Confusion and the skill of backtracking

If you are learning something by yourself it is almost inevitable that you will get to a point where whatever you are trying to learn ceases to make sense.

There can be any number of causes for this. Perhaps you have misunderstood something earlier on and it is only now that that earlier misunderstanding is making itself felt. Perhaps a new concept has been introduced that just doesn't click with you. Or maybe the author is just not that great at explaining things.


In Thinking Mathematically, John Mason describes the experience like this:

In my experience, I have usually been stuck for some time before I become aware of it. At first the awareness is hazy and indistinct. It slowly grows until I am definitely both stuck and aware of being stuck. Only when I feel stuck and I am aware of my feelings can I take action.

Whatever the reason for feeling confused or stuck, one of the most important skills that you can have is backtracking.

What this means is working backwards from where you are, from your current point of puzzlement until you get to a point where everything is clear and then trying to isolate the point at which you ceased to understand.

When I have tutored children, I have used this process in helping them to understand. With one student, who had some difficulty understanding particular kinds of equations, I kept simplifying and simplifying until I reached a point at which he could understand and solve the equations. Then step by step, I added complexity, at each stage making sure that I hadn't lost him and not moving on until I was confident that he was confident, until ultimately we reached the point of understanding where he needed to be.

This is easy in mathematics where each concept builds upon the last, but it is also generally true of most fields. If you are learning how to dance then you can reach a point where you don't understand how to do a particular move. If you have access to a video of the move then you can watch it over and over, and slow it down if necessary to identify the exact point at which your understanding fails and then observe carefully what the dancers do around that point to complete the move. Once you have seen it, you can test your understanding by trying it yourself to see if your new understanding translates into action, and if it doesn't repeat the process until you achieve success.

When I was first learning to dance I had a lot of difficulty with a move called the basket, I always seemed to lift the wrong arm and turn my partner the wrong way. It was only when I slowed down and observed more carefully how the move was done, breaking it down into components I could understand (lift left arm, turn partner anti-clockwise) and then time these components correctly with the footwork that I was able to master this move and then move on to other things.

In Secrets of a Buccaneer Scholar, James Marcus Bach describes a similar process that he used:

To learn the computer's language, I must hop from stone to stone. If the material was too hard, there must be a moment in the book (a sentence? a word? a punctuation mark?) where the gap was too wide to leap.

Maybe if I hopped very carefully, I could find a way across....I would study that gap in the stone bridge and maybe find a way past it. I believed I couldn't learn 6502 programming, but maybe I could discover why I couldn't learn it

In the final analysis, the key is persistence and looking at the problem in different ways until you experience the insight that closes the gap in your understanding. If there is no way forward that you can see then you might try using another learning resource as I have mentioned elsewhere for a difference approach.

Whatever you do don't give up: if what you are trying to learn is worth learning then it is worth the effort of struggling through the transient difficulties to achieve genuine understanding.