How will you know when good learning has taken place?

Case study

A maths teacher was at a loss as to how to involve her pupil who was a wheelchair user in the more active explorative aspects of the maths curriculum where pupils were out collecting data and observing. She wanted to organize activities where pupils could explore the environment and use it to develop certain mathematical and geometrical principles. While talking about and showing triangles on the board, the pupil put his hand up and said That looks like the ramps I use to get up steps from the side, Miss. This then led to the discussion about ramps, doorway widths and turning circles for the wheelchair, which in turn led to a whole range of mathematical activities based on exploring the accessibility of the school for a wheelchair. Dead ends where the chair could not turn around, doorways that were too narrow, ramps where the angle was too steep, and so on.