The Overarching Themes in the new Maths A Level specifications: a question level review
The Department for Education has outlined three key ‘Overarching Themes’ to the new A level Maths specification that all exam boards must adhere to. These themes are deeply embedded in the new format of the questions and will have a direct role to play in the new-ness of the A Level experience for students.
In the last few weeks, I have been doing sample A Level questions from the new specifications to get closer to what this change in tone feels like. Although the A Level is not meant to be more challenging, it has certainly increased the demand for mathematical rigour and ‘on the spot thinking’.
For each theme, I have found a sample question that I encourage you to try. All boards are examining the same content so I have included a healthy mix here!
Overarching Theme 1 : Mathematical argument, language and proof
The example below is entirely new material for the A level.
The striking thing to note is the requirement for students to construct coherent arguments here and present a proof that fully answers the question. Previous exams required students to ‘Show that’ but not ‘Prove’. The material was always quite familiar so students knew how to dive in. Here they have an ambiguous description, from which they need to construct strict arguments with well defined variables.
Students will need to be comfortable with making starting assumptions that they clearly state using set notation. The language they are constructing here is a big step up - describing non zero integers and rational numbers using variables will require students to be comfortable with constructing variables from just the words in a question.
Overarching Theme 2 : Problem Solving
People struggle to describe Problem Solving as simply as the other overarching themes. I was at a seminar on Key Stage 5 where I witnessed this and was just as baffled by the vagueness of it as everyone else. It came down to being described as a skill that kicks in when ‘You don’t even know where to start’. My notes, including some more examples of how to teacher problem solving, are here.
The example below shows how students will need to think on the spot when a clear starting point is not provided. They will also need to be specific in the way they describe their answer - requiring them to think critically about the underlying concepts.
Overarching Theme 3 : Mathematical Modelling
These questions have always existed on the A level Maths papers. They are the ‘wordy’ ones that involve students having to use Maths in context of a real life problem. The new specifications have now placed an emphasis asking students to comment on the validity and underlying assumptions of models. Students will need to understand that models come with possible loopholes and they are a springboard off of which improvements can be made.
The example below struck me as particularly new looking compared with how such questions have been asked in the past.
While working through the papers I noticed just how ‘grown up’ the maths was starting to feel. The overarching themes have a direct impact on how the content is being assessed and students can no longer rely on the familiarity of typical types of questions. The sum of all three themes has resulted in papers that will truly prepare students for university and beyond. We should remember that this is a good kind of change!