Inquiry 2

Having trialled the inquiry approach with a small group, I was ready to unleash it on a full class in year 10.  You can see everything that went on the board in the inquiry here.

The pupils chose repeatedly to spend time on creating contexts for the graphs. I felt that this was partly them rebelling against the idea of inquiry – they wanted to turn it into a more traditional question – but discussing their contexts as a whole class revealed many misconceptions and tackled them before they ever got close to doing any calculations.

This part of the lessons was very engaging for the majority of pupils and as in my first inquiry, I felt that understanding was shared well between the class, as they debated (argued?!) over which context was the most realistic.

In terms of practicalities, I had learned from the previous inquiry and so gave examples of which ‘card’ they might choose the first time round before asking them to decide (but I still haven’t created actual cards!) I found the management of a larger group a little stressful at times; at times it felt a little fake, as if I were saying ‘you decide the path of the inquiry’ but then making final decisions myself. This will be much easier when I feel comfortable running a more open inquiry, allowing different groups to take different paths.

Finally, after around 3 to 4 lessons of 40 minutes, they decided to ‘practice a procedure’ and I was able to set them the questions I’d planned! This inquiry did use quite a bit more class time than a traditional approach, so I won’t be able to do it too often.  Next step… how to choose the most appropriate topics for an inquiry?

A Circle Theorem

The Resource

This worksheet encourages pupils to practice the deductive reasoning required to solve problems involving angles in circles.  At the same time, they develop the theorem that ‘the angle at the centre is twice the angle at the circumference’, either by spotting the pattern, or by generalising in question 5.  I would usually go through the general case the class afterwards.

The back of the worksheet contains lots of hints and tips for pupils who are finding it difficult, allowing those who can to create the arguments for themselves.

One weakness of this worksheet is that it requires pupils to be familiar with the AOB (three points) method of describing angles.  I should really make a version with a simpler notation for pupils who are less familiar with that.

Although this general case proves it for all angles, it’s important to follow this up with a demonstration (I like geogebra, but I’m sure there are alternatives) to show that this rule works even upon moving around the points on the circle, in particular demonstrating the alternative cases such as this…