A level calculus for students and teachers
Tuesday 14th May 2019
Val Pritchard, AC for Hertfordshire
Using a Derivative calculator to check stages
We had 72 students from around the county striving to recall, apply and extend calculus concepts within A level Mathematics. Jenny Forsythe (AMSP Associate) and Val Pritchard (AMSP Area Coordinator) had their work cut out finding appropriate tasks and questions that the students had not seen before and producing revision guides for new material. During the day we journeyed from algebraic proficiency linked to differentiation, through problem solving within integration to interpreting real-life information for differential equations, with detours to differentiation from first principles and Newton-Raphson. Students were extremely well focused on their exercises and took care to think through possible misconceptions.
Accompanying teachers came from John Warner, Marriotts, Monk’s Walk, Nobel, Priory, Samuel Ryder and Sandringham. They attended their own sessions with Joanna Deko (AMSP Regional Lead) and Natalie Vernon (AMSP National PD Coordinator) and appreciated the opportunities to discover teaching ideas and resources, compare revision methods and various resources available online, discuss teaching techniques for some of the new topics and how they are assessed by exam boards, exchange approaches to revision lessons and some of the big topics in calculus. Quite a list! Teachers joined students for key sessions on exam questions and were invaluable in supporting the progress especially on problem solving stages.
For those of you looking out for more problem solving in calculus, one technique is to use a legacy question, but take out the supporting stages. For example a differential equation that needs to be set up and solved: AQA June 2006 Core 4 qu 8, but with only the initial section and aii given and then with the additional requirement to solve the differential equation. If you want a set of integration questions with variety try OCR June 2006 Core 4 qu 3 ii qu 6 ii qu 8 ii (but don’t provide the suggested substitution). For a real-life optimisation problem you could use AQA Specimen assessment materials A level paper 1 qu 14a. Specimen papers are available on the exam board website and for legacy questions Colmanweb gives a nice layout with links to papers.
- “Modelling with differential equations was challenging but rewarding.”
- “It was good to see how different people tackled exam questions.”
- “Good to share with colleagues and get an idea of what does or doesn’t work.”
Indicating why Newton-Raphson works
Problem solving with calculus