With the new school year fast approaching, I have reorganised some pages and resources in the never ending quest to make things easy to find! This is an ongoing project.

There are several additions to the Lesson Planning Pages.

A new series on Tools and Calculators includes for example GeoBoard Activities with GeoBoard resources.

There are many excellent PhET simulations from The University of Colorado Boulder. Look at Trig Tour for example. Note that this is HTML5 so available across platforms.

I do like to use resources in class that my students can use at home, so for example in the calculators and tools collections (see Calculators – Collections) under Equations – Linear and Quadratic, we have from Mathisfun this very clear and easy to use interactive illustrating the solution of linear equations.

You will also see on the same page this calculator from Math Warehouse which shows the solution to any quadratic equation with full working using the formula.

Math Warehouse

The Problems and Activities page has had updates including the addition of Transum, a site I like a great deal as do many students. From Transum, we have the very wel known Maths Starter of the Day. Note that there is a complete index of starters including the topic of the starter. The Transum site is easy to navigate, there is a clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning. The example shown here is one of the Algebra Activities found on this page.

Transum – Algebra Activities

An essential part of every lesson is of course that we check that students are indeed learning, hence my reminder on Study Strategies on the Lesson Activities page.

The Learning Scientists

Time for a series of new calculator pages to make it easier to find information and resources on calculators. The pages in the series:

• Casio fx-85GT Plus & fx-991ES PLUS
• Casio FX991EX-Classwiz
• Casio Graphical Calculators
• Texas Instruments
• Mathematics for Students – Calculators
• Use of Technology – A Level

Some highlights from these pages…

The collection includes manuals from Casio and Texas and also some very clear guides from Dr Frost.

There are some excellent step by step instruction videos on using the Casio FX991EX calculator.

MEI have many tasks for older students using Casio Graphical Calculators (they also have tasks using GeoGebra and Desmos).

On the Mathematics for Students pages you can find everything from a game to help students understand order of operations to a Normal Distribution Calculator.

Following an earlier post on multiple choice questions, I thought it would be useful to put a selection together for older students. I have reproduced this below and it has been added to the A Level 16+ series of pages.

From OCR (MEI) their  Foundations of Advanced Mathematics level 2 qualification covers arithmetic, algebra, graphs, trigonometry and statistics. Assessment is by a two hour examination which consists of 40 multiple choice questions. As OCR suggest these questions could be used for diagnostic tests.

Choose Past Papers, mark schemes and reports. Papers and mark schemes from June 2007 are freely available .

We could of course illustrate the solution well with a little use of technology!

A source of multiple choice A Level questions, particularly for Pure Mathematics is Diagnostic Questions; see for example this quiz I created on  Logarithms and Exponentials.

Dr Frost Maths

The UKMT Maths Challenge questions are excellent for students of all ages. This post includes a selection of links and resources to access the Maths Challenges.

For superb resources for the Oxford Admissions test multiple choice questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.

A trip down memory lane! (Edexcel’s Emporium has some papers from this era.)
University of London June 1986 Mathematics 1

At the start of my teaching career I really liked the first paper of the Mathematics A level from the University of London School Examinations Board – thirty multiple choice questions to complete in one hour, 15 minutes.

For questions 1 to 20, candidates had to select one answer from 5 and for questions 21-30 the instructions were as follows.

University of London June 1986 Mathematics 1

The pdf file here has the paper, followed by the exam board answers followed by notes from the 1986 version of me! These days I would illustrate with Desmos and/or WolframAlpha for example as well where appropriate.

Note the comment from Graham Cummings below, there are further papers available in the Edexcel’s Emporium:

The Emporium has some 17 multiple-choice question papers from the period 1988-1992 – by no means a complete set, but they range across the Mathematics, Further Mathematics, Pure Mathematics and Applied Mathematics syllabuses. You can find them in the “Pre-C2000” cabinet within GCE AS/A Level.

Signing up to Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you use. Register for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number.

So – back to school again and I thought I would make a final and rather important update to Resolutions for (Mathematics) Teachers. Reading John Hattie’s Visible Learning for Teachers is such an important reminder that we should really be looking at the impact of all we do on our students. We might think a particular method or resource is amazing, but do we think so because we have considered very carefully how it will help our students learn?  
For a summary of the book, read this from The Main Idea.

The five dimensions of Expert Teachers Hattie identified were based on a review of the literature.
In summary:

1. Expert teachers identify the most important ways to represent the subjects they teach
2. Expert teachers create an optimal classroom climate for learning
3. Expert teachers monitor learning and provide feedback
4. Expert teachers believe all students can reach the success criteria
5. Expert teachers influence a wide range of student outcomes not solely limited to test scores

Dimensions 4 and 5 remind me of Carol Dweck, these points she made struck a chord with me:  for teachers to develop a growth mindset in their students they need to develop their own growth mindset; do we ever judge our students too quickly? Also, such a useful reminder that we may sometimes worry too much about ‘teaching to the test’ when we just need to remember that ‘The outcomes are natural byproducts of engaging in good practice’.

I have sometimes listened to audio books as I do like to hear authors read their own work, I believe it helps understanding. You can hear John Hattie himself on the principles discussed in Visible Learning in these two videos: Visible Learning Part 1: Disasters and below average methods  and Visible Learning Part 2: effective methods. If you are in a hurry you might want to skip straight to the last part of the second video! For anyone who can’t get enough of Hattie, he was interviewed as part of Radio 4’s series The Educators.

For further reading of current ideas, see Tom Sherrington’s excellent collection: Contemporary educational ideas all my staff should know about.

If you are about to return to school (or have already done so) then I wish you and your students a great year.