It's hard to swim with clenched fists.
Learning isn't really about conveying information. That happens, sure, but the precondition is an environment to ask questions freely, risk being wrong, and updating your mental model for how things work. The student's curiosity ignites a feedback loop of progress, and facts come along for the ride.
However, this all hinges on psychological safety. When people say "I hate math" they mean "I hate how math makes me feel."
And by that, they really mean "I hate being expected to do things I never understood. I feel stupid/worthless/not good enough."
It's not the Pythagorean Theorem or fractions they hate -- it's what it means if you can't do them right. Swimming doesn't work when you're so tense your hands stay closed. Neither does cramming facts into a clenched mind. (By the way, not using the Pythagorean Theorem correctly simply means your mental model needs adjusting.)
I brushed against the edge of my psychological safety in college. A poorly-taught class made me question whether I was competent at math, good enough to do it, worthy enough to continue the path I wanted. Thankfully, my overall academic experience defended me from that conclusion ("I've made it this far...") so I came to another conclusion:
My teacher doesn't seem to care if I truly understand these ideas. I have to find what makes sense for me.
In a psychologically safe world, you ask questions and update your misunderstandings with complete ease. Tests are things you look forward to: don't you want to catch the leaky roof in your house early, so you can fix it?
But that's not the norm. Getting things wrong means you're stupid, or won't pass a checkpoint, not that your mental model has a hole to plug. Education theater has us nodding along and checking the boxes until the next class.
(Pet peeve: lessons on imaginary numbers that state "negative numbers have square roots" and ignore the utter confusion this creates in a student's mind. The population of France is 67 million, negative numbers have square roots. A fact is a fact, what's hard about that? Argh!)
When seeing a lesson, I silently run through a pyschological safety gut check:
- Can I imagine the teacher taking feedback from a student? When was the lesson last improved? How comfortable am I asking questions?
- How long did this topic take to be discovered historically? Did the teacher struggle when learning the idea? Have they told students what confused them most?
- Does the teacher want me to truly understand the material, not just memorize and move on?
When I personify Wikipedia, I see a hyper-literal robot that answers correctly but not helpfully. You asked for a definition, and WikiBot3000 gave it to you. Your understanding was not my objective.
When confusing ideas aren't acknowledged as such, I lose my trust in the teacher. Are they blind to how strange the concept is to newcomers? Are they trying to maintain a reputation as the un-befuddleable genius in the room? My math spidey sense goes haywire: what else will they gloss over?
The ELI5 (explain like I'm 5) subreddit, by contrast, fosters psychological safety by assuming you're speaking with a child. This explanation is simplified, but in the right direction. I genuinely care if you understand it.
Let's foster the psychological safety to ask foolish questions, acknowledge our confusion (in both teacher and student), and constantly refine our understanding. A teacher saying "Here's what confused me, and what finally made sense" goes a long way to an environment where we can actually learn.
Happy math.