Thoughts this week …

A couple of weeks ago I started adding a selection of random items of news, suggested resources and so on to the end of a blog post, basically anything that had caught my eye that week (thanks to Doug Belshaw for the idea; I enjoy his weekly Thought Shrapnel). This week there seem to be several so I’ll make this week’s post a collection of such items. 

Graphing the Sine Function from Math Open Reference

Graphing the Sine Function from Math Open Reference

  • My Year 11 students (age 15-16) are studying for a second GCSE in Mathematics. We are using AQA’s Level 2 Certificate in Further Mathematics, a course which we are all enjoying; it extends these able students and is excellent preparation for further study of the subject. We are currently looking at trigonometry and I want a good demonstration for graphing the sine function. Looking at various applets I came back to a site I use a great deal and have written about before, John Page’s Math Open ReferenceHere you will find many very clear applets including exactly what I want, have a look at Graph of the Sine function. Note that is possible to display full screen which is great for the Interactive whiteboard. Drag the point A around and watch the graph and try Progressive mode. I have put the links for my students in this post.
  • The Guardian Teacher Network has a new Maths hub bringing together maths news and resources.

Misconceptions in Mathematics

classic mistakes 2
Nevil Hopley’s excellent Classic Mistakes site.

For a starter addressing common misconceptions try the excellent Classic Mistakes resources by Nigel Hopley.

Diagnostic Questions - Algebra

A superb resource to use in class (or for students to use at home) to address misconceptions is Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has over 1700 questions with carefully designed multiple choice responses to address common misconceptions. For further details see these posts.

From NCETM, these videos and resources for teaching Key Stage 3 maths topics include common misconceptions and pitfall. See also this document on common misconceptions.

Some years ago a website, which is now no longer available published a very useful document on misconceptions. In 22 sections, in each section misconceptions are given along with the correct version. Further explanations are also provided and also follow up exercises with answers.

The first 8 of these documents, by Ilan Samson & David Burghes are on the CIMT website

Malcolm Swan’s excellent ‘Improving Learning in Mathematics‘, includes a section (5.3) on exposing errors and misconceptions. An activity suggested there is to let your students become examiners and mark the work of others, this works very well, I have highlighted some excellent resources for this on the ‘Spot the mistake!‘ page.

Many of the outstanding resources from the Standards Unit address common misconceptions; see PD2, learning from mistakes and misconceptions. See also the resource hosted by STEM Learning – you will need to create a (free) account to view the STEM Learning resourceThe firsts.


Steve Blades’ site has many excellent resources; on the GCSE page we see under ‘Miscellaneous Worksheets’ (scroll right down the page), 18 GCSE Maths Misconceptions.

Examination boards often publish helpful material which addresses common misconceptions, such resources can promote very useful class discussion as can examiners’ reports. From AQA for example, have a look at the Feedback documents on each unit available here (scroll down the page and look in the section on Teaching Resources) and another resource here.

Great questions can be used to expose misconceptions, diagnostic questions have already been mentioned above; for further sources of questions see Rich Questions.


This year I will ….

Are you making New Year Resolutions? Monina Velarde’s site might inspire you!

Clearly the beginning of the academic year makes us think of  resolutions for the new school year but January offers another opportunity! Some possible New Year Resolutions for Mathematics Teachers:

This year I will:

….and for your students!