We learn subtleness over time, and by making mistakes along the way. Elementary school kids learn that some ways of saying things are rarely appropriate ("I hate you!") and others are perhaps foolhardy ("Go ahead, I dare you to push me off this bridge!").
The same thing applies with math, even the simple math we teach in our Excel Math curriculum. We need to learn to say the right thing in the best way. Let's take a simple example.
I get regular reports on the readership of this blog. The data is compiled to a very low level - meaning I can see how many people are visiting per hour of each day.
Here's the raw data which I have taken out of the email they sent me. I pasted it into my spreadsheet. I think it's more detail than I need to share - but it is interesting to see that on most days, we have readers 24 hours a day!
Here's another view showing the aggregate numbers for about 18 months, rounded to the nearest 100, arranged in columns by visitors and page views. The first month, March 2010, we had 1100 visitors who each, on average, read 1.6 pages while they were visiting the blog.
To clarify what's going on, I added some circles and arrows and a paragraph on the back of each one (sorry, that's an Arlo Guthrie joke).
What do you think? Does this make more sense to you than the rows and columns of numbers in the spreadsheet shown above? I liked it.
I decided to simplify my chart. I've left the data and colors the same, but I got rid of the vertical lines. I eliminated the 7x High-Low line. I added a color background to the descriptive text to match the color of the lines linking my data points. I edited the text down to a minimum.
After looking at the data and doing some calculations, I concluded that our overall site traffic has tripled in the past year; no matter whether you measure the peaks or the valleys - the increase is roughly the same. To save the reader some time, I added this information to the table heading. Now at a glance you can see what I am trying to say. If you want more information, you can inspect the chart more closely.
Does the second graph communicate more effectively? If you said yes, you win a prize. If you have 8 minutes, click here to see Arlo Guthrie explain what he meant by "circles and arrows and a paragraph on the back of each one" resulting in "a typical case of American blind justice."