Visualize, Please don't Memorize

As the old saying goes pictures are worth a thousand words. The best part of a picture is it tells you a story and jogs your memory of an idea. Have you ever stopped to consider how you can check something you memorized.

Much of math can be illustrated into a graph, shape, or be given an analogy to a tangible item. When I'm attempting to teach an idea use of pictures and/or stories are quickly injected often garnering humour.

Students please put memorizing aside and learn through visualizations.

Here is an example when dealing with Arithmetic or Geometric Sequences. Did you notice there seems to be an (n-1) portion to both equations. Why is this. Well a sequence is like a number line that usually skips numbers by either a difference or ratio.

Look at the sequence as a loaf of bread that is cut up. In this picture there are 5 slices, not all even, but it only took 4 cuts. Relating sequences to the loaf (Slices - 1) = Cuts.

In a sequence we start with the first term that has no difference or ratio added to it. Using n=1 for term one in the equation (n-1)=(1-1)=0. Zero difference or ratio added to the first term.