Malcolm Swan

Professor Malcolm Swan, a legend in Mathematics Education died in April 2017 at the age of 64. Today, Tuesday 23rd May, the day of his funeral has been designated Malcolm Swan Day. Mathematics Teachers are acknowledging his work by using his materials in as many lessons as possible and tweeting pictures and examples using the hashtag #malcolmswanday.

MEI have dedicated their monthly magazine M4 to Professor Malcolm Swan. The magazine includes articles describing a particular item connected with Malcolm Swan explaining how that item an impact or influence on the writer’s own thinking or development as a practitioner. Note Carol Knight’s classroom resource in the magazine; some excellent ideas. I think I’ll start Year 9 today with the bus stop queue. As you can see Bus Stop Queuefrom MEI, this is taken from the Language of Functions and Graphs which you can download free from STEM Learning. Both the book and masters for copying are available.

I was fortunate to meet and talk to Malcolm Swan at an event for Maths teachers at Greenwich University some years ago. Having discussed a problem he had spoken about, always cautious about making sure it is permissable to store and share resources I asked him if it would be OK to upload his wonderful Improving learning in mathematics: challenges and strategies to my own blog. He said – “of course”. I think this should be compulsory reading for all Maths teachers. It is certainly something I have often referred back to.

My own favourites include the brilliant Standards Unit Resources. This is available from many sources, my go to source is appropriately I think from The University of Nottingham.
Home page

With all my examination classes on Study Leave I don’t have many lessons today but I do have Year 9. After we have started with the Bus Stop Queue which is a good choice having seen one or two misconceptions in a recent school examination I want to do some Algebra. Mostly Algebra has several resources which work very well indeed and I have used many times. Today I think we’ll have a little Number Magic! Note the html resources too, the Number Magic pyramid for example.
Pyramid

More later when Year 9 have tried this.

 

Bridging the Gap – Student Guide

From OCR, a marvelous teaching and learning resource:
Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide (scroll right down OCR’s page to Teaching and Learning Resources).

I love this resource, the very first example made me smile; I have been teaching for a long time and I think I have been saying this to so many students all that time!

OCR guide eg 1

OCR Student Guide – Bridging the Gap

With sections on Algebra, Trigonometry and graphs including exaamples, question practice on key topics and suggested reading before starting the A Level this will be so valuble for students.

OCR Student Guide

OCR Student Guide – Bridging the Gap

Thank you OCR for making this available as a Word document, I rather like the look of some of these examples for my excellent GCSE students who are studying both Maths and AQA’s excellent Further Maths Level 2 qualification. I feel an edited version coming on!

The A Level pages have much useful information and I will be developing these further over the coming months. This resource has been added to the A Level Resources page, also to the OCR page.

This is quite simply an outstanding resource for students (and their teachers!). Many exercises are provided and the answers are all at the back. OCR have very helpfully provided the document as a Word document.

OCR Student Guide GCSE to AS & A Level

OCR T&L Resources

Mathematical Miscellany #13

TES Resources
From TES, comes a collection of esources hand-picked by the Tes Maths Panel, organised by topic area and selected for their relevance to the new specifications. This is an extensive collection of quality resources. Checking Probability for exmple we see an excellent selection of free resources, including Venn Diagrams for teaching and learning.
Venn Diagrams TES
This Venn Diagrams post with many resources for teaching this topic has been updated to include the TES collection.


Another update to the Venn Diagrams collection comes from Transum.

Venn Totals Transum

Transum

Try Venn Totals 4 different levels of exercises which can all be checked are available. Level 1 – Reading information from a Venn diagram containing two intersecting sets. Level 2 – Reading information from a Venn diagram containing three intersecting sets. Level 3 – Adding information to a Venn diagram containing three intersecting sets. Level 4 – Adding information to a Venn diagram containing three intersecting sets with some problem solving required. There are also exam style questions, to see the worked solutions a subscription is required.

I have written on Transum before, with its very clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning the site is very easy to navigate. The resources are very clear and attractively presented, they display well for demonstration in class as well as being very good for self study for students.
Look at this series on Transformations for example:
Transformations
Level 5 is on transformations and matrices, very useful for older students studying Level 2 or A Level Further Maths.


This GCSE Exam Preparation resource from JustMaths made me smile, a lovely mix of humour and some very useful reminders.
Preparation

Mel’s inspiration came from Edexcel’s Maths Emporium Guides to Life: GCSE Mathematics Examinations. Brilliant!
Edexcel GCSE Maths Guide to Life


On the subject of student advice, one of my Year 11 students asked me to confirm for her which transformations are examined at GCSE, a slight change here from the old spec hence her question. I answered her question with a post on Mathematics for Students as I thought it would be useful for others. Transformations of graphs includes Desmos pages for reflections and translations as required at GCSE (see GCSE content on Algebra:

13.sketch translations and reflections of a given function.

The post also includes a couple of examples on finding the equation of the transformed graph.
reflections-graphs

Another query was just a quick reminder on the required constructions.
bisect angle Math Open Ref


A reminder from Mathematical Miscellany #12, I am very much looking forward to trying Jamie Frost’s wonderful homework site with my Year 9 group.
dfm


And finally another reminder because I think it is such an important resource – just in case you missed the news that Underground Maths are helping teachers everywhere who are preparing for the new A Level. Many brilliant resources suggestions are clearly mapped to the subject content for the new A Level.
resources-by-specification

 

 

 

 

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.

In Class …

Everybody is revising, though review of work is a regular activity for all my students all year round. I have been using a wide variety of resources detailed in the posts Revision Time 2017 and Mathematics Revision Resources.

Some recent favourites with the students:

My Year 9 and my Year 11 students all like the exam collections on Diagnostic Questions. Looking at the Insights for my classes I can see they have answered thousands of questions between them. I find it very quick and easy to create a quiz which can provide a great starter. For Year 11 I have used questions where I can see students have had the most misconceptions.


The Maths Teacher

Many of my Year 9 students as I do really like David Smith’s ‘The Maths Teacher’, which includes GCSE exam questions by topic at both Foundation and higher tier. What I particularly like about David’s site is the choice between video, the video transcript or straight to questions and worked solutions. One of my year 9 students told me she had been using the various formats. She has been trying the exercises and really appreciating the very clear written solutions which she can then check with her own. She has also used the video lesson where she has been unsure of any exercise questions.

Another site which Year 9 have found helpful for revision is Transum Mathematics. A student asked for some practice questions for factorisation and I remembered the excellent Algebra activities on Transum; lot’s of factorisation practice, note the various levels.

Transum Mathematics


Questions which are working really well for Year 11 include AQA’s AO2 and AO3 questions which I have included on the AQA GCSE page and Edexcel’s Problem Solving questions – included on the Edexcel GCSE page. Edexcel have added another set of problem solving questions – 24th April. Note too Edexcel’s very useful Maths Emporium Guides to Life: to  guide for GCSE Mathematics Examinations. This applies whichever board you are using. My Year 11s will enjoy that this week!

GCSE Advice

Funny – but such wise exam advice from Edexcel

More resources which work very well are our sets of questions we have created using the enhanced results analysis. To help your thinking have a look at the AQA’s Guide to AQA Enhanced Results Analysis  

AQA (use the login button at the top of the screen and then choose e-AQA box).
Edexcel Online

My Year 13 students have done many different past papers between them; I find delving into the archives to find old papers with some of the same content very useful, also using papers from other exam boards has been helpful.

 I do like the fact that for GCSE the subject content is common for all boards; from September 2017 this will also be true for A Level. We can use resources from all the exam boards!

Mathematics Revision Resources

I wrote recently on Revision Time 2017, noting several updates as well as checks of the revision series of pages. In this post – some more additions:

For GCSE, from Steve Blades on his excellent m4ths.com, have a look at his Right or Wrong Challenge, a series of 10 quick questions for Foundation GCSE students. Steve Blades has designed and written this section to test students understanding of the concepts involved in GCSE topics. Watch the video as Steve works through 10 questions and work out which answers are correct. It strikes me that many of these questions would make an excellent revision resource for younger year groups too – a great starter for my Year 9s I think! Note that Steve has very helpfully provided a pdf document with all the questions, (scroll to the bottom of the page).

I have mentioned reources from m4ths.com elsewhere, on the exam questons and solutions page I have included Steve’s eBook GCSE Higher wordy questions. On the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book. And of course don’t forget his GCSE Help Book, included here for students.
m4ths


PixiMaths

On Danielle Moosajee’s piximaths.co.uk you will find an extensive collection of outstanding resources for teaching and learning and revision. The Revision Resources are very clear and comprehensive revision booklets, packed with things to remember and examination questions by topic, answers are also provided. Five booklets are available for students aiming at grades 1, 3. 5, 7 and 9.

PixiMaths Problem Solving

Also from PixiMaths resources I really like the set of Problem Solving Booklets by curriculum area, all with very clear fully worked answers. Danielle has created these using collated Edexcel questions that will be on both higher and foundation tiers so can be accessed by most students. Like the first resources from Steve Blades mentioned above I think there are many useful questions here for younger year groups. We should clearly be looking at problem solving skills with all our students.



From Danielle Bartram, on Miss B’s Resources see her GCSE Maths Passports Grades 1 to 9 Revision. Five different passports are available.


For A Level I have two pages in the Revision series, MadASMaths with it’s excellent series of revision questions and solutions increasing in challenge and UK A Level (16-18) Exam Quesions and Solutions with resources good for all examination boards.

From Underground Maths, to challenge students I find the Review Questions excellent, so many excellent questions from old A Level papers clearly organised and with very full solutons.

Calculus meets Functions


From the Underground Maths team have a look at the Bundle Tying it together, which looks at effective mathematics revision. To quote Underground Mathematics “The resources in this bundle encourage students to bring together their experiences in multiple areas of mathematics, helping to reveal and reinforce connections between a variety of mathematical ideas and problem solving strategies.” Note the associated recorded webinar. I particularly like the fluency exercise Pick a Card which will be a great way to revise Quadratic Functions, linking together many student experiences in Algebra, functions and graphs; this is also useful for high ability students. What’s the shared area for these two circles? another resource  in this bundle illustrates so well how a good diagram can help.


Revision pages for students.

UKMT Maths Challenges

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 extended solutions.

As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.

UKMT Extended Solutions


Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)

UKMT Diagnostic Questions


Another way to access Maths Challenge questions by topic for Junior, Intermediate and Senior is from Dr Frosts’s wonderful website full of outstanding resources.

DrFrostMaths.com

DrFrostMaths.com

Very conveniently it is possible to download zip files of questions by topic.


UKMT Skills Builders Topics

From UKMT, try their free Skills Builders, on-line problem solving questions for both junior and intermediate level. Note the user guide, which applies to both Junior (age 11-13) and Intermediate (age 13-16); this offers clear step by step instructions with screenshots.

jmc

UKMT Maths Challenge – Junior


Another possibility, generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.

UKMT Mathster

UK Maths Challenge Online Quiz – Mathster


Team Challenge

Links for students, including advice for young mathematicians are provided on Mathematics for Students. Further outstanding resources from UKMT include the Team Challenge resources.

The UK Maths Challenges are included on the Problems & Activities page.

For more sources of multiple choice questions see this post.

Daisy C Multiple Choice

Daisy Christodoulou on Multiple Choice Questions


Mathematical Miscellany #11

Desmos Geometry
An exciting space to watch! Chancing upon this tweet I saw that indeed we have an exciting possibility here as Desmos does Geometry! Early days right now and this is still in early beta.

Have a play – it’s very easy to use. There are some examples to investigate. Excellent to have vectors as an option in the line tool and I like the way that once a line or segment is drawn construction options are available.

See the Desmos blog post The Desmos Geometry Tool. Such a thoughtful post. Reading it reminded me why this is one of the few websites I use on a daily basis to help my students learn.

First, our goals are different than those embodied by most of those other tools. When we design products, we design first for students who struggle with math and we assume they may also struggle with technology. We strive for a student’s first creation with our tools to feel effortless and joyful. For that reason, our geometry tool has a far shorter list of features than some of those above. We will carefully expand that list over time, never trading power for ease-of-use.

I have always said that what I like about Desmos is the ease of use. A young student can just ask for a graph of a straight line and my Year 13s can play with Polar Curves for example.


With revision for examinations very much in mind at this time of year, have a look at Tying it together, a bundle from Underground Mathematics which looks at efficient revision for mathematics; to quote Underground Mathematics: “The resources in this bundle encourage students to bring together their experiences in multiple areas of mathematics, helping to reveal and reinforce connections between a variety of mathematical ideas and problem solving strategies”. (And note the free webinar on April 19th looking at revising effectively and sharing resources for AS revision.)


Being very conscious of our first students aiming for grade 9 GCSE I particularly like the fluency exercise Pick a Card which will be a great way to revise Quadratic Functions, linking together many student experiences in Algebra, functions and graphs. What’s the shared area for these two circles, another resource  in this bundle illustrates so well how a good diagram can help.


Pick a card is a Fluency Exercise, Note that you can search resources in many ways including by type.
(More on Underground Mathematics).


Staying with the subject of exam revision, The Learning Scientists have an important post here on studying with Retrieval Practice. For further valuable resources to support study techniques see the excellent downloadable materials on study strategies. Note how each strategy is backed up by research.
study-strategies-research

retrieval-practice-learning-scientists


MEI Maths Item of the Month example

From MEI this curriculum mapping for their Maths Items of the month resources is a great resource, both for GCSE and A Level. (This has been added to the A Level Resources page.)


See all Mathematical Miscellany compilations.


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