Teaching integration – which method will your students choose?

Sue Pemberton

Research has shown that the topic students find most challenging at A Level is integration. Having time to consolidate their integration work is vitally important. Learners benefit from a lot of practice at recognising the structure of the integral that they are tackling and hence deciding which method of integration they will choose to use. 

Learners need to develop an appreciation that there often isn’t only one way of doing integration, and that depending on which method is used their answers might appear to be different whilst they are actually equivalent.

Where can we help? 

Cambridge International AS & A level Mathematics: Pure Mathematics 2 & 3 coursebook devotes a whole section to dealing with these issues using the Explore features which contain enrichment activities involving group work and peer-to-peer discussion to deepen understanding. Additional integration activities are also found in the teacher’s resource which includes a card activity and some excellent resources from the Underground Mathematics website.

Whether working through integration or a different topic, you will find Underground Mathematics resources linked throughout our new books. This popular resource-rich website is created by mathematics experts from the University of Cambridge to enable students to explore the connections that underpin mathematics.

Try the integration activity below with your students. You could even arrange them into groups, each working on a different method, and ask them to report back on their approach and findings.

Integration activity screenshot

Click here to download the PowerPoint activity (2.3Mb).

If you already have our coursebook, a suitable place for tackling this challenge could be after Explore 8.2 from our Pure Mathematics 2 & 3 coursebook and before the teacher’s resource card activity ‘Sorting functions by their method of integration’

About the author – Sue Pemberton

Sue is a former teacher and lecturer with over 30 years’ teaching experience. She is passionate about promoting active learning in the classroom and has delivered training around the world. She has examined for numerous examination boards and is the author of many education resources including the Cambridge University Press titles Cambridge IGCSE® and O Level Additional Mathematics Coursebook, and the Cambridge International AS & A Level Mathematics: Pure Mathematics 1 and Pure Mathematics 2 & 3 Coursebooks.