When I look at a student who knows what they’re doing while solving a physics or mathematics problem versus someone who has no clue what they are doing, there’s an enormous difference in their confidence. The former can usually zero-in on the objective of the problem and knows the strategy needed to tackle it while the latter will try to remember useful formulas or try to do something more or less random.
This is relevant with almost all the students I tutor. I can tell the difference almost right off, because the person that doesn’t know what they are doing is usually unsure of the appropriate strategy and seems lost. This is only further exemplified when they pick the correct strategy to answer the question, but then ask me if what they are doing is correct.
I try to rarely give encouragement like this. The reason is simple: actually solving a problem (unless it’s a real hairy differential equation or integration) is relatively straightforward. It’s the logic of going from one step to the next that is more difficult, and the point of learning. Therefore, by answering the student’s question when they have to make a decision of what to do, I am taking away the most difficult part of the problem.
Instead, I do my best to let them choose the path to follow. Consequently, they get to figure out what works for them and what doesn’t make sense to do. If I just told them which steps to do, the crux of most questions would be gone.
As a tutor, my goal is to give the students I help the confidence they need to figure out the steps to a problem on their own. That is also why I try to stop them from referring to a memory aid or their notes during every problem, because I want them to feel comfortable with saying, “This is the next step. Not because my notes say so, but because it’s the next logical thing to do if we want to answer the question.” In my eyes, my job is only to do this, and definitely not to give them the procedure during each question. There’s a time for refining a procedure for a certain kind of problem later, but when they are first having problems it tends to be due to something conceptual.
When I think back to my own experiences in tests where I’ve felt confident on some questions and not so much on others, the reason I did not feel confident at some points was because I didn’t know what kind of steps to take. But when I was confident, it was due to practicing many times and internalizing the process. That’s confidence, and it’s what I want the students I tutor to have when I’m done working with them.
If you want to work on a particular quality for a student, work on their confidence, and the rest should follow.