Narrow Paths and Open Forests

Imagine you’re walking through a forest for the first time. This forest has trails, so you follow one of them. Since the forest is unfamiliar to you, the only thing you have in mind for your walk is the destination. You know that if you follow the path correctly, you will get to where you were hoping to go when you checked the map at the welcome station. You’re moving along the path, and suddenly…

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Liking Without Doing

When I find an activity that I enjoy, I have a tendency to think I should immediately do it. After all, how can I claim to like something if I don’t do it? Even if I have a lot on my plate, I feel like the only way to say I like an activity is to do it. But that’s not the only possibility. Instead of feeling the need to do everything that looks interesting,…

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Learning to Teach Yourself

I’ve always liked teaching others. I enjoy being able to connect with students, understand their struggles, and offer what I know as a way to help them make sense of a concept. My particular subjects of interest are mathematics and physics, but the real joy I get from teaching is simply being able to help others. Teaching has a fairly good reputation. It’s seen as a respectable profession. I don’t doubt that teachers do important…

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Glimpsing Connections

Learning a new subject in mathematics is always interesting. You learn new techniques to analyze problems and get to investigate the relationships between objects. Whether you’re learning about probability, algebra, geometry, or any other field, you will do these two things. The idea is to expand your toolbox to apply to various mathematical problems. That’s fine, but it’s not the reason that I enjoy mathematics. For me, it comes from a slightly different place. The…

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