You’ve never seen the GCSE Maths curriculum like this before…
What you’re looking at is the GCSE Mathematics curriculum. Each node represents a topic, e.g. transformations, ordering decimal numbers, frequency polygons etc. There are 164 nodes in the diagram representing all topics on both the foundation and higher tier curriculum. The nodes are connected by 935 links. Each link represents a connection between two topics whereby one is the prior learning required to be able to access the other. For example, equivalent fractions is linked to adding fractions because you need to be able to do the former before you can learn how to do the later.
I created this diagram using Gephi to investigate which topics are the ‘essential skills’ required to access as many topics on the GCSE as possible. If pupils need to completely master certain topics in KS3 in order to be able to learn as much of the GCSE syllabus as possible, what are those topics? I have scaled the node size based on how many links they have, i.e. how many topics they are prior learning for. The larger the node, the more topics it is prior learning for. The largest nodes are the essential skills needed to be able to access the full GCSE.
The nodes have also been colour-coded based on the part of the curriculum they relate to:
Number and calculating- red
Shape space and measure- purple,
Data handling and probability- light green
Before I started the project my experience led me to predict that number was going to be the most connected topic in the diagram and it certainly is. The largest nodes are red indicating that if pupils have not mastered the important number topics you will struggle to teach them much else. My teacher’s instinct knew this already but the diagram certainly confirms it in a visually powerful way. If you removed all the red nodes, and those they are connected to, you would have little left that you could teach.
What are the topics specifically? Here is the diagram again with the node labels shown. These are also scaled proportionally like the nodes.
In rank order, the most important topics for students to master, based on the number of topics they are prior knowledge for are as follows:
Multiply and divide whole numbers (90 topics this is prior knowledge for)
Add and subtract whole numbers (73)
Multiply and divide decimal numbers (43)
Understand place value and identify the value of digits in a number (38)
Add and subtract decimal numbers (34)
Multiply and divide negative numbers (34)
Write a fraction in its simplest form (29)
Round to decimal places (29)
Substitute into an expression or formula (26)
Add and subtract negative numbers (24)
Put a number on and read a number off a number line (23)
Round to significant figures (23)
Two letter notation for a line and three letter angle notation (21)
Use a calculator to evaluate complex calculations (20)
Plot and identify coordinates (19)
Use and calculate with index notation including squares, cubes and powers of 10 (19)
Equivalent fractions (18)
Express one number as a fraction of another (18)
Extract data from lists and tables (16)
16 out of the top 20 topics are number and could be summarised as four operations, BIDMAS, place value, rounding, negative numbers and basic fractions. I’m sure this comes as no surprise to the experienced maths teachers out there. It has reinforced my own belief in the importance of pupils mastering number skills in KS3, in particular mental and written techniques for the four operations.
There are of course limitations to this analysis which I should highlight. I grouped topics together to keep the analysis manageable within the timeframe I was willing to put into it. For example, I haven’t differentiated between mental, written or calculator based four operations techniques. This may have accentuated the importance of the top two skills to a certain amount. There were many assumptions built into my decisions of which topics were required prior knowledge for the others. Too many to explain and we could debate endlessly about particular links.
However, all I wanted from this analysis were the key trends and I think in that regard it is a success. It confirmed what my experience has told me. Number skills must be mastered early in secondary education if we want to keep the other topics accessible to students at GCSE. In addition, seeing the complexity of the connectivity of the topics also reinforces how difficult it is to come up with a sequential syllabus. It shows the importance of good AFL in lessons to establish whether pupils are secure with all the necessary prior learning before teaching them a new topic. It shows what a skilful job being a good maths teacher is! We as teachers have our own versions of this network in our minds, but seeing the complexity of it in the diagram really brings home why students find it so hard to make links between topics and ‘see the big picture’!