Calculus is algebra with changes? or calculus is algebra on speed (velocity if you add vectors).
In high school, I think we only had to complete Geometry (which was, generally, 10th grade). Algebra II (11th grade) and trigonometry/analytical geometry (1 semester each; 12th grade) were electives. When I signed up for them, I still had some kind of delusion about being an architect or engineer. When I had ruled those out, I tried to believe that Algebra II would prime my brain for something bigger. To my own great surprise I did better on the math part of the SAT than the verbal (I also discovered that I had measles the morning of the test, and I think my semi-panicky state gave me a boost).
What I did get out of all that extra math, was that I avoided taking any math whatsoever during college â my major only required one semester of math and I tested out of that. I couldâve substituted a semester of science with a semester of math, had I chosen to do so, but the placement test said my next recommended class would be pre-calculus.
By the time I finished college, I was interested in stuff like Ohmâs law and visiting the engineering library more and more often, so I wonder if I shouldâve stuck with it.
You could, or use proportions. What if it is 3 shirts for $40 and 2 pairs of pants for $50 and you only have $60? How many of each can you buy to make the most outfits? We could try every combination.
You donât have to set up an algebra problem to make these decisions but it is a way to be more sure you have the definitive answer rather than an estimate. Maybe the estimate is good enough and I could show you some algebra and calculus that would let you include the cost of the time of estimating into how long you should take to answer.
Itâs all around usâŚ
Yeah, which is why it doesnât make much sense to learn in high school I guess, unless itâs tied with physics. I remember asking why something worked the way it did, and being told that that was just the way it was and if I went on to study math Iâd understand. Not very conductive to learning. I need to understand, not just memorize. Not the teacherâs fault though. I had her for chemistry too and she was demanding but not a bad teacher.
I found it much easier to study calculus in the Khan Academy than at school - you can work at your own speed and it took much less time before I understood it and could practice with examples. The whole gamifying aspect works with me too, so I can stay interested for longer and progress faster, while having a visual idea of how it all fits together.
I would counter that itâs actually the instant internal understanding that â3 shirts for $40 means 1 shirt for $40/3â that the ânumeracy literacyâ folks want, and not the âhow do you turn this into an algebra equation?â question.
âLetâs think of this question in terms of xâ is exactly what turns millions of kids off math every year.
There was a study on kids who sell things and handle money, who can trivially do the kind of arithmetic you describe, who completely failed to understand math classes, even though the operations they needed to do were the same. But thatâs fine: what we should be aiming for is that kind of intuitive mathematical understanding, not âAlgebra II.â
So, sure, you can say âwell, you happen to be using algebra.â But when a 3-year-old says âDrive faster so we can get there quicker,â itâs kind of pointless to say that they âhappen to be using calculus,â because of their apparent understanding that a steeper distance-time graph will integrate to more miles for the same amount of time.
3x = 40, solve for x.
Yep, thatâs algebraâŚ
From the Slate article: algebra âmostly useless in real life.â!?
Wha? Maybe if youâre a poli-scientist. I use it all the time, idiot.
The big game-changer for me in high school wasnât my proper math classes, but Chemistry. At some point I decided I wanted to be a bio-chemist and got really into science stuff, and our Chem II classes were split into two halves. The first half of the year was all labs, and it was non-stop playtime, mixing and boiling and titrating. We made plastic and beer and vodka. So much fun. But the second half was all theory: molarities, Avogadroâs number, etc, and it just killed me; I had such a hard time getting my head around this stuff. This was at the same time as Algebra II and pre-calc. A rough year.
But at the same time I was taking a required art class, and unexpectedly loved it. By the end of that year I was applying to design schools and was able to test out of all but one semester of math requirements.
My point is that it should cut the other way too. Some people donât learn how to apply math when they are taught algebra or calculus. People propose âfixingâ this math problem by eliminating algebra/calculus and teaching some kind of statistics class, rooted in ârealityâ, but unmoored from the logical fundamentals that these classes teach. This is great for the folks who âdonât getâ math, but itâs terrible for those who do in the same way that English (English Lit.? Literature? Writing? That shitty course with that bullshit by Tennyson?) classes are terrible for some people.
Yet we donât see people calling for a change in the way English is taught, now do we? Even though about as many people are terrible at making arguments, conveying opinions or making interesting presentations as there are people who canât comprehend how having a five dollar coffee at Starbucks every working day costs them over a thousand dollars a year. This is a kneejerk attempt to address a societal problem and while it will benefit many people, I posit that it will be to the detriment of many others.
I agree. I donât think we should eliminate higher math from high school any more than we should eliminate AP Literature or Chemistry III. But I think that having higher math as an across-the-board requirement makes little sense, especially in senior years, when kids are already looking to college majors and their math requirements. Higher math should be an option, not a requirement. I mean, realistically, it helps to have awesome teachers who can show you how calculus could be applied to daily life or why a quadratic equation is a cool thing to do, rather than be told âread this chapter. Do these equations. Move along.â
I was probably on track to take Calculus in high school anyway, but this wonderful series* from Annenburg/CPB/Cal Tech was on PBS during lunchtime after morning football practice one summer and I got totally hooked. Physics was the hook to learn calculus, curiosity about how the world and the universe works was enough to keep my interest. And getting a year head-start on he concept of derivatives and shrinking-to-zero really helped once I actually got to calculus class. My high school physics class was calculus-less, which I understand from an inclusionary point of view, but letâs face it, thatâs pretty weak, so this series helped with that as well.
https://www.learner.org/resources/series42.html
And just to prove that being a fancy prestigious institute doesnât mean you have taste in web design, another page about it:
I algebraâd and I didnât ev en know it!
Sometimes I am tasked with providing a digital photo for a designer. When I ask, âHow big?â, the designer usually replies with â300 dpi,â which tells me nothing, since I havenât been told the dimensions of the image. At times like this, I wish people knew more about how numbers work, not less.
Also, âdotsâ and âpixelsâ arenât the same thing, but thatâs another topic.
If Iâm getting a photo from a photographer, Iâll often specify â72dpiâ or â300dpiâ depending on whether itâs for web or print use; if they ask the size, Iâll typically tell them to send the actual size they shot it at. Itâs way easier for me to crop on my side than to spec a crop over the phone. I know how numbers work, but often times âsend it as big as youâve got itâ is easier for both people than figuring out final sizes.
algebra 2 is kind of useful for geometry and trigonomety. Now, computational linear algebra is mind numbing, especially with only a hand calculator
Thatâs a 13% drop!
13% ? Why, thatâs almost half!!!
Pfft, a for loop solves every problem (donât ask me about determinism, completeness, proofs, or performance :D)
When I was a high school freshman I talked my way into senior physics. Having never even heard of trig.
I got a B+ in the class by drawing very precise triangles and measuring them with a hand waay steadier than I have today.