How to Make Mathematical Concepts Easier to Understand

This is the goal of everyone that has ever taught or is teaching math. I'd like to take this opportunity to share my experience in this challenge. It has always been my opinion that math is not merely a collection of equations, and any more than a novel is a collections of words. What an author does for me is to use wordsto create in my mind an image. In theMagic of Thinking BigDavid Schwartz says that words are "the raw materials of thought". We have to admit that our minds are not manipulating words or equations, but instead our minds work with images. In order to get an idea across to a fellow colleague, weneed to get an image of that idea in his mind. As able as words are in creating images in our minds eye, it can still be a daunting task, but it is even more difficult when trying to do so with an equation. So why start with the equation? Why not start with the image? This is what I am doing in my Elementary Statistics course at the Community College where I teach. I've been using MS Excel and its graphic capability to "show" the math concept, giving students a qualitative understanding with an image first. Then follow up with a more quantitative explanation using equations. In addition to the graphics capability of Excel, it also has the ability to run macros that is, short programs. Thesecan be used to manipulate the parameters of the data displayed by the graph, which clearly demonstrates the impact of the parameter on the function. So, imagine a graphic display of the Sampling Distribution. And on the same graph you could fill a 1% area under the Sampling Distribution in the left tail and another 1% under the right tail. Now the area in between is 98% of the area, the Confidence Interval. Now imaging a cleverly designed macro that would increment, or decrement, the Sample Size. The area of the Confidence Interval remains the same, but the limits move closer together as the Sample Size increases, and move apart as theSample Size decreases. No one in my class has ever escaped without understanding the impact of Sample Size on the Confidence interval. This is just one example. The possibilities are limitless. I'm lookingforward using these techniques in my College Algebra and Pre-Calculus classes as well.