A Checklist for Every Topic in the New Maths A Level
Why I need a new checklist
In the old specifications, each topic came with an array of predictable ways in which it could be examined. It became a routine at the end of every topic to make sure I covered ‘that type of question’ or ‘that thing that has come up every year’. This was my checklist and it helped me feel prepared. It also gave students reassurance to be able to keep tabs on the most likely things to come up in an exam.
The comfort of a decade’s worth of standard questions is being taken away with the new A Level. There will no longer be ‘typical questions’ that I can use as a checklist to go over.
The Overarching Themes have taken over and it is the expectations that have been standardised, over and above the look and feel of the questions.
- Mathematical argument, language and proof
- Mathematical problem solving
- Mathematical modelling
These themes apply across all exam boards and provide the basis for my NEW checklist.
At the end of each topic; follow this checklist:
1. MIX IT UP - can they be flexible?
Avoid only setting questions on one topic in isolation. Mixing it up does not mean a mixed topic worksheet either, I mean one single question that incorporates several topics in one.
How this helps:
Making students think across several topics tests Problem Solving skills. By making this part of the routine at the end of every topic, you will create a culture of Problem Solving as students will need to really think about ‘How do I start to tackle this problem’.
The new specifications are designed to produce students with a deeper and broader understanding of Mathematics and we need to teach them NOT to compartmentalise to truly prepare them for exams.
If you have just finished teaching geometric series and arithmetic series had been covered in the past, set them a question that is on a geometric series for which some of the terms also form an arithmetic series. Such questions exist and are also super easy to create! The few minutes of work on such a question will set the right tone at the end of the topic, showing students they cannot just rely on predictable questions.
2. DISGUISE IT - can they cope with unfamiliarity?
In the past it has been easy to tell what topic a question is testing by simply reading it. This is changing in the new specifications. End a topic with a set of questions that do not make it obvious what they are testing. Make them wonder if you set the right worksheet!
How this helps:
It encourages students to think independently and allows them to build coping mechanisms for unfamiliarity. Without immediately recognising the problem, can they pick a starting point and present a clear solution using sound mathematical arguments?
Suppose you have just finished teaching differentiation. It is very likely that you have covered sketching curves in the past. Set them a question that involves sketching a quartic curve, for which the roots cannot be found in exact form. With no hint to differentiate, they will need to think of it on their own, find stationary points, and also piece together a sketch!
3. MODEL IT - can they work within context?
Possibly the most prominent new addition to the new Maths A Level is the expectation that students should understand Maths in context of real world problems. Take any topic and turn it into a question that brings it into practice. Modelling was seen very little in past core papers - we will need to be resourceful for this one!
How this helps:
The key aspects of modelling are understanding the assumptions, using a mathematical model and criticising where it may fail. This process can be incorporated into the majority of topics and without it, their learning is not fit for purpose for the new exams. Doing contextual questions routinely will make students apply what they know and interpret results so they have meaning, making this new style of question less alien in the final exam.
Quadratics have been tested in predictable ways for years. Little to no modelling has come up with quadratics even though there are so well suited to it! Take the trajectory of an arrow and model it using a quadratic equation. Ask students to find the maximum height and the range of horizontal motion for which they will simply be completing the square or finding and interpreting the roots. Make it wordy and make the context meaty, without necessarily complicating the underlying Maths.
That’s the end of my checklist
As you can tell, it is more to do with flexing the Problem Solving and Modelling muscles regularly than it is about covering ‘types’ of exam questions. Given that there is greater ambiguity about what could come up in the exams and specimen papers will not be enough, take the time to plan your teaching around the Overarching Themes. If it is a question that challenges your own familiarity, it will do that and more for students too!
Where to find inspiration for questions
- MAT (Mathematics Admissions Test) papers
- TMUA (Test of Mathematics for University Admission) papers - more here
- AEA (Advanced Extension Award) papers
- STEP (Sixth Term Examination Paper)
- IYGB (for the old specifications) papers
- A Level papers from the 1970s