are so many outstanding resources on Underground Maths. In our department, like many others I am sure we will be exploring the resources and bookmarking our own favourites.

I have a series of pages on Underground Mathematics. This is a work in progress and I will be adding more content over the coming weeks. Some of my many favourites are on these pages…

Follow Underground Mathematics on Twitter or Facebook.
Note there is also a closed Facebook Group for teachers. We’d love to hear which Underground Maths resources you’ve been using, share your thoughts, ask questions or show your students work for discussion.

Mathematical Miscellany #12

On his outstanding website full of very high quality resources, drfrostmaths.com, Jamie Frost has now launched his new Homework Site.

Completely free this does a lot! Practise questions on National Curriculum and enrichment topics, choosing questions by topic and by diffculty, perhaps choose UKMT Maths Challenge questions as these are in the extensive database too. Students can practise independently and earn points and trophies. Teachers can set and monitor work using the powerful Data Analytic Feature. I will certainly be trying this with my students and easily uploaded my Year 9 class which took moments.

Something I alway do is add myself to my classes so I can get the student view, Colleen Student is a very busy student – she’s in a lot of classes! Jamie Frost has this as an easy feature already provided; you can be Demo McDemoFace (love the name!) in any class.

So here’s Demo McDemoFace practising her Algebra!

DrFrostMaths

What a sophisticated way to choose questions, not just the subject but the difficulty as well and additional skills to include or exclude.

So I can confirm that it is very easy to use as a student, Demo McDemoFace did a bit of Algebra and earned a trophy!

The interface for entering solutions is intuitive and very easy to use,

dfm3

Explore this site and sign up your students. Thank you Dr Frost from teachers everywhere! This looks superb. More to follow on this.


MEI have published this video (18 minutes) to introduce features of the new MEI AS/A level Maths specs, explaining the decisions made and how they support good teaching, learning and assessment. MEI’s YouTube Channel includes this and other helpful videos. This is helpful in its discussion of the new requirements for Statistics


On the subject of new A Level Specifications I am working on the series of pages on  A Level Reform. There have been several updates recently, a work in progress, there is much to do here and I am very much looking forward to working with the new specification. Using for example Desmos is something I do all the time anyway so I am delighted that the new specifications require the Use of Technology. Quite right too to assess the Use of Data in Statistics and the use of large data sets. MEI discuss their use of Data in the video above.


For schools who use AQA’s excellent Level 2 Further Mathematics Qualification, news from AQA states that this qualification has been extended and will be available for all students in 2019. AQA’s intention is “to redevelop it for first assessment in 2020 to ensure that it still fulfils its stated purpose of filling the gap between GCSE Maths and further studies in Maths at Level 3.”

My Year 11s this year have been studying both AQA’s GCSE 9-1 course and the Level 2 Further Maths; these have made a wonderful complementary pair. Many of the Further Mathematics questions have provided additional practice for the standard GCSE course. The extension will allow us some breathing space to keep working on the new GCSE course and take on the new A level specifications.


And finally..
This has been doing the rounds recently and illustrates beautifully that caution is required in our statistical analysis! Be a little wary of summary statistics! From AUTODESK Research, “Same Stats, Different Graphs… Note that you can download a detailed paper by Justin Matejka and George Fitzmaurice of Autodesk Research.

A Level (16-18) Resources – STEM Learning

STEM Learning hosts hundreds of Mathematics resources, resister free here. Log in to STEM Learning to download any of the resources here.

For the new A Level Specifications from STEM Learning comes this A level mathematics resource packages. To quote STEM Learning “Each resource has been hand-picked to cover key subject content in Pure, Mechanics and Statistics, as well as meet the overarching themes of mathematical argument, language, proof, problem solving and modelling.”

The package includes resources covering all the sections in the subject content given for Pure, Mechanics and Statistics in the Department for Education’s document: Mathematics AS and A level content. The references I have added to the images are those used in that subject content document.

STEM Learning A kevel mathematics resource packages

STEM Learning A kevel mathematics resource packages

Indices – Odd one out. Susan Wall

Each section begins with a reminder of the subject content and leads to several resources selected by STEM Learning, Have a look at Algebra: Indices, linear and quadratic functions for example.

Marking from Further Indices

I see some resources from Susan Wall’s excellent resources. (Resources from Susan Wall can be found in this Active A Level Mathematics collection on STEM Learning.) I do like marking activities such as the one illustrated here and have used many such resources successfully.

Exploring these resources I see familiar excellent resources such as those from the Standards Unit; note the Mostly Calculus resources and I have been happily side-tracked looking at some less familiar collections, Exponential Graphs for example which is part of the Exponentials and Logarithms collection comes from the Core Maths Support Program resources.

The collection includes a great variety of resource types, we have for example Michael Bawtree’s Prove It Algebraically

Prove It algebraically – Michael Bawtree

If you like this resource then take a look at the Virtual Textbook Secondary collection.

Turning to Mechanics and Statistics examples, we have a great variety of resources including some great use of Excel. I like this Descriptive Statistics resource very much, a combination of Excel sheets and work cards this should really help understanding. This and some of the other resources could be adapted for use with younger students too.


I see a Mechanics resource which is a link to one of the PhET smulations; I would recommend the HTML5 collection as this will work across platforms and devices.

Moments – Revision

These resources have been added to the A level resources page.

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


ofqual-April

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.


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.

See more in the Mathematical Miscellany Collection.

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.