Active online learning: seeing calculus take shape in Year 11 Maths Advanced

A student working at a laptop
“Like what you do, and then you will do your best.” - Katherine Johnson

Having a visual way to explore equations makes a world of difference for a student’s confidence. Good online Year 11 Maths Advanced tutoring keeps them doing the thinking, with a tutor working alongside them in real time.

Calculus is far easier to understand when you can watch it happen. On a shared screen, the idea behind a derivative stops being a rule to memorise and becomes something your child can see.


Why seeing it helps in Year 11 Advanced

The derivative is the gradient of a curve at a single point. That’s hard to picture from a definition, and easy to picture on a moving graph.

What we show live What your child sees The idea it locks in
A line through two points on a curve, with one point sliding towards the other The line settles into a tangent The derivative as the limit of gradients, which is differentiation from first principles
A slider on a in y = a(x − h)² + k, and on h and k The parabola stretches, flips and moves How each part of a rule transforms a graph
y = 2ˣ and y = log₂x graphed together Two curves mirrored in the line y = x Exponentials and logs undo each other

How a session works

Sessions run on Google Meet with a shared digital whiteboard, and Desmos comes in whenever a graph helps. Your child can write on an iPad or type and draw with a mouse.

  1. Check-in: how they’re feeling and what’s come up since last week.
  2. Set the focus: based on upcoming assessments and anything from previous sessions that still needs work.
  3. See it, then write it: the idea shown live in Desmos, then worked algebraically on the whiteboard.
  4. Your child drives the practice, step by step, with the tutor watching each line.
  5. Review and next steps, written into the shared Google Doc.

How we check it’s landing

Signs it’s working

  • Your child can explain what a derivative means using a sketch.
  • They can predict how a graph will change before typing it in.
  • They rewrite functions with indices before differentiating, without being reminded.
  • They connect the algebra on the page to the graph on the screen.

Every session’s notes sit in the shared Google Doc, so you can see what was covered at any time.

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How we track progress in Year 11 Maths Advanced: keeping the foundations firm

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Year 11 Maths Advanced: calculus, logs and the foundations that hold them up