When I was young, I struggled with maths because I couldn’t see what the formulas were for.
I could memorize them and reproduce an answer. But without context or something I could visualize, I didn’t understand what I was doing. Science was a little easier to approach because there were experiments. There was something to look at.
With algebra, I was looking at symbols and trying to remember the right move.
Give the unknown some context
One way I’ve been thinking about algebra is as a way to work with unknowns. X stands for something I don’t know yet. The relationships I’m given help me work out what it could be.
That gives me a reason to care about the formula. I can start asking what X represents, which information I already have, and how that information relates to the thing I’m trying to find.
Once I have that context, I can draw parallels with problems outside the classroom. I’m trying to find a direction, understand a situation, or work out how something could be different. Experience gives me patterns I can try to apply.
The comparison makes maths feel more approachable to me. I can see why I might want to learn the pattern instead of just remembering it for a test.
What would teaching look like from there?
I think the lack of context is something worth spending time on when we design learning experiences.
Before asking someone to use a formula, can we show them the unknown it helps them work with? Can we make the relationship visible? Once they understand what they’re trying to find, we have somewhere to attach the notation.
I find myself asking similar questions about writing and persuasion. If I can understand the basic operations involved, I can start seeing how they fit together and where I might use them.
That is what I was missing when I memorized maths. I needed to understand what I was trying to do with it.