yewler

My hot take is that math class doesn't do the one thing that justifies its place in core curriculum. We're told that the reason we all have to take math is to strengthen our logical thinking skills so that we can apply it to life. Sort of like how you can go to the gym and lift weights, and the ability to lift them isn't inherently useful to you, but you're keeping yourself healthy and building muscles that you can use elsewhere in life. Everyone needs to know how to think, regardless of what you do in life, and in theory mathematics is a great "gymnasium" to practice that skill.

But is it doing that? In my experience, it doesn't. Not even in the slightest. Being told a formula or algorithm, lectured on exactly how it works and how to use it, and then being given homework that drills your ability to apply this new concept 20 times or so does nothing for a person's ability to think. All this requires is blind rule following with essentially no real purpose in sight. This ends up alienating many students who don't care, have no reason to care, and have a hard time learning things they don't care about. Math class is boring as shit, if we're being entirely honest, but it doesn't have to be that way.

Fundamentally, above all else, mathematics is a creative art. Painters are artists who express themselves through the medium of pigment. Musicians are artists who express themselves through the medium of rhythmic sound. Mathematicians are artists who express themselves through the medium of thought. As such, math class should function like an art class. Students should be given the reigns to be able to do their own thinking. They should be able to create their own ideas and make their own art. Genuinely fuck the quadratic formula, fuck the Pythagorean Theorem, fuck difference of squares. So few people have any reason to care about these things. Are they wonderful pieces of math that have their own wonderful nuggets worth studying? Hell yeah. But if a student has no reason to care, in my opinion they should be allowed to think about what they want to think about, to express themselves through mathematics in their own way, and in doing so, strengthen their thinking muscles the way math class should be helping them to do.

Finally getting to your actual question, the only thing I care about is if the thing the student is using is something they've thought about themselves (almost certainly with instructor assistance). They need to have done some of their own thinking. FOIL is just a series of letters in an order, and I don't imagine a student is going to divine that from thin air. The box is closer to what I'd want to see, since it demonstrates actual mathematical conceptualization, but it ruins everything if the teacher just shows the box and tells the student to learn it.

One progression that a student may go though to discover this type of stuff for themselves is by thinking about multiplication. Say I want to do 6*32 in my head. That's kind of a pain in the ass, so what can we do? Maybe with a little help (and a few drawn rectangles) they can see that it's a lot easier to do 6*30 and add it to 6*2. That's pretty neat. We've turned something I probably needed a pencil and paper or calculator for into something that's quite easy. But there's nothing special about this number problem is there? Thinking about this, a student may discover distributive property for themselves. In standard mathematics, we symbolize that as a(b+c) = ab + ac for all a,b,c, but the student may symbolize it another way. They may even just say it as a sentence or paragraph, and that's okay because they have an actual concept in their mind that is tangible to them. Okay then what about (a + b)(c + d)? Well a+b is just a number, so we can use our neat little property:

(a + b)(c + d) = (a + b)c + (a + b)d = ac + bc + ab + bd

Three applications of our fancy new trick and what do we have? FOIL!

Okay but what about trinomials?

Using the fancy trick 4 times spits it right out. A student may notice they're just multiplying everything in the first bit by everything in the second and adding everything together and can explore whether or not this works in general.

Would this style of math class slow content learning down big time? Ohhh yes, and there's a conversation to be had about how to fit this into a world where more advanced math is useful for a lot of people, but for everyone else, there's no reason anyone should be graduating high school with calculus under their belt. If we took our time with math ed instead of trying to over standardize an art form, we'd have better thinkers.

Math class kills the very thing it aims to build up, and I'm sick of it.

What do I need to do to be given a math reeducation camp after the revolution? I need everyone who uses the word foil when multiplying binomials to be gulaged with me immediately. We will be doing some arts and crafts.

Not trans related but I want few things more than to neuralyze math knowledge from the general populace so we can break this cycle of math being taught and retaught in the stupid ass way it's currently being done.

What are you into? If topology sounds fun, Bert Mendelson's Introduction to Topology is such a wonderful text. It's extremely dense but also the best written intro level text I've ever seen.

Consider: A.J and Big Justice on Jimmy Fallon

People can be sucky for sure, but consider:

Most trans people are more satisfied with their life after transitioning, even with the existence of transphobes. A lot of people talk about the sucky parts of the trans experience, but there's also so much stuff that is so wonderful and awesome about it.

I'm so happy you're thinking about taking little steps and experimenting. But if at any point you realise you're not trans? That's totally 100% valid

Other posters have hit on this already but you don't have to be the version of trans person you see and hear about everywhere in order to be trans. The trans experience is exactly as diverse as the number of trans people there are. You don't have to fit in some box.

Just a few months ago I was right where you are now. "If I can get by as a cis person why the hell would I make things so much harder on myself? I don't look at myself in the mirror and want to throw up, so I'm probably not trans anyway."

But when it comes down to it, you only get one life, and the question a trans person has to ask themselves is would you rather spend that life letting other people define who you are, or be the happiest version of yourself you can be?

To me the answer was not at all obvious at first. What if I'm not happy enough to justify the hate I'm going to bring on myself? But there's so many ways you can safely experiment to see how you feel. You don't have to decide you're trans first before you can experiment. I highly recommend playing around a bit just to see how it makes you feel. You lose nothing just by playing around.

It's so nice to be free of the "what if I'm not actually trans" thoughts that used to plague this girl's noggin. Having the freedom to just to the shit I want to do and not do the shit I don't is actually the best thing ever. I've done so much gender stuff lately that I would have never done with those fears rotting me.

Guess who has an HRT consultation scheduled 👀

I'm wearing one of my sweaters from the shopping trip out in public today 👀 feelin' gooooooood

Omg this is horrific