Depth of Understanding

I frequently criticize our overly broad view of what qualifies as learning. There are two uses in particular that I like to single out. My preferred use of the term refers to the development of skills and abilities. The frustrating usage that I single out most often is memorization. There is something that I have not yet made clear that I need to mention. Learning has been used for more than these two vastly different concepts.


I have decided that it's time to share an example of another way people supposedly learn. Many people insist that those who are developing a deeper understanding of a subject are learning. What is depth of understanding? Let me use multiplication to explain.

When we were in school, we have all had to fill out worksheets solving multiplication problems. Although there is certainly value in knowing how to multiply numbers, this process is worthless if you don't have an understanding of why you would multiply numbers. If anyone needs to just multiply numbers, they will not ask you to do it. They will do it themselves, use a calculator, or use computer software. Simply put, depth of understanding means that you learn when and why you multiply numbers together.

This brings us to three very different ways in which children "learn" multiplication. Children are expected to learn (as in develop the ability) to calculate the numbers, learn (as in memorize) the multiplication tables, and learn (as in developing a deeper understanding) when to use multiplication. I can think of at least one other way in which children "learn" multiplication, but I will save that for another day. For now, let me just say that there is far worse use of the term than anything that I have discussed so far.