A common
mis-conception about the field of mathematics, especially among students
growing up, is that the field has reached its limits and there nothing more to
be discovered or no problems that have gone unsolved. Math is a poured set of
concrete that has settled, never to be changed over time.

It is this sort of
mis-conception that allows students to enter into a math course without any
excitement or anticipation. Any one with a somewhat advanced interest in math
though knows that this is not the case and that mathematics is a field
paralleling the sciences in terms of modern breakthroughs and ancient problems
yet to be solved.

At the beginning of a
course a teacher has the perfect opportunity to convey this sort of thinking to
their students in order to spark their interest and let them know that this
course is going to be engaging. A great way to do this is through the use of
multimedia which often is over looked in the math classroom. If you can set the
tone early as a teacher, then you have the opportunity to create an engaging
classroom in the future.

A great concept to do
this with is the concept of

*infinity*. Most people have heard of the concept but have not taken the time to try and wrap their minds around it. It is when you do that things get interesting. Take the following video for example:
The video is an
exploration on how big infinity is. This is a perfect chance to begin a
discussion with students: what does infinity mean? How big is infinity? The
video explains how there are infinities within infinities which means that
there are larger and smaller infinities. Surely this will get some of them
interested. The video then goes on to explain how "there are unanswerable
questions in mathematics". Suddenly the solid cement has melted and
mathematics is now a field much like the sciences where inquiry is encouraged
and questions remain unsolved. This short discussion and video can prove
fruitful for future inquiry based activities in the classroom.

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