Math: A Different Approach

The Greeks studied mathematics not solely for its 'usefulness', but also for it's inherent properties and beauty.  This builds strong logical reasoning abilities, creativity, and strengthens ones ability to see the disconnectedness of ideas.

This does not mean that there are no uses for math, nor that we should not study them.  What it shows us, is that if we study the inherent properties of math (both numbers and shapes) it is easier to understand the applications.

As a long time math teacher, the biggest problem I have seen is that students are taught various procedures to solve different problems.  A better approach, the way I was taught and teach, is to start with numbers and their relationships -- how to manipulate them, both 'arithmetically' and 'algebraically', and how to visualize them using graphs, etc.  Once these techniques and ideas are internalized, and connections begin to be noticed, applications can be introduced.  The beginnings of the necessary critical thinking skills needed for the STEAM fields start here.

Having worked with pre-engineering students, the hardest thing for them to see is, which mathematical object 'lives' behind each particular application.  This requires VERY critical thinking.  If this can be determined, it then becomes a simple task of applying the right technique.  This is also very important for students of the Social Sciences.  All of the same ideas and techniques can be applied to the data collected in all of these subjects, all while looking for the mathematical connections.

So, what if we taught math as the interaction of numbers with each other?
Instead of teaching with applications, what if we allowed numbers to have a life of their own?

As a Christian, I think it is great that we can use the conceptual tools of math to help us understand God's creation.  But, isn't it so much more beautiful to see that these tools have their own inherent properties and relationships, that are beyond the need for an application?  This gives us a glimpse at the fact that there are truths that are external to our perceptions.  Understanding this allows us to more easily grasp the idea of an eternal God.