Whether you are a student, have school age children, or have used math at all in your life, you have no doubt struggled at some point with mathematics. Math is one of those things that can be difficult no matter how good you are at it. I know – I am very good in math but I still struggle.
I wanted to share two excellent resources that make that struggle much, much easier. So much easier that, for many of us, math may cease to be a struggle.
When it comes to solving and visualizing mathematical problems, good math solving software can make a difficult task significantly easier. Unfortunately, the mainstream offerings such as Maple, Matlab, and Mathematica are way too expensive for casual use. Now there is an alternative called Sage.
Sage is open source, and you can both download it (and run it on just about any OS) or run it from a browser. It has a simple interface, and is fast and powerful. This video gives a history of the project and at about 38:45, you can see a short demo.
With Sage, you don’t have to toil over an algebra or calculus problem. Just type a few letters and numbers and you get your answer – both symbolically and graphed in 3D color. It even supports the use of 3D glasses for viewing.
It also makes a good tool for younger students and home-schoolers as well. With calculators eliminating the need for tedious arithmetic in most cases, should we really be forcing our children to spend hours perfecting high-speed long division by hand? Why not help them to learn advanced concepts by turning them loose with this software? A few keystrokes and clicks and a student can explore the wonders of mathematics without breaking a single sweat-bead of frustration. Motivation is the biggest obstacle to math education, and tools like this can go a long way to removing that impediment. I wish this kind of tool was available when I was a youth. It would have made math so much easier and fun. I could have learned a lot more.
On the subject of math education, many people still are not aware of Khan Academy. If you have never heard of this wonderful resource, I will give a brief overview. It is a very large (and growing) set of excellent lectures on math, science, economics and even other subjects such as history. Most are given by the founder Salmon Khan. He is an excellent teacher. His videos are easy to understand and are actually charming at times. He started by simply tutoring his niece in math via videos posted to YouTube, and people from all over the world discovered them and started learning math themselves. His success just exploded from there.
His site sports not only lectures, but has expanded into math software to help with the lessons, and tracking software along with progress badges. His teaching style is so successful, some enlightened public schools have done the smart thing and stopped teaching math. Instead, their students learn from Khan Academy and the school’s math teachers become little more than tutors and coaches. For more info, see his TED talk on what he is doing and how it is used.
As to his effectiveness, I can give some personal testimony. My children, like most, have struggled to learn Algebra. We homeschool and have tried every Algebra curriculum there is. Nothing came close to Khan in how well they were able to learn. I even watch some of his lectures myself. His lecture on the French revolution was outstanding, as are the ones on economics, and I even tried some of his lectures on Calculus. I remember struggling with a particular type of integral called a Line Integral. When I had the subject in college, it just never made any sense. After watching one of Khan’s lectures, it made perfect sense. He was able to take a rather intangible mathematically idea and give it some physical meaning – something I was never able to grasp before.
I wish I had Sage and Khan Academy when I was younger, or that had more time and a faster mind now. Whether you homeschool, send your children to a school, are a student yourself, or would like to learn something new – do yourself a favor and look into these two incredible resources. You won’t regret it.