I'm in the position to have a teaching assessment with a tutoring agency next week. This assessment will include me teaching the assessor a topic of my choice in 15 minutes, demonstrating the Socratic method that the agency has chosen as its teaching philosophy.
The problem is that I know very little about the math background of the assessor (I expect GCSE or equivalent), which makes it difficult to find a topic that they will not already be familiar with or have little chance of understanding in 15 minutes.
I am therefore looking for suggestions of math topics satisfying the following criteria;
- self-contained enough to be taught in 15 minutes
- largely independent of math taught beyond GCSE or equivalent
- not already familiar to someone with math GCSE or equivalent
- lending itself to the Socratic method, i.e. requiring little factual knowledge, and more about logical thinking and applying concepts. If a few basic concepts need to be introduced at the beginnings, that's fine.
- ideally, involving a model (of some sort) that can be played around with, or a graphical representation that can be developed with the student.
So far, I've been mostly thinking in the direction of discrete math, and applications like mechanics, biology, computer science, but have not really found anything satisfying my criteria.
Thanks.
I am guessing that they do not want you to teach them something novel, but instead something similar to what you will be teaching your students. I would recommend transformations of functions: people have a lot of trouble teaching that topic, so if you do a good job you will make a good impression.