# Ruth Tanner`s Circle Theorem Notes

```Inspire me: Using ICT to support Hard to Teach Topics in Mathematics
5. Using ICT to investigate Circle Theorems
Ruth Tanner ( Wrenn School, Wellingborough, Northamptonshire )
This case study involved my Year 9 learners who had limited experience of using the
Geometer’s Sketchpad software (GSP). It was important that learning to use the software
did not get in the way of the mathematics and also that the individual learner’s
investigative approaches to their work was developed, so I devised and used the following
3 different sets of cards.
1. Each card has explicit GSP instructions and a task which should enable the learner
to discover one circle theorem (A4 Card)
2. Each card has a description of a diagram that should be constructed, and a task for
the learners to make conjectures relating to the construction (green cards)
3. Each card states a circle theorem and requires the learner to construct a diagram
that confirms the theorem and allows them to generate a proof. (orange cards)
The learners were grouped in pairs and shared a computer, which encouraged discussion
and collaboration.
1
Learners enjoyed the freedom in the activity as they were continuously asking and
answering their own ‘what if questions’, for example “what happens if you move it
anywhere on the circumference? ......the angle isn’t changing”. It is the ability to move
objects that brings the constructions to life and makes them so meaningful for the
learners, and it is this that a paper and pencil method does not achieve.
Listening to their explanations and observing the learners as they worked highlighted the
need for me to ask probing questions if they were to fully develop the mathematics. For
example the learner who said “I know those two lines are the same length” but needed
me to ask “how do you know” in order for him to tell me “because it is an isosceles
triangle”.
“the computer lets you
experiment ........you can learn
so much out of it”