I've been working as a private tutor of math and computer science for a few years. Previously I got a degree in computer science and worked in aerospace for 16 years. I've always been interested in teaching, and I've trained in mindfulness applied to education. So, I love tutoring, especially compared to a desk job. But I don't have a teaching degree, so I'm finding that I have a lot to learn. I wanted to get feedback about a math teaching idea. I tell my students that "sometimes you have to be a mouse, and sometimes you have to be a robot." A mouse sniffs its way through a maze, searching for cheese. This is like exploring a math problem, brainstorming, or guessing what math technique to try next. For instance, you are given a problem in which you have to simplify a rational expression. You're not sure what to do next. You might have to guess at something and try it. A robot follows instructions. It does exactly what it's told, methodically This would be like deciding you are going to factor the top of the fraction. At this point, you need to use the exact steps for factoring. You need to check your work methodically. You may need to recall a list of common errors and check for them. It seems that mixing up these modes causes problems. For example, at the beginning a student may be afraid to explore. They've been told that math has "right and wrong" answers, and they don't want to be wrong. They may shoot down their ideas before they've even given them a chance. So their concerns about "being right" get in the way of brainstorming. Then, when it's time to be methodical, they get distracted because they are thinking where the problem leads. The whole time they are factoring, they are wondering if it's the right thing. In other words, their desire to explore and "think outside the box" is distracting them from being methodical. So I ask them to be clear in any given moment whether they are being a mouse or being a robot. Perhaps this idea corresponds with the pedagogy taught in a teaching program. If I ever go back to get my degree, I might encounter something like this. I'd be interested in any feedback. I've noticed it has another benefit. Whenever I ask a student to switch modes, they pause for a moment and gain a little extra mindfulness of their process. This slows down and calms their thoughts, and keeps them from rushing forward heedless of mistakes. This little pause doesn't have to come from switching modes -- it could come from anything. I could ask them to pause and switch pen colors, or pause and listen to music. But it's efficient to have it happen automatically as part of mode switching.