How do you help students build an intuition for algebra?
Hello maths lovers,
I'm fairly new to maths tuition, so I'd really appreciate some advice.
Yesterday I had a 1-to-1 GCSE lesson that focused on algebra. We covered collecting like terms, expanding double brackets, and solving linear equations.
I came away feeling that the student knew many of the rules but didn't really have an intuition for them.
For example, he knew that you can only collect like terms, but it didn't seem obvious to him why. He knew that you have to perform the same operation on both sides of an equation, but it felt like something he was trying to remember rather than reason about, and he struggled to apply it consistently.
It felt as though there was a missing mental model tying everything together.
Has anyone found good ways of helping students build that intuition? Are there any books, worksheets, activities, or teaching approaches that you've found particularly effective?
At the moment I'm exploring ways to connect algebra to his interests, such as football or drumming, to make it feel more concrete. I'm also wondering whether visualisation or "mind's eye" exercises have a place in helping students develop an internal picture of what's happening.
I'd be interested to hear what has worked for others.
Thanks in advance!