Students asking “why do we need to learn this” or worse graduates who proudly proclaim “Day 19,337 of never using the quadratic equation” are a symptom of teachers who haven’t read their Thorndike.
Learning is an active process. It takes effort to do. People do not like being made to waste effort. Students will be much more effective learners when they understand the value of the lesson to them in their lives. “You never know when this will come in handy” is not good enough. This is Thorndike’s principle of readiness. And especially high school teachers are bad at satisfying it.
Math teachers get it very often, because for some reason we approach teaching math to a nation full of hormonal teenagers as if they all want to grow up to be mathematicians. Starting in about the 7th grade they stop giving practical examples and teach math as a series of rules to be applied to contextless problems, and to the student it feels like years of pointless busywork.
And while I can’t claim to have ever factored a polynomial in my daily life since leaving school, I did recently come up against the order of operations. I calculated the width of some cabinet doors, and I factored in the gaps between them wrong. 3 doors, 4 gaps between the doors. I did door_width = opening_width / 3 - 4 * gap_width. When I needed to do door_width = (opening_width - 4 * gap_width) / 3. In the first case, you end up subtracting all 4 gap widths from each door. I would be better at math today if you’d explained it to me like that when I was 12.
SmartmanApps@programming.dev 12 hours ago
No we don’t.
No we don’t. Just check out some final exams to see plenty of them still included.
Most teachers do, but some aren’t very good, especially in the U.S. where it’s not even required to have Maths qualifications to be a Maths teacher.
HeyThisIsntTheYMCA@lemmy.world 4 hours ago
there’s more of the country than florida
SmartmanApps@programming.dev 4 hours ago
And there’s more of the country falling behind the rest of the world in Maths than just Florida. It was all over the news, again, just a few weeks ago.
captain_aggravated@sh.itjust.works 11 hours ago
I mean, go ahead and lie about how I spent 6 years of my own life to my face. Memorizing proofs and working endless assignments of just…equations. Here is an equation. Do thing to it. Solve it, simplify it, factor it, graph it. I plugged and chugged so many numbers into the quadratic equation, I don’t think I was ever told what that’s for. Some chapters had token word problems.
A lot of the math I actually know I learned in physics class, where you’d do unit math. That 25 meters traveled in 5 seconds means a velocity of 5 meters/second. Science class math comes with sniff tests that math class math doesn’t.
The way I was introduced to order of operations was, the teacher wrote a long expression on the board, this plus that divided by such minus thus times such plus this times that. Spend a second solving this. Okay, who got 7? Who got -23? If you got -23, you’re right.
That is FUCKGARBAGE teaching. It may be the flight instructor in me, that my classroom is an actual airplane that we fly over actual people and their homes, but few things piss me off as deeply as setting up your students to fail. Because introducing the subject this way separates your class into two groups: Those that already have a functioning understanding of the topic whose time is being wasted, and those who don’t already understand it and need you to teach them this skill, who now feel tricked, confused and frustrated.
This teacher went on to explain Order of Operations as a series of rules you follow because following rules is what you do. “You do parenthesis before exponents before multiplication/division before addition/subtraction.” PEMDAS, Please Excuse My Dear Aunt Sally. This was taught with the same “This is how nature is” attitude as the planets of the solar system or how ionic bonds work, except algebraic notation is artificial. It’s manmade, like the English language. It’s a method of communicating ideas, except it was taught as a series of rules and procedures that you were supposed to memorize how to do without understanding the goal, and fuck your life if you lacked the vocabulary to describe what about it you didn’t understand.
SmartmanApps@programming.dev 3 hours ago
I’m not lying. It’s there in the textbooks. There are many available for free online these days.
No students are required to memorise proofs, only how to do proofs to begin with.
They’re not token problems - learning how to do word problems is a central core of Maths. They’re thrown in often.
Not really. v=d/t, s=ut+½at², and similar equations are used often in teaching Maths (such as in non-linear graphs).
That’s right. We teach that if you follow all the rules you will always get the correct answer. Now witness adults on social media arguing about the answer to an order of operations question because they’ve forgotten the rules but refuse to admit that’s even possible, and yet the rules are still there to be found in Maths textbooks now, same as they were then, still the same rules (despite some of them claiming the rules have been changed).
No it isn’t.
The notation is, the Maths isn’t.
It’s not at all like language, any language.
No, it’s a method of calculating things, like rocket trajectories, etc. Got nothing to do with communication at all.
I can’t help it if you yourself had a bad teacher, but look in the textbooks and that isn’t how it’s taught at all.
captain_aggravated@sh.itjust.works 7 minutes ago
I LOOKED IN THE TEXTBOOKS FOR YEARS. AS A STUDENT. YOU USELESS TWAT!