Presenting Mathematics to students as a seemingly unending set of facts and concepts to be learnt makes no sense. Mathematics has a grand history. The centuries are littered with examples of great discoveries. Why not share some of these with our students?
The number strand is rich in symbols, patterns and conjectures. Starting with the simple numeral 1, we can work our way up to the much more abstract idea of infinity.
Infinity is a very rich topic for discussion (when students are ready). For example, there are a number of famous paradox’s associated with infinity. Hilbert’s Grand Hotel is one example.
Investigation of fractals is another rich area of study. For example the Koch Snowflake which has a finite area, but an infinite perimeter!
I remember a heated discussion in our staffroom a few years ago about the value of n divided by zero, etc. This could be a good topic for research by students.
So why not inject more life into our Math lessons by including some history, examples, applications, images, videos, etc? I think most teachers probably do this already?
I would be interested in your comments about the importance and use of History in Mathematics!