# How do we know that something is true?

I’m trying to frame/structure my units with essential questions this year. I don’t really know how to use them meaningfully to add coherence to a unit, but I’m going to track one of my attempts here:

In Geometry our essential question (at least for this unit….perhaps for the year?) is: How can we know for certain that something is true?

I don’t have a clear goal, but I suppose I’m mainly trying to provide some context for the need for/tradition of formal proofs. Middle schoolers are often deep in the throes of existential crises, anyway….why not enrich math class with the occasional epistemological debate?

Day 1: To launch Unit 3: Reasoning and Proof, I explained that our guiding question for the unit was, “How do we know for sure that something is true?” and asked them to free write for a few minutes. I told them they could think about how it applied to math or think about it more generally.

After a few minutes, they shared out, and I jotted down their ideas. It was a lot of fun, everyone was super engaged and math class felt MEANINGFUL.

Afterwards, we talked about “inductive reasoning” and then used it to explore and make conjectures about vertical angles, linear pairs, and triangles. Some of the energy faded because the explorations felt obvious…sigh.