Geometry was so fuckibg stupid omfg “prove this is a triangle” I literally know it’s a triangle like intuitively bitch
Yep, rant time.
High School Geometry, the way it was taught to me (late 90s in the US public school system – I would have been 13 at the time and most of my classmates were 15-16, for a frame of reference) is incredibly dumb and extremely valuable.
Let me explain.
The reason why you need to “prove this is a triangle” is because HS Geometry is really trying to teach two classes at once – geometry and mathematical logic.
Mathematicians use Triangles to teach logic because Triangles are simple – they have three vertices, three lines, live in a 2D world, have simple and easy to understand laws (when in a Euclidean world, that is, but that’s a different awesome ballgame), and they’re awesome. However, academia has decided that, “well, we teach Triangles in this class, we need to teach Logic, Logic works best with Triangles, therefore we teach Triangles and Logic in this class!”. That’s not actually sound logic!
Look at why Mathematicians use Triangles again. Those all sound great to people like me who already know these things about Triangles and are likely the ones practicing this pedagogy rather than someone looking at the situation from the perspective of a kid. It makes zero sense to the kids who just want to know what makes a Triangle a Triangle without knowing how to get to Triangle from Lines In The Ground. Some kids (like me) survive in Mathematics in spite of the nature of how we teach, and that’s just wrong. These styles of curricula are treating the idea that is supposed to be taught (”this is a triangle. See? It has three sides, three vertices, …”) as a law (”this is a triangle because you obviously know your shapes”) instead of something that can be proven. That’s not proper logic, that’s either circular (”Triangles are Triangles, duh”) or authoritative (”This is a Triangle because I said so, now prove it!”) instead of letting kids actually think for themselves and figure out new and interesting situations because they follow basic logic – which is the entire bloody point behind teaching kids mathematical logic to begin with.
Logic is incredibly useful to teach. It is practically a foundation of people learning things both inside and outside of mathematics. Teaching Mathematical logic before Geometry… heck, before Basic Algebra, makes a lot of sense. It lets kids see the “why” behind mathematics and go off in their own worlds, the ones that gets kids asking “wait, what if two parallel lines could intersect after all, what would that look like?” and you get to introduce someone to Perspective Geometry (3D art, optometry, computer graphic design…). Mathematics, regardless of what has been taught, isn’t a linear progression from A to B to C so much as an open world RPG where you ignore all of the mainline plot because the sidequests are much more interesting. Why do you think the person typing this does so bad in certain areas of mathematics (advanced calculus) and so freaking awesome in others (Probability)? Because I ignored the mainline plot and went for the shiny things that taught me how math rocks work.
If someone taught kids Mathematical Logic at an appropriate time in their academic lives, you can expect students to actually be able to “prove this is a triangle” – because they already know how to formulate basic mathematical logic to begin with and you’ve given them the tools to learn instead of making them think they’re dumb because they don’t know how to use the tools you’ve given them. On top of that, HS Geometry is no longer a “this is the next step in your academic career that you must do” so much as “this is a plotline that you can pick up if you want, and the rewards kind of make you feel like you’ve discovered a universe on a bad acid trip”.
I thrived in this environment, because I had already had a strong background in other types of logic (philosophical and binary/computing logic), which is tied to mathematical logic. In short, I was taught how to learn before expecting to regurgitate garbage factoids about three sided two dimensional figures in a Euclidean world. I was actually able to take the steps the mathematicians intended students to take back when they designed the dang class to begin with.
That’s why you’re supposed to be able to prove something is a Triangle. Not your fault no one taught you how. Mathematics can be (and are) beautiful and can expand the minds of those who learn it. It can also be frightening and contract the minds of those having it crammed down their throats. Guess which is the most popular way of teaching this?
Tune in next time when Old Man aetherspoon has other bold takes like how very basic Calculus should be taught to six year olds and anything more advanced should be college level only or much further down those proverbial quest arcs. Or that any mathematics class considered to be a weed-out class is horribly antithetical to the entire concept of mathematics.
* Yes, I used mathematics logic to disprove the teaching methods of mathematics logic. Deal with it.