Underground Mathematics provides such an outstanding collection of resources that I have begun to create a series of pages on the site. The resources are not only good for Advanced Level but for GCSE students too, particularly for students aiming at the very highest grades. This series of pages is very much a work in progress which I will be updating regularly.
I have used many of the Review questions for my able GCSE students. As you can see from the descriptions of resorce types, the review questions are ideal for the new GCSE specifications as they have been selected to test students’ understanding of one or more topics and to exercise their problem-solving skills. The questions which have been chosen require non-routine thinking. You can browse all the Review questions or narrow your search by question type; note the O/AO-level questions which are questions from old papers. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.
If you create an account you can easily save and organise your favourite resources. This list of favourites can be easily downloaded as a csv file. To further organise your favourites you can create subcollections.
This too is a work in progress, I will create a collection of resources I believe are particularly useful for GCSE. I have several Algebra favourites so far. This Excel file has hyperlinks to all the resources shown here. algebra-gcse-9-1. Alternatively this pdf file also has the relevant hyperlinks. algebra-gcse-9-1
As more news and documentation has become available for new specifications I have reorganized the A Level Reform series of pages.
Further Maths Supposrt Programme Summary of Changes
With any change of specification I have always found any documents on summaries of the changes and also mapping documents very useful indeed. Clearly much of the content is still on the new specifications and resources we already have can be used again.
With a greater emphasis on modelling and problem solving in both AS and A Level specifications resources such as Underground Maths with its aim of “Enabling all students to explore the connections that underpin mathematics” will be very valuable. This page highlights useful resources.
The Specifications and Support page includes links to the specifications for all the examination boards, including specimen materials. Other supporting documentation and news updates. Can also be found on this page. We see that OCR’s AS Specifications are now both accredited as well as the MEI A level Specification.
There is also a separate Edexcel page; I recommend signing up to the Mathematics Emporium. I suspect some of those old A Level papers might come in handy!
This is an ongoing project; pages will be regularly updated and new pages added.
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.”
I 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.
2017 Year Game from mathforum.org
It’s that time of year again and we can play the 2017 Year Game in our January lessons.
On Simon Job’s MathsClass, he suggests writing a number sentence under the date; as you can read on his blog he endeavoured to write the number sentence using the digits of the date in order in 2016. It strikes me this idea could be used as a starter, ask the students to come up with such a number sentence.
2017 is a prime number and as we see from the WolframAlpha properties below, in particular a Pythagorean prime, so another source of starters and investigations perhaps? The last time the Year was a Pythagorean prime was 1997.
We can always turn to Number Gossip from Tanya Khovanova for information on properties of a number.
We can also look at WolframAlpha which provides further information including what 2017 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. Some possible starters for January lessons here I think!
The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.
For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.
We should make a calendar for 2017.
Really good if you happen to be teaching Nets. From trol, Teacher Resources on Line.
Wishing educators and students everywhere a very Happy New Year.
Resolutions for (Maths) teachers.
Direct download – Powerpoint File: 2016-2017-resolutions-for-maths-teachers
or as a pdf: 2016-2017-resolutions-for-maths-teachers
(The presentation hyperlinks work in both formats.)
A new year tradition of my own is to review my resolutions for the new Academic Year so the presentation here has been checked and also updated where any new information is available.
For readers familiar with this presentation, note updates include:
(Images link to relevant information)
A reminder about all the brilliant Diagnostic Examination Questions.
Remember Carol Dweck’s wise words.
‘The outcomes are natural byproducts of engaging in good practice’.
There have been several updates to the specification series of pages since September.
Note this post on Assessment Updates with a December presentation from Ofqual on GCSE grading and A Level news from OCR who have had a specification approved. heir
More on diagrams…
How to Study.
The Learning Scientists have published their excellent and important video on Study Strategies.
A complete update of recommendations for students.
Reading and Research
I have made several updates to this series of pages, particularly the Research page which includes Espressos from Cambridge Mathematics.
….and finally, an updated 11 Commandments of Mathematics.
The presentation has also been added to my Presentations Series.
I have several references in various places on this blog to some great visualizations.
Time to put them all together!
Jeffrey Ventrella’s Composite Number Tree
From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.
Stephen Von Worley
Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled.
Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s ptolemy.co.uk. Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.
Alec McEachran’s Furbles
Note to get to your chosen Furbles, complete your requirements and press Go!
Alec McEachran – Primitives
Returning to the factorisation theme, note that Alec McEachran’s ptolemy.co.uk is also home to the Primitives application. As you can see from his site, you can read Alec’s article he wrote for the ATM magazine Learning About Primes.
Fawn Nguyen – Visual patterns,
On the subject of Diagrams generally I have several posts on the subject. You can see Fawn Nguyen’s lovely Visual Patterns in Diagrams in Mathematics.
GCSE 9 to 1 Grading
From Ofqual, December 2016, very usefully note that a clear transcript of this session is available from Ofqual as a 5 page pdf document
…and read the 9 to 1 news!
See also Comparing like with like in 2017 and note too this recent statement from AQA on Grade Boundaries.
I have updated the GCSE Reform page. Also kept up to date with further updates to come shortly, see GCSE New Content.
A Level Mathematics
Use this Twitter List to see updates from all the exam boards. As you can see @Ofqual are making announcements about accredited specifications. OCR Maths has been accredited.
I have updated the A Level Reform page.
Really important – talk to your students about how to study not just what to study.
A common theme of my own – Mini Tests / Retrieval Practice.
For valuable resources to support the techniques described here, see: The Learning Scientists. See their blog for more information and note the excellent downloadable materials on study strategies including Retrieval Practice.
..and appropriately – last words from a student:
Jane Hart is the Founder of the Centre for Learning & Performance Technologies and 2016 marks the 10th year of her annual Top 100 Tools for Learning list. Jane has put together all the presentation slidesets as well as an alphabetical list of ALL the tools which have appeared on any of the lists.
The 2016 slideset is shown here.
Note from Jane’s overview she has done a finer analysis for 2016 including the Top 100 Tools For Education (for use in primary and secondary (K12) schools, colleges, universities and adult education.)
Back in April, I wroye about my own choices for 2016 and I am always interested to see where my own choices are in Jane’s list.
|CY 2016 votes
||Personal Learning & Productivity
||Place in Top 200 2016
||Place in Top 100 Tools for Education 2016
Those were my own 2016 choices as top tools for learning because these are tools I use all the time in my job, both in my teaching and in my role as a senior leader. Note that we are not discussing subject specialist resource sites here, but tools for education generally; I think it is very useful to remind ourselves of Jane Hart’s own definition:
“Any software or online tool or service that can be used for your own personal learning or for teaching or training”.
Two more very useful views that Jane has compiled is this Quick View showing the place in the top 200 list, compared to against the Top 100 Tools lists for Personal & Professional Learning (PPL100) for Workplace Learning (WPL100) and Education (EDU100) and the Movers and Shakers.
Looking at the Movers and Shakers, I see WolframAlpha has crept in at 198 on the Top Tools list, so I wasn’t the only one who voted for it! Quite rightly Google Forms is another new entry; I think my own vote for Google (search) was actually also a vote for Google Docs / Google Apps for Education / Google Calendar! Google forms is such a good way to collect feedback. See for example slides 63-83 for Student Feedback on Low Stakes Testing. where I used this form.
Noted in the Movers and Shakers list are tools which have jumped up more than 15 places. Trello is indeed good for organising information and is easy to use for collaboration. With my interest in retrieval practice I want to revisit Quizlet. Also on my list is One Note, though not to replace Evernote but complement it. More to explore – Canva and I see Richard Byrne has posted on Canva new features.
The home of the Teddy Bear and a whole lot more! The wonderful Underground Maths site has a whole new station – Circles.
Really challenge your students with the resources here.
I rather like this review question on circles:
Can we show that these four points lie on a circle?
Good for A level mathematicians – also for my Year 11 Level 2 Further Maths Students.
And of course – Desmos to illustrate.
This diagram could make a rather nice starter…
See all posts in Underground Mathematics.