About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.


Personal Learning Login

Sign Up | Forgotten password?
Register with the NCETM

Secondary Magazine - Issue 120: From the Library

Created on 10 March 2015 by ncetm_administrator
Updated on 29 April 2015 by ncetm_administrator


Secondary Magazine Issue 120'Books HD' by Abhi Sharma (adapted), some rights reserved

From the Library
Shh! No Talking!

Our regular feature highlighting an article or research paper that will, we hope, have a helpful bearing on your teaching of mathematics. You can find previous features in this series here.

In this issue we share with you a paper first presented at the BSRLM Proceedings in 2006. Celia Hoyles’s (the founding Director of NCETM) and Dietmar Küchemann’s paper Secondary School Pupils’ Approaches to Proof-related Tasks in Geometry gives an account of two pupils’ attempts to solve two GCSE geometry questions involving circle theorems. The paper identifies some of the characteristics of such tasks, some of the pupils’ emerging strategies, and some of the difficulties the pupils encountered, especially with using the givens and extracting information contained in diagrams.

diagram 1

The paper starts by recording how the pupils find (a) angle CBA and (b) angle CDA in the diagram above. Subsequently they work on a different problem:

diagram 2

Here AOB is a diameter, TCS is a tangent, angle ABC = 57˚ and pupils are asked to find (a) angle CAB and (b) angle ACS.

The paper presents a transcript of the pupil/researcher conversations as they work through the problem: we think it’s a conversation that will sound familiar to you, and that you’ll recognise many of the misconceptions and difficulties that the pupils encounter. We hope that this paper will help you steer your pupils’ development of more secure conceptual understanding and procedural fluency, so that they start to tackle circle theorem questions, not least on GCSE exam papers, successfully and confidently. Let us know what you think.

Image credit
Page header by Abhi Sharma (adapted), some rights reserved



Download the magazine as a PDF
Secondary Magazine Archive
Magazine Feed - keep informed of forthcoming issues
Departmental Workshops - Structured professional development activities
Explore the Secondary Forum
Contact us - share your ideas and comments 


Comment on this item  
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item



There are no comments for this item yet...
Only registered users may comment. Log in to comment