Mathstrolabe

Mathematics, the study of logic, reasoning and deduction.

Welcome to the home of the Mathematics branch of NeoSki.

Key Ideas and Topics


A dissertation upon the importance of topics within GCSE mathematics


What makes topics important?

Many teachers have asserted key topics and concepts over the years such that there is now a plethora of different articles and pages such as this one on the internet. But what makes a complex topic and are these any more important than those that are simple?

Complex topics often link many other topics together with an endpoint such as solving quadratic equations which pulls upon the assistance of calculations, algebra and multiplicative reasoning to draw the topic of algebra to an abrupt and indefinite end. And whilst the factor of complexity is certainly worth contemplation, it is not always a direct proportion.

A factor that is also in the equation is new concepts. Whilst non-right-angled trigonometry is certainly more complex than right-angled trigonometry, right-angled introduces the trigonometric functions and the ideas that come with them such that non-right-angled trigonometry naturally follows. Students vary rarely get stuck with more complex topics if they fully understand the component parts and thus it is always important to evaluate the simplest solutions for their struggles before those that are more difficult.


How do the two factors of importance impact teaching?

The rather obvious way that this affect teaching is that simpler topics are taught first and then the complexity should increase linearly. But this is not what happens, because topics are often taught to reveal new ideas at regular intervals. This ensures that students are not overwhelmed by the contents of the course. Furthermore, it is most impactful to ensure that students are at least mostly certain and confident around a topic before proceeding such that when more complex topics require the skills of previous topics, students are able to apply them without issue.

With the correct application, this will enable the course to feel free-flowing and yield students confident in their knowledge. However - as anyone could probably tell you - no actionable plan is fool-proof, there will always be students that struggle more than others and thus will require extra support to 'catch up' whilst other students are learning. This increases the complexity of the operation through introducing additional provisions and, as such, I hope the below list of topics which I view as important or key will help to inform your decisions when teaching.


A ranking of important topics

Topics are ordered by importance on the Topic Specific Question Packs page and this should be your first port of call when looking for the importance of topics. It orders them logically such that a clear teaching plan is established.

Another good place to look is the Edexcel Two-Year Scheme of Work which presents the examination board's advised teaching order.


Additional Resources

Finally, I have some additional resources to aid with the more difficult topics which can be found below.

A thank you is extended to Maths Helper for some of the tasks found below.

Written tasks are represented with a paper icon (description) and interactive activities are represented with a button symbol (control_point_duplicate).

Explainers

Tasks