Over four lessons, my year 12 students have been learning how to use the equation of a circle, as well as various other geometrical methods and theorems, to solve a wide range of circle problems. This post is an account of my planning for the first lesson of this unit, and in a second post, an account of that lesson.
I started by choosing an image that looked interesting, that would require students to consider a large number of the key ideas for this topic. I settled on this diagram from a previous exam question, which contains a circle and some perpendicular lines:
Instead of directly 'teaching' any of the ideas involved, or attempting to solve the exam question, I planned to open up the discussion by asking these questions:
I wanted students to think about what we know to be true about this diagram, rather than what we think might be true (because it looks like it). I also wanted us not to be looking for a single answer, but rather to attend to the diagram as a whole, to be thinking about relationships between the circle, points and lines, and to be making connections to previous knowledge.
That said, I did want to guide the questioning towards finding the centre and radius of the circle, with a view to discussing the equation of a circle in upcoming lessons - the key bit of 'content' in this unit of work. So, following some initial exploration, I planned to present this question to the students:
What might students attend to?
The next part of my planning was to consider what students might attend to, in a similar way to the Thinking Through a Lesson Protocol, described by @davidwees in this post. Here are my thoughts:
In the second post I will describe what the students in my class actually attended to...
The final part of my planning was to decide how I might go about structuring the lesson, what pedagogical techniques I might use. I have been thinking about modes of teaching, based loosely around pedagogical patterns, brought to my attention by @pepsmccrea.
Pedagogical patterns are approaches to planning or teaching that you use regularly, that form the basis of your practice. I sketched a few teaching modes for this lesson that I might choose to invoke:
There is nothing new here, but I think it is an interesting/re-usable way to plan. These modes are something we are developing as a department. The idea is that when planning we might reach a point where we do not need to write the pedagogical techniques we plan to use each time, but rather just refer to them by name. It may also be the case that this might improve the standard of teaching, as everyone is developing 'shared' teaching techniques. I will write more about this soon.
There are possibly three parts to this plan: the prompt/questions, what might students attend to, and the possible modes of teaching. I have noted that there is no explicit mention in this plan of how I might assess students understanding; I think this is implicit in the pedagogical patterns. Also, I have not mentioned that usual teaching practices of checking students written work - does this need to be made explicit in the plan?
So, to what extent might this structure be used to plan any lesson?
Here is the lesson plan in its entirety; what needs to be added in or taken out?