We all know confidently incorrect people. People displaying dunning-kruger. The majority of those people have low education and without someone giving them objectively true feedback on their opinions through their developmental years, they start to believe everything they think is true even without evidence.
Memorizing facts, dates, and formulas aren’t what necessarily makes someone intelligent. It’s the ability to second guess yourself and have an appropriate amount of confidence relative to your knowledge that is a sign of intelligence.
I could be wrong though.
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.
there’s more of the country than florida
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.
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.
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.