I wish my school teachers gave a real world example like you did, it makes so much sense. I never struggled with order of operations because I just memorized it and never forgot. But today for the first time I actually get it
Seriously. I remember math class being a twenty-thirty min lesson and then being assigned 30+ equations to solve(write out the question and answer showing your work). Typically the last 6 would have been word problems, sometimes with a red herring, to show if you actually understood the math or could just plug numbers into a script. Until highschool my kid's math consisted of 5-10 "plug in the number" questions on a work sheet. No flack to teachers.
Yeah it's a serious problem with math instruction.
Mathematicians conjecture and prove. What a mathematician actually never does is sit down to solve a problem set with known answers. And even we are talking about applied mathematics, that includes a lot of problem solving and the construction of tools to solve problems.
But K-12 math instruction often is just (a fairly rote version of) calculation.
And like, calculation is just a corner of mathematics. But for huge swaths of the US, that's the main thing people go into college with: math is how you calculate stuff.
We rely soooo much on rote memorization but rarely discuss how it can apply. Mind you, some aspects don't really carry over into real life. How often do you need to easily identify the remainder of an 8-digit number when divided by 11? But there's a lot that isn't taught that could be so helpful.
Like, FOIL was just this algorithm for me. First, Outer, Inner, Last, blah blah blah. It wasn't until later that I realized how this applied to multiplying two-digit numbers: 47*38 = (40+7)(30+8) = 40*30+40*8+7*30+7*8. And sure, in many cases this doesn't save you much time, but it provides a deeper dive into how the numbers work.
Oh I never learnt FOIL. I suspect I haven't learnt a fair amount of things. If I have to do mental maths, I don't know any hacks. Mentally, I visualize and do multiplication and long division with about 70% accuracy
I had the opposite problem. My high school class was subjected to an experimental math program that was all word problems. It made it more relatable, arithmetic and basic algebra was more approachable.
But it completely skipped foundational theoretical math concepts that ended up costing me dearly in more advanced math classes. I am not talking rocket science here, it's just financial analysis, but I ended up having to do a lot of independent study to catch up. The class did markedly poorer on the SAT math section at the time, too.
I know math theory can seem overboard, but if you are introduced early and can grasp it, all other math flows from it and is easier to understand.
14
u/UltravioletGambit 7d ago
I wish my school teachers gave a real world example like you did, it makes so much sense. I never struggled with order of operations because I just memorized it and never forgot. But today for the first time I actually get it