Why is learning mathematics compulsory?

In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and multiplication are taught to the children.

But for many high school students, especially those who are keen on pursuing the humanities, they do not see any point in studying Mathematics for the rest of their schooling life, or how any concept in Mathematics could possibly be applied in their future work.

Why is Mathematics a compulsory subject for high school students, especially those who are clearly studying in Humanities streams?

• "for many high school students, especially those who are keen on pursuing the sciences, they do not see any point in studying humanities for the rest of their schooling life" – Peter Saveliev Feb 16 at 15:07
• Comments are not for extended discussion; this conversation has been moved to chat. – Chris Cunningham Feb 21 at 15:14

Why is Mathematics a compulsory subject for high school students, especially those who are clearly studying in Humanities streams?

1. A kid at age 14 is not ready to make irrevocable decisions that will affect them for the rest of their life. That's why we don't let them get married. I have a friend who, at age 30, decided to apply to grad school in sociology, and she is now tenured at a research university. A huge obstacle for her when she was re-entering school was that she needed to learn enough statistics. She had had a fine high school and college education, but hadn't concentrated much on math. If she had simply been encouraged to stop studying math completely at age 14, then I can't imagine how she could have ever gotten over this hurdle at age 30.

2. The kid may want to study the humanities in college but then, say, go into business. If they don't understand enough math to get through a watered-down 9th grade algebra class, then they aren't going to be able to do the relevant quantitative reasoning.

3. The reason why a country like the US has universal, free, and compulsory education is not (just) that it helps kids get jobs and boosts the economy. Education is also necessary in order to have a functioning democracy. Voters who can't do basic algebra are going to be severely handicapped in making decisions about issues like nuclear power and global warming.

4. When you provide multiple tracks for students through the educational system, it can have nasty side-effects. In the US, there was a time when African-American and Latino students were routinely sent into one academic track, while white kids were put on a more demanding one. It's pretty common for kids to get put in less demanding classes because of superficial issues like poor handwriting. For these reasons, I think it's better simply to provide classes at a variety of levels, but not to classify kids into different categories.

If you want to criticize the practice of forcing kids to take math, then I think there are some more appropriate targets for criticism:

1. Efforts to force kids to take algebra at lower and lower ages, such as attempts in California to make all kids take algebra in 8th grade.

2. Requirements that college biology majors take a full year of calculus (including stuff like doing integrals using trig substitutions) and calculus-based physics.

3. Unrealistic government requirements that encourage public schools to pretend that all students are succeeding at a high level in math, when in fact many aren't succeeding at all.

Questions like this, or variants (from students, the notorious "when will I use this in real life") seem to be pretty common, and I'm always a little surprised, because the unstated premise - that high school is supposed to teach students things narrowly tailored to their future career - is so obviously false.

It's obviously false because almost no academic subjects in a conventional high school curriculum are widely applicable career skills. The actual essentials for functioning in ordinary society - literacy, basic arithmetic, a minimal ability to write - are covered by middle school, if not elementary school. (I'm distinguishing academic subjects, because, at least in the US, it's common for high schools to also offer more practical classes.)

I've never understood why math is the target of these questions so much more frequently than other subjects. Many fewer people need social studies in their professional life than need high school level math, but we understand that we don't teach social studies primarily as a career skill: we teach them because they're necessary to being an informed citizen.

You can get through a day at most jobs without knowing anything about history. What you can't do without some knowledge of history is make any sense of the news. Math has a similar role: we live in a world in which math plays a central role in nearly everything that happens around us - it's central to the technology we all use on a daily basis, to understanding the flood of scientific (especially health related) information that surrounds us, and to the decisions that affect us being made by corporations and governments all the time. We teach math because understanding what's going on in the world requires some basic fluency in math.

There are good arguments that current high school curricula don't do that as well as they should. Most high school curricula do, especially in college-oriented tracks, mix that with more specialized material needed for students going into STEM fields. So I don't mean this as a defense of any particular curriculum. But I do mean this as a rejection of the premise: the math curriculum, like the rest of the high school curriculum, will never make sense if the main question you ask is "how will I use this in my job".

• "the flood of scientific (especially health related) information that surrounds us": Nice point. – Joseph O'Rourke Feb 16 at 15:55
• Learning math (or any subject) is like exercising. People don't go to the gym and lift weights because they have a need to lift heavy objects. They do it because that action trains your muscles to make other parts of your life easier. Similarly, anyone who can make the mental flexes to master something like trigonometry will find other complex subjects easier to master as well. That will serve you well whether you end up using trig in your adult life or not. – Seth R Feb 16 at 22:40
• "What you can't do without some knowledge of history is make any sense of the news" It's far more than that. If nobody were taught history, then in a generation or two nobody would know anything about what had gone before (save those few who self-taught from books, but let's pretend they're included in this hypothetical). Yet society is doomed to fall into darkness if it does not progress using the past as a guide. People forget that they are not just individuals, but part of a society. Indeed, society is solely comprised of people, and that's irrespective of what careers they chose. – Asteroids With Wings Feb 17 at 1:42
• In other words, keeping these basic elements of knowledge alive from generation to generation is valuable in itself. Of course, the current age of individualism has people more concerned with their own selves and about what the knowledge can do for them. :( – Asteroids With Wings Feb 17 at 1:42
• @HenryTowsner Sorry, if you don't see the link, I'm not sure I can explain it to you... – Asteroids With Wings Feb 17 at 12:17

The OP may be interested in the controversial 2012 article by Andrew Hacker in the NYTimes: Is Algebra Necessary?

Here is one reply, by Peter Flom: A reply to Andrew Hacker. His closing remarks:

Is algebra necessary? In the strict sense, no. You can live without it. You can also live without art, music, literature or sports. Would you want to?

And here is a response from the MAA (Math Assoc Amer): Denny Gulick. It includes a point-by-point rebuttal to Hacker's five main points.

• Both responses tell what algebra is good for. Neither response addresses the "compulsory" part of the question. – Peter Saveliev Feb 16 at 17:33
• Andrew Hacker was a non-STEM, political science, retired CUNY professor -- who was very useful to CUNY at the moment when they wanted to cut out all their remedial English and math programs for under-served students (which they now have). There are scores of math faculty in the CUNY system who could have made a coherent counterargument, but for some reason none of them got featured space in the NY Times on multiple occasions. – Daniel R. Collins Feb 16 at 22:19

Many people think that the clientele of our public school system is the students. Others act as if the clientele were the parents of the students.

Those people are wrong. The client is the citizenry of his state and nation, who need the electorate to be educated and informed, in order to secure the benefits of a well-ordered government.

The question, "How does the study of mathematics1 benefit the student at any point in his life?" is irrelevant. The student has not contracted for the education he is receiving, and has no right to dictate its form.

The proper question to ask of publicly funded universal compulsory education is, "How does the study of mathematics benefit the state, nation, and society that the student will eventually be called upon to supervise and control?"

When the studies, that contribute to a citizen's ability to keep his republic, also augment his ability successfully to pursue happiness, that is a fortunate serendipity. But the educational purposes of the student do not trump the educational purposes of the state.

So the answer to "Why is learning mathematics compulsory?" is "Because the people have decided that you need to know mathematics in order to be a worthy citizen."

1. For "mathematics" substitute any subject that the people consider necessary to an educated voter.
• "citizenry of his state, and of the U.S.A" Other countries also available! – jonathanjo Feb 18 at 0:36
• @jonathanjo: Good catch, I'mma change it. – A. I. Breveleri Feb 18 at 2:00
• The reduction of the citizen to a mere voter is unfortunate, I think. An educated citizen can contribute much more than a vote to the general welfare of the republic. (+1 anyway) – user1027 Feb 18 at 3:33
• @user1527: You make a good point and I am inclined to agree with you. I'll work on a rewrite but I don't know if I can broaden my thesis without diluting its force. – A. I. Breveleri Feb 18 at 4:00
• @user1527: You make a good point and I am inclined to agree with you. I got focused on the vote because that is where the public schools where I live have failed most obviously. There are too many schools in the U.S.A. where students are not taught to think critically, and are led to believe that one person's facts are as good as anybody else's. Teachers, principals, and school boards all live in mortal fear of the Irate Parent, so they're afraid to make any students uncomfortable, so the little snowflakes never really learn anything. – A. I. Breveleri Feb 18 at 4:09

I'll make some observations from a Western perspective (which may or may resonate with a Chinese student, say). Consider: Mathematics has been at the forefront of all education forever -- since long before the idea of compulsory education itself was conceived.

In Classical Athens (~420 BC):

More focused fields of study included mathematics, astronomy, harmonics and dialectic – all with an emphasis on the development of philosophical insight. It was seen as necessary for individuals to use knowledge within a framework of logic and reason... Wealth played an integral role in classical Athenian Higher Education. In fact, the amount of Higher Education an individual received often depended on the ability and the family's willingness to pay for such an education... Women and slaves were also barred from receiving an education... The people in a pythagorean society were known as mathematikoi (μαθηματικοί, Greek for "learners").

A system for higher education was described by Plato, and used as the structure for university studies through medieval and Renaissance Europe:

The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium, consisting of grammar, logic, and rhetoric. In turn, the quadrivium was considered the foundation for the study of philosophy (sometimes called the "liberal art par excellence") and theology. The quadrivium was the upper division of the medieval education in the liberal arts, which comprised arithmetic (number), geometry (number in space), music (number in time), and astronomy (number in space and time). Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts (essential thinking skills) of classical antiquity.

Note that in each of these systems, mathematics comes first. In the quadrivium, all of the components are actually numerical; including music, which one might consider today as a humanities subject. I'll emphasize again of this all-numerical higher education course: "the quadrivium was considered the foundation for the study of philosophy (sometimes called the 'liberal art par excellence') and theology".

Now, why do these connections and foundations seem hard to understand today? I might suggest that there's been a historical progression in which education and mathematics have become so monumentally important -- an existential issue for any modern nation (say, since the military conflicts in the 19th and 20th centuries) -- that every nation is nearly frantic to produce a maximal number of STEM professionals, scientists, and engineers. These nations have demanded that everyone have some amount of compulsory schooling, with emphasis on the mathematics that would be a pipeline towards engineering and the like (specifically: algebra leading to calculus). Unfortunately, this systemic stress has cracked the educational institutions into producing a Kabuki theater version of mathematics -- students can pass relatively mindless algorithmic tests, without understanding or insightful explanations.

On that latter progression, see Campbell's Law (thinking here in terms of the assessment, "it would be good if students in our schools could get high test scores in math"):

The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor.

Perhaps the major missing component, which has set mathematics education on a foundation of sand, is the lack of prior training in logic (see above: in the classic trivium, grammar-logic-rhetoric were prerequisites to the all-mathematics higher education). Without this, mathematics teaching tends to have the appearance of a huge list of random and disconnected non-meaningful procedures, instead of the training in reasoning and persuasive speaking which mathematics was long held out to be (and which you'll hear many mathematics educators proclaim, although it's not generally understandable by recipients of the current educational system).

In summary: Mathematics really is about connections and developing provably correct deductions from available information we have about the world. That's not a rhetorical flourish; the field is really a concrete crystallization of all we know about necessary conclusions. Historically it was synonymous with higher education itself, neither of which were considered appropriate for most people. It's unfortunate that in an attempt to pretend that most people in a modern nation understand it, the logical-reasoning component has been largely wrung out of the system, rendering the whole curriculum as not making very much sense.

A question I always ask U.S. non-STEM people who express frustration with their math education: How did you feel about your high-school geometry class, with its emphasis on proofs and justifications? I find that very frequently people respond with, "Oh, that's the only math class I liked; I really enjoyed it!" And my follow-up is to say (again in the U.S. system): that's the only course in high school that counts as real math from a mathematician's perspective (as a prover of theorems). If you like and feel confident with the work in a geometry class, then that's the best possible sign that you're a real mathematical thinker, even if you didn't get that message previously.

I'll end with an open question, to pivot from the original query: Granted that mathematics is the core subject matter of all education in general -- why is education itself now compulsory in modern advanced nations? Maybe it shouldn't be? That's a perhaps more essential and much harder question (and unfortunately not appropriate for S.E. Math Educators).

• On that latter progression, see Campbell's Law: --- I thought for sure this was John W. Campbell (extremely well known in science fiction circles), as it sounds a lot like the kind of adages/sayings he and his writers might have said (e.g. Asimov, Heinlein, Hubbard, Sturgeon, etc.). But then I clicked your link . . . – Dave L Renfro Feb 17 at 19:54
• Regarding compulsory eduction, some level of education — or you may call it indoctrination — must be compulsory in a democracy for the society to function well. In a totalitarian society only the knowledge and skills necessary for the proles to operate the machines are needed to be taught. Well, this is basically what George Carlin said much more eloquently, and he clearly thought the U.S. is more like a corporation controlled by the one percent, not a real democracy. – Rusty Core Feb 19 at 18:36

Underwood Dudley answers the question "What is mathematics education for?" in this article from 2010 (Notices of the American Mathematical Society, vol. 57, no. 5, pp. 608-613) (even though the title of the article is "What Is Mathematics For?").

So that there is no confusion, let me say that by “mathematics” I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic. There is no question about what arithmetic is for or why it is supported. Society cannot proceed without it. Addition, subtraction, multiplication, division, percentages: though not all citizens can deal ﬂuently with all of them, we make the assumption that they can when necessary. Those who cannot are sometimes at a disadvantage.

Algebra, though, is another matter. Almost all citizens can and do get through life very well without it, after their schooling is over. Nevertheless it becomes more and more pervasive, seeping down into more and more eighth-grade classrooms and being required by more and more states for graduation from high school. There is unspoken agreement that everyone should be exposed to algebra. We live in an era of universal mathematical education.

He concludes:

What mathematics education is for is not for jobs. It is to teach the race to reason. It does not, heaven knows, always succeed, but it is the best method that we have. It is not the only road to the goal, but there is none better.

Because

many high school students, especially those who are keen on pursuing the humanities, they do not see any point in studying Mathematics for the rest of their schooling life, or how any concept in Mathematics could possibly be applied in their future work.

shows they have no clue what mathematics is worth, therefore it needs to be compulsory to protect them from themselves.

• That's definitely part of the point; not being able to see how something is useful only speaks of your ignorance. Much of human argumentation fails on something like "I cannot see how something is useful, therefore it is useless", whether you're talking about things like following traffic laws ("I don't see why the speed limit is there, therefore it must be useless/harmless") or communism ("I don't see why private property is useful, therefore it must be useless/harmless") :) I wonder if humanities-inclined students are more likely to make such arguments. – Luaan Feb 17 at 13:13

Citizenship

The health of a democracy depends on the electorate being thoughtful and informed. And said citizens can only be informed if they understand the information around them (e.g., the news). Very few policies boil down to: "A is morally right and B is morally wrong." Those issues were mostly settled long ago or established in the Constitution. The issues facing most legislators are questions like: "Is A better than B? By how much? What are the costs involved? How much uncertainty do we have?" And while we will always take qualitative values into consideration, the difference between A and B often comes down to quantities.

Only a few people debate whether we should have a minimum wage. Most folks instead debate: how large? To do this reasonably, we need studies with results, which means statistics. The very process of conducting an election is rife with statistics. Which means, at the very least, every citizen should have a solid understanding of basic statistics, and the stronger that understanding, the better. But it's hard to get a foundational knowledge of statistics without some algebra, and even calculus is helpful in understanding continuous distributions.

Economics

Related to the citizenship issues above, but worth mentioning on its own, is the centrality of economics to every citizen. We all need to know how to spend money wisely (except the few of us born into extreme wealth). It's hard to answer a basic question like: "Which is cheaper: the 16 oz jar for \$3.88 or the 24 oz jar for$4.96?" without knowing some algebra. And even if you can do this math without having passed an algebra course, you are doing algebra whether you call it such or not. So students would probably be more motivated if algebra were taught in the context of personal finance.

And that's not even getting into more difficult questions like: "Should I pay an extra $10,000 on my mortgage to take off a point?" Or: "How much should I invest in my 401(k) vs. directly buying ETFs?" Anyone who lives a life without math lives a life without money. Capitalism is rife with value judgments of a very precise numerical nature. Even computing the tip at a restaurant or coffee shop requires math skills. Formulating a retirement strategy at the start of your career requires more than simple arithmetic. Computer Science As a professional software engineer, I obviously think that programming is valuable (but the salary : education ratio of CS also speaks quite loudly). I think most of us recognize that the future is automation. Virtually every scientific field is inundated with software and automation. Every startup wants to call itself a "tech company" (including obviously not-tech companies like mattress-maker Casper). But every corporation benefits from tech-savvy employees, even if that just means knowing how to put together a few formulas in Excel to aid planning and scheduling. The ubiquity of personal electronics, from laptops to smart phones, means that the youngest generation is practically born as "power users", especially relative to older generations. At the very least, computer science needs combinatorics. And for combinatorics, you need algebra. Eventually, some very basic scripting capability will be required of virtually all white collar jobs. So I would double down and say that not only should math be required education for all high schoolers, but also computer science. Anyone who says we don't need math and CS is living in the past. • I wouldn't say you couldn't solve these kinds of problems without algebra - it's more profound than that. Algebra gives you the very simple tools that allow you to quickly and easily solve a wide variety of problems. The reason learning algebra is worth it is because it's a pretty good generally useful tool that you can learn very easily. Things like differentiation and integration are also generally useful tools, though they get progressively harder to learn - they still make your life easier, but it's also harder to justify the learning cost. Algebra is ridiculously simple for its power. – Luaan Feb 17 at 13:04 • Algebra is a well-sized hammer suitable for a wide selection of nails, and sometimes for rivets, screws and bolts. – Rusty Core Feb 19 at 23:05 Math teaches reasoning using scenarios that are exact enough for there to be concrete right and wrong answers. Many areas of life require reason, but mathematics forces students to actually engage in the discipline of finding the right answer, because there is only one right answer. For example, some people think that we can teach reasoning by doing mock trials, and that this is a much more practical mode of teaching reasoning that people can relate to. It may be more relatable, but, the problem is that it is not always clear in such a scenario why certain answers are right or wrong. In other words, it allows bad reasoning to be perpetuated as long as it is done sufficiently glibly. In math, no matter how well I speak, I will not convince my math teacher that X + 5 = 7 means that X = 3. When I give presentations about mathematics, I always include a slide that says: Math gives you practice on core reasoning skills with concrete problems that have definite answers in order to achieve mastery of the reasoning process which will allow you to apply the skill to fuzzier problems where answers are not as certain. There are also many analogs to specific mathematical techniques which I have (informally) found that math-trained people are more likely to do well in. One is in reconfiguring processes. In math, we train people to do prime number factoring. This is exactly the type of skill needed when figuring out what is needed to reconfigure a process. You have to be able to break down the process into its primary components, and rebuild it using those. Being able to look at something and "see" what basic building blocks it is composed of is essential to thought. Again, math gives us practice in these core reasoning skills on concrete problems that have definite answers so that we can achieve mastery of the reasoning process which allows us to apply the skill (with confidence) to fuzzier problems where the answers are not as certain. There are parts of math which are needed just to provide grist to the logical reasoning process. There are parts of math which are good direct (or indirect) analogs to specific reasoning processes that will be used in the future. There are parts of math which are just part of being an educated human. And, for sure, there are parts of math that we should probably stop cluttering the textbooks with. But the latter are few and far between. One example - I think it was Hacker that complained about logarithms and exponents being taught to everyone. That is literally the most useful thing that math teaches that isn't evident from normal everyday life. Knowing how exponentiation looks like is a key component of understanding (a) debt, (b) interest, (c) investing, which are things that everyone will likely be involved in at some point in life. If you don't understand how debt grows exponentially, you won't understand its danger. Final note - I do think we should teach math with the reasoning skills we want students to know more clearly in mind (and even should share them with students). I think this would improve (a) the student's attachment to the curriculum, (b) the quality of the curriculum itself, and (c) the public's understanding of why the curriculum is there. • Shameless plug - I use these ideas (explicitly showing how these reasoning skills apply outside of mathematics) in my own book, Calculus from the Ground Up. You can see one of the take-home lessons from it here: mindmatters.ai/2019/08/… – johnnyb Feb 16 at 19:52 • You won't convince a good teacher, anyway. There's plenty of "proofs" that 1 = 2 and such, and they rely on people not actually being very good at applying the rules (like "do not divide by zero"). It's like perpetual motion machines and such - at some point, you must have missed one thing that balances everything out. – Luaan Feb 17 at 13:09 Math, taught well, teaches modes of thought, not facts. A person who is exposed to a wider variety of modes of thought will be more prepared to critically consider new ideas. It's the same reason we teach history and literature - I can't honestly say that I've had reason to use my middle-school knowledge of Macbeth for anything, but the tools of critical reading and strategies for considering interpretations of a text have been useful for spotting articles that are meant to provoke a certain feeling and bias the reader. I've never needed to know when my hometown was founded, but a basic understanding of what kind of historical facts we know and what evidence we have of them helps me distinguish between historical fact and conspiracy theory. And I've never needed to be able to do algebra (except, of course, in my capacity as a math instructor) but the ability to mix systematic thought with creative strategizing -- the skills that come out of long algebra problems, especially word problems -- allows me to manage my finances, cook a decent meal, organize my closet, or schedule a vacation. The ability to pay attention to key details without losing the big picture allows me to follow detailed instructions well (have you ever assembled a piece of Ikea furniture?). The ability to reason precisely, as in a geometry proof, helps me spot when other people's arguments are appealing to emotion rather than reason. To be honest, of all the skills I learned at or below the high-school level, math seems like the most useful. To give a German-centric answer which would certianly apply to other countries as well: The German Abitur is the right to study any subject at a university (Allgemeine Hochschulreife). As such the pupils need to be taught everything such that they need in order to be able to succeed. After all, they may want to change the subject after finishing school and you do not want them to have to decide at an early age. In other countries, a similar concept exists at different levels. As such, a broad education is necessary. Which is why me, as a mathematician, needed to study history and social studies, which I clearly did not have any interest in. The simple answer I would give is that there is a good chance they go into the business world at SOME TIME in the future of their life. Perhaps they will get an MBA at some point to help them move up. And you'd laugh at how deer in the headlights the English major types were with finance math. And how the STEM majors ate it up like Valentines Day heart candy, As such, no they won't be doing algebra, per se. But some basic training in algebra is helpful to be more numerate when looking at spreadsheets or presentation slides where percentages, ratios, compounding, etc. occur. I do think you could cut the cord before trig/calc, though. Of course that means they can't handle high school physics. So they won't know that either. But high school chem is fine with algebra 2. P.s. I disagree on the counterpoint that STEM people can skip humanities. You absolutely do need a knowledge of writing (more and more). Also a knowledge of your culture from history. I would draw the line on lib'rul college foolishness like Rigoberto Menchu. But classical Western Civ (or Chinese for a Chinese) is absolutely something an educated...person should know (to read the newspaper, discuss politics, etc.) • The counterpoint I had in mind was not that "STEM people can skip humanities" but rather that compulsory education is a bad idea no matter the subject. – Peter Saveliev Feb 16 at 23:12 • @PeterSaveliev Compulsory education is always bad? What should happen to all the people who wouldn't be educated if it was not compulsory? – user253751 Feb 17 at 14:02 • Why have you picked out a specific Nobel Peace Prize winner as the place where you draw the line? – Chris Cunningham Feb 18 at 1:45 • -1 Oh noes, someone made me read something by an indigenous non-American woman once. – Daniel R. Collins Feb 18 at 2:46 • @ChrisCunningham: because "@guest" is a culture warrior looking to spread propaganda. – nomen Feb 19 at 17:49 Mathematic notation and numbers are fundamental to basic communication and problem solving. Our existence depends on it. It is also very fun. I think this question would come up less often if we presented kids with problems to solve, and then they realize that they need tools. My physics teacher derived formulas from observation and testing. Memorising tables sucks. recognizing a pattern can be fun. We are allowing people with less than even basic numeracy to leave school. We are allowing people to enter university with not only no knowledge of basic algebra or calculus but also with no realisation that basic algebra and calculus are essential tools when dealing with subjects such as history or social sciences. A social scientist or historian needs a basic understanding of exponential growth or decay - if only enough to provide a platform for more learning when the need latterly becomes obvious. Higher levels of knowledge can be far more easily be built on a basic foundation than being obtained with no prior introduction. Consider: You buy 5 items that cost 0.30 currency units each. You give the shop assistant a 5 currency unit note. They pick up a calculator to multiply 0.3 by 5 and then to subtract this answer from 5. They give you 3 currency units in change. They wonder why you look at them in what used to be astonishment until it happened many many many times. That's just the most basically basic of numeracy. Now for some basic mind bending with algebra and geometry ... If we are releasing people into the world who cannot calculate 5 - 0.3 * 5 (as we are) then we are stopping far short of a reasonable target. I have seen social science papers which are utter unmitigated and irredeemable balderdash BECAUSE the writer has no grasp of basic mathematical concepts, and doesn't know that they don't know STAY AT SCHOOL*. *Failing to gain a minimum broad education is functionally failing to 'stay at school' • Are you saying that we teach people mathematics so they can mentally compute$5 - 0.3 * 5\$? – Chris Cunningham Feb 18 at 1:35
• @ChrisCunningham Yes. And much more. If we are releasing people into the world who cannot calculate 5 - 0.3 * 5 (as we are) then we are stopping far short of a reasonable target. Are you suggesting that a social scientist or historian does not need a basic understanding of exponential growth or decay - if only enough to provide a platform for more learning when the need latterly becomes obvious. | I have seen social science papers which are utter unmitigated and irredeemable balderdash BECAUSE the writer has no grasp of basic mathematical concepts, and doesn't know that they don't know. – Russell McMahon Feb 18 at 3:02