Do You Understand?
In English we seem to use the words `know` and `understand` interchangeably, but in reality they have subtle, but important differences. For example, we may know a lot of people, but we will probably only understand a few of them. Understanding carries a greater depth of knowledge, but also an ability to figure out how something works.
Take the example of a cake (or as some think just take the cake!). I give you a recipe; two eggs, two cups of flour, two table spoons of marg, half a teaspoon of bicarb. Cook at 180 C for 15 mins. OK you know my recipe for cakes. If you understand the recipe though you will be able to make changes to do something different. Will adding sugar make them better? What if we use butter instead of marg? Can I make a chocolate version? Can I cook them for less time if I turn the oven up?
You, perhaps, know the answer to some of these questions because you have made cakes before, or because you understand how they are made. Just knowing the recipe doesn`t give you understanding.
There is a big temptation in maths particularly, to learn methods, rather than understand what is happening in the maths. However, you will find, as one of my students did, by understanding the maths its much easier to recall it and also to use it in new situations (ie an exam question!).
I have tried to structure the material here towards understanding, rather than simple recall. This way your learning will, in effect, become self-supporting and the more you learn the easier it will be to learn more!