An understanding of double-entry accounting is more-or-less equivalent to an understanding of trigonometry. It’s not necessary for a basic real-world view on how things work. It’s absolutely essential if you’re involved in a field that uses the concepts of that discipline.
I know basically nothing about bridge building. I remember a few things from high school about levers. In trigonometry class, I remember a few applied math problems about suspension bridges. I’m sure that civil engineers have a greater understanding of applied trigonometry than I do.
I know a bit more about corporate financial reporting than bridge building. It’s a fundamental concept that your credits and debits will net to zero. Indeed, there’s usually a check line on trial balance reports that ensures all account balances have been categorised. Furthermore, at the end of the year, revenues minus expenses equals profits. That profit (or loss) is moved onto the balance sheet as retained earnings, which is categorised as equity. Corporate reporting of a company’s balance sheet is a basic, required component of annual reporting. God help a company that submits a end-of-year financial report where assets minus liabilities <> equity.
Yes, but the vast majority of people are NOT the folks making sure the books balance. That’s my point. Would it hurt people to learn a bit about double-entry bookkeeping? No, but frankly, I’d rather the time be spent on, say, learning a second language (such as Spanish in the US) which is arguably far more useful on a practical level for most people.
There are only so many hours in the school day and we can’t teach everything to people before they’re 18. If you’ve mastered basic arithmetic and entry-level algebra then if you need double-entry bookkeeping down the line it won’t be hard to pick up the basics and go from there - meanwhile, kids need to be able to write coherent sentence, cook a meal, think logically, know some history, and a bunch of other stuff before they get to college.
If you don’t know calculus you cannot fully understand physics and engineering. I don’t think we need a world where physicists and engineers don’t understand what they are studying. Don’t like calculus? Don’t go into those fields.
I have no idea what the topic is. Calculus is the study of change. If you never need to understand the calculation for the rate of change then calculus is a waste of your time.
That said. Education opens windows of opportunity, perhaps the American educational system is over educating future muffler repair technicians. I would actually rather have that than the very organized German system that determines based on tests early who will be muffler repair technicians and won’t bother teaching a possible late bloomer the skills needed to excel later in life.
Is it correct that education deliberately goes beyond what is necessary, in order to leave a stronger impression? For example, is something like the Magna Carta or English Civil War taught even knowing that the student will forget the details, in the hopes of giving the student a better grasp of contemporary political affairs? Working with calculus will reinforce simple familiarity with and understanding of functions — understanding which will be useful even when no calculus is needed.
Many careers require no real math at all, and many “hard science” careers will require some math, but let’s look at careers that are in between. I suggest that the conversation focus on computer programming specifically.
Simple discrete math comes up often when designing software, but most programming work uses zero trig, calculus or even algebra. When trig is needed, there will often be a textbook recipe that can be plugged in. I can think of many examples where familiarity with or intuition about math is useful in software, but detailed application is unnecessary. I wonder how often most of the engineers and programmers here have needed to solve a quadratic equation, let alone do any non-trivial calculus.
I use trig, calculus, algebra, linear algebra, and other math all the damn time. Could I look up textbook recipes most of the time? Sure, but that would make me completely useless in the case where something goes wrong, which is always. Computer graphics in particular is impossible to develop without a solid math background. That doesn’t mean you can’t make a pretty game, but you’ll be very limited in what new things you can do.
Some examples:
Surfaces in graphics are often defined as polynomials, and rendering requires intersecting a ray with them. Need to find the roots of a quadratic, cubic, quartic, or worse.
How do you generate those polynomial surfaces in the first place? Most likely, you’ve specified a few points that they need to pass through, and maybe some tangents as constraints as well. You need linear algebra to turn that back into a polynomial.
Need a fast approximation of a function? You can sometimes use Newton’s Method to refine a crude approximation into a better one. But you need to find the derivative of that function to make it work.
All transforms in graphics are done with 4x4 matrices. You need a little trig and a little linear algebra. Not a lot, but the more you have the better you’ll grok it.
If you’re doing any kind of frequency analysis, you need to understand Fourier transforms. And complex numbers, of course. I had a friend ask me why he was losing half the energy in his transform. I had to explain negative frequencies…
The I and D in “PID controller” stand for integral and derivative. These are discrete, so only a very little bit of calculus is needed, but if all you’ve got is Algebra II you probably aren’t going to understand things.
Any database work (and a lot of other things) need at least some degree of set theory. “Gimme all the things that meet this criteria or this other criteria, but not this third criteria”.
Any case where samples need both amplitude and phase information (like Software Defined Radio) needs to be understood as complex numbers.
This is true for a society which is content to remain forever mediocre, and stagnate.
You cannot possibly know what a person will “need” for the remainder of their life when they are still in high school–aptitude is developed in the process of learning itself. To presume that you know what a person in high school will need to know for the remainder of their life is effectively to limit that person arbitrarily.
The thought processes and cognitive development that are required to engage in calculus by nature make a person that much more capable of the kind of creative thought which drives not only obvious things such as innovation in entrepreneurship, but arguably innovation in any field, including the arts.
Compared to many countries, U.S. high schoolers are not especially taxed, and if they have the time–as they normally do–there’s every reason to study calculus.
Because it’s something I’m familiar with. I’d be interested in any “in-between” career, perhaps “technician” but not “scientist.” Setting aside math-intensive careers like computer graphics or mechanical design, how many people ever solve a quadratic equation or use calculus?
I should have noted exceptions like rendering, robotics, statistics as programming areas where math is required, but I stand by my claim that “most programming work uses zero trig or calculus.” Even for something as technical as optimizing discrete wavelets for signal compression, Fourier transforms and regularity measures are something of a detour! Intuition, experimentation, and a little algebra are enough. It’s fun to follow the proof that DCT is the asymptotically optimal block compaction transform for Markov-1 signals, but for most implementers the theoretic properties are irrelevant.
This is not to say that mathematical intuition is useless. Consider the common test if (Dist(x1,y1, x2,y2) < Dist(x3,y3, x4,y4)). Most programmers will end up taking a sqrt inside each Dist, and this might dominate execution speed in some applications. With even a little intuition one notes that sqrt is monotonic and eliminates the sqrt’s!
I shoulda figured my first pitting would come as a result of a math thread…
Yep, you’re right, I mis-phrased the response. Of course it should be taught, but to everyone? That’s where I don’t necessarily agree.
That is more my point. I know of very few people in my career paths (business management) who need to know implicit differentiation using infinitesimals. Hell, I had never heard that phrase until today. Any time in my career where I have needed advanced math I have either found what I needed on the internet or asked someone to help me. My poorly expressed point was that I did not need to spend pre-secondary school time learning implicit differentiation using infinitesimals, I needed to spend that time learning how to learn. That more than any other is the skill that really enables one to thrive.
Agreed. Only debating what constitutes “a certain amount of exposure”.
Thanks, had I said it that well initially we probably wouldn’t be here.
Thanks for agreeing with me! I knew as a freshman in HS that I would not be an engineer or physicist. I had less than no interest in those fields. Rhetorically, why did I have to take those classes when I (and many others) would have been better served taking more logic classes so we could better understand how to learn?
I’m an accountant, so a math oriented field. As far as I am concerned, Algebra is just arithmetic. There is no difference between 2+2=? and 2+2=X. Geometry has it’s real world applications. When I was in high school my father used geometry to figure out which pizza place had the best price for pizza, Little Caesar’s (before it was garbage) had square pizzas, and the local chain had round pizzas, so what is the total surface area of each pizza order, and then what is the price per square inch of pizza. I have used calculus, though rarely, professionally. I think that Trig is specialized garbage math, but we might as well learn it. We could fix the educational curriculum to cut down on some of the repetitive subject matter, maybe once less unit about the Underground Railroad, one less rich white teenage boy coming of age novel, one less unit about the Renaissance.
I used to code scripts in a language that was product specific (DocuDraft). It was clearly a stolen and slightly modified version of SQL. It had all the trig functions available sine, cosine, tangent, secant, cosecant, and cotangent. Yet the only thing you could do with these scripts is create invoices for an accounting package directed at medical and legal practices. For the life of me I can’t think of a reason why I would need to know the cosine of an hourly rate, or the secant of a due date.
It means that accountants always enter a transaction twice: they debit one place, and then credit another place in an equivalent amount. “Debit” and “credit” are the two entries. When a bank informs you that you have a credit balance, they’re informing you from the perspective of their account. Their liability to you represents a credit entry in their ledgers. When that credit entry was entered, an equivalent debit entry was also entered somewhere else: double-entry.
This system is used by accountants all over the world. It’s been used continuously for over 500 years. The system was originally described by Luca Pacioli, a friend of Leonardo da Vinci, based on his observations of the Venetian businesses that developed it. It’s quite a simple innovation at its core, really, but it can really help organize ledger entries in a way that avoids mistakes and increases comprehensibility.
I don’t personally see why any regular folks need to know how double-entry bookkeeping works. Including high school students. I would absolutely not make it part of any required curriculum.
But it’s probably worthwhile to know that It Is A Thing. It’s not archaic. It’s not criminal. (At least, not always…) It’s standard accounting. Every debit is balanced by a credit. Two entries. That’s how accounting has worked for centuries. It’s probably worth knowing that much about it.
I don’t think calculus is fundamentally more difficult than algebra or geometry. If students are introduced to the concepts in simpler and easier ways at earlier levels, it wouldn’t be the giant leap when the formalism is taught at the high school or higher level.
While students don’t need to know all the finicky details of accounting, understanding the basics of double-entry bookkeeping would help them improve their financial skills. Besides the basics of budgeting, credit and debit cards, using banks for savings and loans, it gives them something more to defend themselves against predatory lending and investing.
This was probably my problem with Calculus. It was introduced to me when I as already 21. All my public education gave me was Algebra for two years and then Algebra 2, which at my school was exactly the same class as year 2 Algebra 1, but with the “harder problems at the end of each lesson.”
College is hard when you aren’t prepared for it. I survived it but it took me an extra year to get caught up. That cost a lot of money. It would have been better if Algebra was maybe in middle school or something, and if we had Geometry at all at some point.
By some grace of god I was able to test into the college level classes right off the bat, but I had no idea what was going on. My good guesses were a curse. My professors were patient with me though, they knew where I grew up and went to school. I was smart enough, just uneducated.
I edited to add that I don’t buy the idea that only people that “need to know” should “know.” With things changing in the world so fast, I have no idea what I am going to need three years from now. At least if I was exposed to everything, it wouldn’t be such a hard haul to learn new things.
I’d be interested in any “in-between” career, perhaps “technician” but not “scientist.” Setting aside math-intensive careers like computer graphics or mechanical design, how many people ever solve a quadratic equation or use calculus?