A popular game played in English lessons is one where words have to be combined to create compound nouns, such as bus stop or swimming pool. If presented with the word connections, how many compound nouns can you find in the next thirty seconds?
I would suggest that words associated with the digital world occurred fairly frequently such as internet connections or personal social media connections. The importance we currently place on making connections in the digital world is clear, but what about other types of connections? Educators may naturally think about the connections between cells within the brain and how this impacts on learning.
As mathematics educators, we may think about how we develop awareness in our students regarding the connections between different areas of maths and whether this is happening often enough in our classrooms.
Maths can sometimes be perceived by students as consisting of many distinct topics which need to be mastered which can lead to feelings of overwhelm, particularly when there is a lot to be covered and pupils feel that they are being moved on before they are comfortable with a particular area.
It is therefore pleasing to see that schemes of work are now more likely to block topics together such as addition and subtraction or fractions, decimals and percentages. However, it is also interesting to see that percentages often appears after decimals when in fact, introducing percentages as fractions with a denominator of one hundred then leads more easily into decimals by linking these fractions to place value. Another consideration worth bearing in mind is how ratio and proportion are being linked to fractions within the curriculum.
Making connections also needs to go further than just blocking topics together. It can be an interesting exercise to ask older pupils in primary school to define what the word fraction means to them. Having tried this with many groups of students, it has been rare to have a pupil who connects fractions to division. Few pupils would also write a division calculation involving larger numbers (that have a common factor) as a fraction first in order to find an equivalent fraction comprising smaller numbers that they can work with more easily.
Challenging students to find different ways in which to represent an idea can highlight connections. If some representations are not correct, even better, since this allows an insight into misunderstandings that may not have otherwise been uncovered.
These links need to be made within our teaching and encouraging students to look for, and reflect on, connections is a worthwhile exercise. Providing time for the sharing of these observations allows students to develop a deeper understanding of mathematics as a web of interconnected ideas rather than discrete concepts, each with procedures to be followed. Creating an ongoing web (which can be added to throughout the year) on a wall can prompt students to notice connections.
Making connections can also strengthen understanding within topics that can be considered more difficult, such as finding the nth term of an arithmetic sequence. We can teach pupils a process whereby they start by finding the difference and multiply this by n, but this is easily forgotten if they do not see why this works. However, connecting the given sequence to the multiples of n sequence, using number lines, allows students to see the connection.
We must not forget, of course, that teachers in primary or elementary schools are often expected to teach many different subjects and may themselves have been taught maths in discrete chunks, rather than in an interconnected way, so educators must be allowed time to explore the connected nature of maths before they can adapt their teaching to heighten students' awareness of connections, other than those on their Snapchat account.