In recent days I've been brushing up on my math, a subject I haven't touched since high school - decades ago. I was very careful in my couple incomplete years at the university to not touch math all. As I think about it, the distaste I had with math was how algebra was pushed upon us kids in high school... without enough focus on the visual eye candy you have when you get into functions and such things. I was definitely an A student in math as far as I pursued it. However, it's interesting to see how little what I learned has done for me in my adult life. I think that you have to go into a career like engineering which uses mathematics in order to benefit from the courses that all young people are required to take.
As I see it, these different forms of math are the old computers that people used before folks had invented silicon chips. It was very important even back in the ancient Greek empire and ancient China and India to have the tools to be able to build things and to calculate taxes and all that stuff.
I think it's still valuable to teach young people the concepts of mathematics. However, it's important that they see these different "maths" as invented tools, rather than as natural phenomena. It's also important that they learn the history of when which parts of mathematics were invented, and why it occurred. What were the tasks that needed to be tackled?
There have been some great films I've seen in recent years which were aired on the BBC. There's one called "The story of one," and there is a series by Marcus du Sautoy called "The story of maths." These have really piqued my interest and filled in a lot of gaps for me, that were left by primary and secondary school teachers who neglected to talk about historical context when they drilled us on math technique.
Just a few days ago, I discovered the Khan Academy which is a free set of internet tools and videos that people can use to brush up on their math. Some schools even use the website to help their kids in the classroom.
Here's a video presentation by Salman Khan, who started this website:
At any rate, one thing I've remembered as I work through the Khan Academy exercises is that calculation technique with pencil and paper is very important. I don't believe I'm up to snuff. I've been inventing new ways to more quickly calculate problems.
I've been enthused to learn about the lattice method of multiplication which was not taught to me and my peers when we were kids.
One thing that I think is important is working from left to right - rather than right to left - when adding, subtracting, or multiplying. Where you have a sequence of calculations where the former ones affects the latter ones, there's a danger of losing precision in the latter calculations. In real life situations, it's best that the error affects the precision of the number, rather than the bulk of it.
I've also always been curious about savants like Daniel Tammet - and how they can sometmes do big mathematical tasks in their minds quickly. I figure that multiplication and division problems are the hardest because we have to roll up or unpack these decimal numbers in order to calculate them.
I decided to make myself a little computer program to help me start looking at the patterns that different sequences of numbers make across tables of decimal numbers. It's always kind of nagged me that there are these sequences that I haven't ever bothered to learn about - which might really help me when I am down in the trenches calculating a problem.
This is the program if you want to try it out for yourself. I've named it simply: "Tenschart."