New Year Resolutions

Resolutions for Maths Teachers PowerPoint file
or as a pdf Resolutions for Maths Teachers 

Rather than follow the now usual tradition of commenting on popular posts of the year I thought I would simply check on my Resolutions for (Mathematics) Teachers – many popular posts are included there anyway. This was updated at the beginning of the academic year and I am happy to report that I am indeed conscious and act on the resolutions shown in these slides in my planning.

In particular:

I try and use a good variety of resources including those that students can use at home and use technology (I would not be without Desmos or WolframAlpha!) where it enhances learning but always strive to put the learning firstwhy this or that resource? How will it help them learn?

A calm and prompt start to a lesson is so important, using some sort of activity for everyone including the older students sets the expectations for the lesson immediately. Something like Corbettmaths 5-a-day for Core 1 for example would get your Sixth Form students busy and provide some useful revision too.

I have used RAG123 regularly for marking and found it particularly successful with Year 7 (age 11-12). I use it very simply – it’s a way for them to let me know if they are not too sure on something (I hope they would ask in a lesson anyway – but it can be useful to note in their books, knowing that I will see their comment).

On the subject of Feedback, I see that the Verbal Feedback stamp idea thought to be wonderful not that long ago seems to be now on the scrap heap of ideas – why does everything have to be good / bad, black or white – isn’t there some middle ground? Exercise books are for students to learn from, what’s wrong with the stamp as a signal to the student that they should record an aspect of the verbal feedback which will be useful to them in future? So long as the emphasis is on usefulness for their learning and not merely to please somebody else I see no problem at all. I expect students to make a note of useful feedback in their books anyway, but now and again perhaps the stamp as a signal to do so could be helpful, particularly for younger students.

In any planning we should consider the very useful What makes great teaching? Review of the underpinning research. Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major (October 2014). When I asked students about good teachers, it seemed to me that their comments fitted very well with the categories in the review.

Making things stick is as important as ever and we need to help our students easily recall all the basics if they are to be able to make links between all the material they learn and apply this to more involved tasks. It strikes me that with the greater emphasis now on Problem Solving Simon Singh’s wonderful quote is highly relevant and encouraging students to be great problem solvers is something I want to continue working on this year.

.Somon Singh quote

In fact I would say we want all our students to be happy with being baffled (appropriately for each student) and help them find ways to get unstuck. Isn’t that a good resolution for Mathematics educators everywhere?


GeoGebra Graphing Calculator

GeoGebra AppGeoGebra announced the release of their GeoGebra Graphing Calculator earlier this month; currently available for Android, the app will also be available for iPhone and Windows – watch for announcements.

For all the information you need to learn how to use this outstanding app for Mathematics see “What is the GeoGebra Graphing calculator?” and all the Tutorials available.

Having downloaded the app to my phone I can confirm it works really well and i was easily able to follow the instructions given in the links here.

I very quickly created the diagram in the screenshot from my phone below. Using a finger one can drag point D around and note the angle at the circumference. With an account you can also save your files which are standard GeoGebra files.

GeoGebra App

GeoGebra App

Follow GeoGebra on Twitter or Facebook

Problem Solving

Zeitz, P., 2007. The art and craft of problem solving. 2nd ed. John Wiley & Sons, Inc, p.2
Zeitz, P., 2007. The art and craft of problem solving. 2nd ed. John Wiley & Sons, Inc, p.2

This March 2021 post, Polya – Problem Solving includes many resources for problem solving.

Links to the resources are all provided in the notes below.
Files:  pdf: Problem Solving in Mathematics 

PowerPoint:  Problem Solving in Mathematics

Further Notes (relevant links for each section  are also given here)

What is a problem anyway?
GCSE & A Level Reform in particular: GCSE mathematics subject content and assessment objectives where the assessment object AO3 defines what is regarded as Problem Solving at GCSE. It is helpful to look ahead to A Level – see:  A level mathematics working group report which is very clear on what may be considered problem solving.

Ask the students
For our students to be good problem solvers who have the confidence to start on a problem without necessarily know where they are going with it they need a classroom environment where they are comfortable to take risks and know that it is OK to make mistakes. They need great teachers who not only understand their subject but the importance of the teacher / student relationship. Here’s what some Year 9 (ages 13-14) students said about Good Maths teachers and this from Year 7 (ages 11-12).

Teaching Ideas
You can see some questions to consider on the slides.
There are several slides here on using diagrams; sometimes we run the risk of getting too formal too quickly – some great diagrams can help with understanding and be very useful in our teaching. Giving students just a diagram and asking them what the question might be can be a very useful exercise too and also be a good way to discuss the vocabulary used in exams.

I always tell students that going backwards can be great for understanding and also making connections – consider expanding brackets and factorising for example.

Links to the resources in this section:


Making It Stick

Further Resources


Christmaths 2015

Christmaths 2015

Christmaths 2015

I’ll be posting on Monday this week – to coincide with Christmaths 2015 which I am very much looking forward to.

In the meantime – just in case you are not following the various speakers (you should):

Mel Mulowney JustMaths
ColleenYoung     that’s me    (and not to be confused with the other Colleen Young)
Bodil Isaksen & Dani Quinn  Bodil’s blog 
Kris Boulton Back to the Whiteboard
And of course…. Jo Morgan who is making the whole thing happen. (Resourceaholic)

Circles & Tangents

Circle & tangent

Desmos – Circles & Tangents

Use Desmos to explore tangents to circle through given point

Teaching Year 10 about the equation of a tangent to a circle at a given point I have created a Desmos page. I have also created a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent)

(Also added to GCSE New Content page)

Further Desmos Updates

An early introduction – plot some points and functions
Desmos – points & functions (for PowerPoint file)

 Graphs-GCSE for PowerPoint file