Transition Time

It’s Transition time of year, with many students having completed their courses and about to embark on a new stage in their education. A reminder of some valuable resources to help their learning.

Mathematics for Students

As we come to the end of an academic year and look to a new one, it will be a time of change for many students. Perhaps you have completed GCSEs or equivalent qualifications (UK age 15-16) and are about to start on your A Levels or perhaps you have completed those and are about to start studying Mathematics at university.

To be in a position to begin your new courses well you should be thoroughly familiar with the essentials of the work you have studied to date. At whichever level you are studying your Algebra should be at a standard where you can manipulate expressions with ease.

Some resources to help you prepare and will be useful reference material for you during your course…

OCR – Bridging the Gap – A Student Guide

For students going on to A Level then the best thing you could do is use…

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ATM Resources

From the Association of Teachers of Mathematics, comes a wonderful range of resources.
Publications include activities for students of all ages. As a thank you for reaching 15000+ Twitter followers ATM have created a FREE open access 43-page resource document. This offers a brilliant collection of ideas and activities.

Looking at the contents we see ideas for the youngest students through to Advanced Level students.

ATM aims to develop a creative and thinking approach in mathematics learners which is evident from its publications. Many free Open Resources are provided on ATM’s website and all publications can be found in the shop.

I do like explorations with Geoboards, so headed for Pentagon Areas by Geoff Faux (page 9).

Pentagon Areas – Geoff Faux

I can stay with square dot grids and try Overlaps from Preparing for GCSE Problem Solving.

I do like ATM publications and have successfully tried many of the ideas in the classroom over a long teaching career. I used Points of Departure in the 80s and I’m still using it today!

Do explore this collection and also the Open Resources. For many more problems to explore, try Question of the Week for example.

For some discussion on two problems from Eight Days a Week, have a look at this Twitter chat. (#beingmathematical)

We have much to explore! Thank you ATM!

End of term…

Relay from Chris Smith

The end of term approaches, so time for the usual complete check and update for the End of Term Activities page.

I will, as usual, be using this great Summer Relay from Chris Smith; students can have a more informal lesson but still do some useful maths! See the complete set Relays from Chris Smith. 

If your students have their own devices, don’t forget all the excellent free apps available. Note MEI’s Sumaze for example, or from Naoki Inaba we have Area Maze.

For many more ideas including pencil and paper games, see the updated End of term activities page.

Nrich – Sprouts

Area Maze

MEI – Sumaze

Perhaps try some of Clarissa Grandi’s wonderful, fully resourced mathematical Art lessons.

Clarissa Grandi – Artful Maths

For more end of term activities, see the End of Term Activities page.

 

 

 

Retrieval Practice – it’s not all about quizzes

For my latest slides on Retrieval Practice from the ATM & MA London Branch Summer Conference, please see these files:
PowerPoint or pdf

Retrieval Practice is not all about quizzes – low stakes quizzes play an important part but there are many other ways to help your students get the learning out! We spend much time thinking about how to get the learning in – think in your lesson planning how to get the learning out of your students! How can you help them actively recall and apply their learning?

Don Steward has published the slides from his wonderful session on his Median blog. So many good ideas! Thank you, Don.

The slides include all the various resources I mentioned including SENECA Learning which looks excellent; I will be writing more on this in the coming weeks.

Join the conversation on the book Make It Stick on Facebook.

If you are looking for particular resources or have questions/suggestions/observations, please contact me.

The slides include all the various resources I mentioned including SENECA Learning which looks excellent; I will be writing more on this in the coming weeks.

Highly recommended is the Retrieval Practice website from Dr Pooja K. Agarwal.

SENECA Learning

Links to the resources and further reading:

From The Learning Scientists see these valuable resources to support the techniques described here. Note the excellent downloadable materials on study strategies. Each strategy is backed up by research.

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Rosenshine’s ‘Principles of Instruction‘ provides a very valuable list of research strategies teachers should know about and I believe it is well worth asking ourselves if we are incorporating these strategies regularly into our lessons. This UNESCO pamphlet on the Principles offers further reading and for a very clear summary of these principles of instruction, see from TeachingHOW2s this excellent summary; stick this poster on your walls! (Alternative version – yellow background).

Links and Further Reading

• Is the Feedback You’re Giving Students Helping or Hindering? Dylan Wiliam, 2014
• What Makes Great Teaching Review of the underpinning research.Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major, October 2014
• Students on good Maths Teachers
• Aural Tests
• Desmos Graphing Calculator
• WolframAlpha   
• Learn to use WolframAlpha includes many useful examples including queries for younger students.
• Here’s the Diagram, What’s the Question?
• Algebra Snippets
• Good Mathematicians Can Go Backwards!
• Problems and Activities
• SSDD Problems
• TES Collective Memory
• A Box – GCSE Revision Activity 
• Underground Maths

A really useful source of questions which can be used for Aural tests are the mental tests from CIMT; these are included with their resources for Years 7, 8 and 9 and also for GCSE. For Key Stage 3 (ages 11-14) scroll down this page for the Year 7, Year 8 and Year 9 course material, the resources include mental tests as part of the teacher support material. On the GCSE page scroll down to the teacher support material and note the mental tests available for most units, see this on Formulae for example.

This Custom Starter from Transum allows teachers to select the number of questions and the topics to include; scroll down the page and choose the topics you want from the Concept Selection.

It is possible to save a particular selection of topics as the URL for your selection will be generated. It is also possible to drag the panels so your questions are displayed in the desired order. The beginning of a lesson can be an ideal time to review previous learning, starters like this can be ideal.

The excellent MathsBot site also provides Starters which can be customised.

Included with Spot the mistake we have excellent resources from Andy Lutwyche, look at his excellent Erica’s Errors series and if we check on TES, these free resources also include plenty of errors from Clumsy Clive! I have found these work really well in class.

A very useful resource is this booklet of sample questions which has been created as part of a project funded by the NCETM on Questioning the use of Bloom’s Taxonomy. I have tried many of these in the classroom, they really make students think and encourage a deep understanding. Not just for Maths but applicable to any subject I’d recommend very highly the Brighton and Hove Assessment for Learning  project – Questions worth asking. This includes many practical suggestions for the classroom and concludes with a self analysis. The project includes the use of Bloom’s Taxonomy as an aid to thinking about the level of challenge / thinking required for a question.

Further Reading

• • Research in 100 Words, Chris Moyse
  • Improving Students’ Learning With Effective Learning Techniques: Promising Directions From Cognitive and Educational Psychology John Dunlosky, Katherine A. Rawson , Elizabeth J. Marsh, Mitchell J. Nathan, and Daniel T. Willingham
  • Retrieval Practice website subscribe (free) for research, resources and tips

Guides from retrievalpractice.org

• Retrieval Practice Library (guides to download)
• Retrieval Practice Guide to Make It Stick book    
• Join the conversation on Make It Stick on Facebook
• What Works, What Doesn’t 
• Highlighting is a Waste of Time
• Learn How To Study Using Retrieval Practice, Learning Scientists,  June 2016, 
• What is worth reading for teachers interested in research? Professor Robert Coe, June 2016
• 7 Recommendations to Improve Student Learning based on Pashier et al, 2007 – Organising Instruction & Study to Improve Student Learning, Belmont Teach
• Test-Enhanced Learning in the Classroom: Long-Term Improvements From Quizzing – 2011, Henry L. Roediger III, Pooja K. Agarwal, Mark A. McDaniel, and Kathleen B. McDermott Washington University in St. Louis, 2011
• Retrieval as a Memory Modifier: an interpretation of negative recency and related phenomena.
  Robert A Bjork, 1975
• Who’s the most tested one of all? Tim Oates, 2016

Mathematics – Irish Leaving Certificate

I recently mentioned that the brilliant Maths Emporium team have been busy with the filing cabinets! You will find many International GCSE Mathematics papers. The Mathematics Emporium is a free website intended for the use of teachers of mathematics in secondary schools, wherever they are located and regardless of what awarding body they use.

Maths Emporium

On the subject of papers from beyond UK shores, from Ireland, we have the Irish Leaving Certificate Qualification.

Students normally sit the Junior Certificate exam at the age of 14 or 15, after 3 years of post-primary education and from the Graduate Recruitment Bureau A Level Equivalents Guide we see that An Irish Leaving Certificate is roughly equal to two-thirds of an A Level and is the main basis upon which places in universities, institutes of technology and colleges of education are allocated.

These qualifications with their very clear mark schemes provide us with another source of very useful examples. Once you have clicked the checkbox to verify that you have read, understood and accepted the terms and conditions, you can search for papers and mark schemes by subject. As well as marking notes, an excellent feature of these mark schemes is the model solutions provided.

For example, if we look at the Junior Certificate 2017 higher paper, question 6 is on Venn Diagrams; the mark scheme provides a model solution.

Looking at the 2017 Leaving Certificate paper, I see, for example, differentiation from first principles and De Moivre’s Theorem. Again, model solutions are provided as part of the mark scheme.

I mentioned the Project Maths site in a previous post, this is an Irish site supporting Mathematics teachers. These teacher resources are for Leaving Certificate students. A site well worth exploring, looking at Algebra we see for example under expressions:

• Pack of visual linear patterns
• Pack of visual quadratic patterns

The student resources include many activities with accompanying GeoGebra files.

Junior Certificate resources are also available.

These whiteboard templates caught my eye, simply download the file, project it onto your whiteboard, use the interactive menu to choose the background you need and start writing!

Project Maths Ireland – Whiteboard Templates