If you don’t understand the mechanisms of arithmetic, algebra is going to be a challenge. If you don’t understand algebra, lots of other things that are applicable to daily life and trades are also out.
I use geometry and trig for gardening. I do unit conversions (algebra) in cooking. I use simple probablilty in gaming.
All of this comes down to my ability to perform arithmetic operations on abstract symbols. A calculator can give me the numeric results, but it can’t help me manipulate the equation to get the answer I need.
Your reasoning is also exactly why I don’t like the “You won’t have a calculator” excuse. It completely leaves out the importance of understanding the concepts of mathematics. If you don’t understand how the math works, you’ll have no idea I’d what the calculator spits out makes sense or even put it into the calculator in the first place. And even then some calculators do actually do things differently.
By the time I was in grade school we already had basic calculators that fit in pockets and that’s ignoring that pocket sized slide rules have existed for decades before that.
Exactly. Math isn’t about numbers, it’s about understanding operations and how to perform them. It’s how the numbers relate to one another to produce a result.
Of course. But this is about stuff like multiplication tables and things that are clear calculator fodder.
I can do stuff like 36 * 15 in my head if forced to, but my calculator can do it faster and more reliably then I can.
Also would you ever long divide 7/13 if you needed now? Of course not, use your phone.
Sometimes phones are not accessible. For example, if I’m running I’m not going to pull out my phone to do some basic math to figure out time splits and the pacing. I do that math in my head, including long dividing 7/13 if needed.
A lot of that stuff is about internalizing rules. By doing times tables up to 10x10, you have just enough memorized to understand patterns of multiplication, how it behaves and how to manipulate it. By working out long hand you understand the patterns of positional notation and some mechanisms to manipulate it. Division long hand also gives you an opportunity to experience how division is the inversion of multiplication, as long hand division is literally running long hand multiplication backwards (it’s trickier cause you are more likely to run into a fraction tho) - and the concept of modulo is also incredibly useful for daily life.
Even these things are building foundations for later math. Times tables and long hand division aren’t the only way to teach math, but they are a way that works. It’s not directly relevant, sure, and hasn’t been for almost 100 years. But it’s a foundation and has importance in that way
True, but you’ll save lots of time if you keep the ability to do simple math in your head.
Classmates always wondered how I could finish the tests before the time limit while they weren’t even finished when the bell rang. Well, who’d have thought, entering 20*5 into your calculator takes longer than just doing it in your head? I don’t want to know how long these people take shopping groceries now that everyone has a calculator in their pocket.
20*5 sure that’s easy. But are you actually going to opt for a piece of paper to long divide 4/17 if presented with the need?
If I need more than 2 decimals of precision, I’d use the calculator. But by the time I type it in I already know to expect an answer of about 0.23. If the calculator give me anything else, I’ll redo it more carefully.
A good student knows enough basic math to know whether or not their calculator did what they thought it did, or if they mistyped something, had it in the wrong mode, missed order of operations, etc.
Gonna be honest my guy I don’t believe you did 4/17~=0.23 in your head. And if you did, great for you but, most people can’t do that.
I did, and you can too. Here’s how: 4/17 is about 4/16 = 1/4 = 0.25, but a little less because 1/16 is greater than 1/17. The error term is about 4/(16^2) or 4/250, so subtract about another 2 hundredths to 0.23.
Or my thinking:
4/17 is less than 4/16 (0.25) but more than 4/20 (0.2). It’s on the fatter side of that difference, so I would go with 0.225 with some rounding… If I need a better answer than 0.22 or 0.23, I’ll use the calculator
I keep my 25 year old TI-83 in my work bag that I carry every day. Probably use it once every 3 months, but it’s always there for me.
I found an iOS app that is basically a near perfect clone of the TI-83 (GraphNCalc83). I use that nostalgic mf nearly every day for the most basic stuff.
Used to have one for Android called Andy-83, but it was so good that TI took notice and threatened litigation. Though I still love the tactile response of the physical buttons on the real thing. Plus its a good place to find some AAA batteries when I need them.
You just have to install it in your brain.
The app is called “Math”.
Arithmetic, really.
Fuck math(s).
Incompatible with my brain OS.
You still need to understand math enough to know what to put into the calculator. To figure out what the problem actually is. Sometimes it’s not going to be clear-cut and fed to you.
Cursive is so much faster
Typing is even faster and is universally legible.
For notes combining text with graphs (e.g. economics for instance), computer might be less efficient than pen and paper
I used an iPad with an apple pencil and bt keyboard for all of my college courses. Best of both worlds.
Not to mention more comfortable on your writing hand.
So. for those who can’t use cursive, there’s something I’ve always wondered. How do you sign your names? You just print it?
If you have to get out your phone to add 7 to 34 you look like a numpty.
Still write notes in adult writing too…
Adult writing lol. Get over yourself
