Having a concept for which one does not have a simple explanation is one thing. Critiquing someone else’s understanding of that concept is another thing entirely.

I did the latter with a TA last week on algebra. She explained the essence of the concept to me in layman’s terms and then quickly added, “It’s important for our next slide because this is why.”

As something I’ve never done before, I was confused—almost petrified at the same time—about the conceptual lifeblood of algebra: calculation.

I tried to explain what it is we were talking about in the slide after which she offered another helpful explanation:

**Probability**

This was the wrong way to approach the subject, I had thought. How do we define probability? How do we test the existence of something?

And what is the meaning of a value? These are questions I’d not thought about before and that concerned me.

With algebra’s underlying idea, the amount of probability, and the meaning of probability, standing in the way of an explanation were weighing me down. The topic took me on an emotional rollercoaster of confusion, uncertainty, and I didn’t even know where to start.

I was stuck, I didn’t know what was going on, and I felt like throwing up on the floor.

In my quest to get a grip on the subject, I managed to figure out probability. I had to.

Simply. I could feel my estimation as I attempted to make an analogy of the concepts and then a mental arithmetic to tell me I was being too literal.

I have to be more concise and descriptive—with a little bit of trust. There is a fine line between scientific accuracy and the slightest bias or faulty interpretation.

Many discussions about math cover topics that are confusing, ranging from concepts that many students don’t know about, to what math concepts are and are not conceptual.

So what should I do? Could I demonstrate with examples? Could I use terminology? Why am I not using the math term? How do I even begin?

As I have said before, when you talk to someone about math, we should say what it is we’re talking about and then explain it to them immediately. Don’t backtrack. Tell us how and what it is that you’re explaining. And then show them.

When I walked away from my discussion I’d presented more than I could have.

And this was just me! There are millions of math and math-related discussions happening on Twitter every minute of every day. Let’s learn it by example!