How Much Math Do Kids Really Need?

In what other course of study would a student learn how to handle logical processing or how to handle abstract concepts? Or at least, be exposed to these concepts? Shouldn't a student at least know what algebra is and how it works, even if he never uses it again? Or trigonometry?

I think that professor ought to read some of Robert Heinlein's science fiction books.

On this subject of Math education I think the best counter-argument is provided via Heinlein:

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house."
--Lazarus Long, Time Enough for Love, (Robert A. Heinlein)

Heinlein has many reasons to deserve respect and admiration. But like all humans he had flaws. This statement,

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house."
--Lazarus Long, Time Enough for Love, (Robert A. Heinlein)

confirms one such flaw. It is the commentary of an effete scientific snob. One who has little understanding of the breadth and complexity of human intelligence.

Certainly our high school students would do well to have an exposure to algebra, trigonometry and other abstract mathematical concepts to gain an appreciation of their method and validity. But spending 100 to 250 hours of valuable secondary school instruction time on this for students who have no further need to use such skills is an awful waste. And this doesn't begin to address the harm that is caused by requiring mastery of these subjects by all students as a condition of high school completion.

Ed Weldon

....and that from a $20 banknote. But I am sure that the one that gave that kind of change knows very well his math

I agree, other than when shopping, buying a house, gambling, investing in stocks, programming, buying insurance, understanding the national budget, analysing complex arguments or general clear thinking, maths isn't much use to most people.

It's a bit like learning Latin, the effort, organisation and innate intelligence required to master this (admittedly arcane set of skills) make it a good indicator of future success.

But this begs the question, if maths shouldn't be compulsory what, if anything should be?

As a kid I didn't like PE, why did I have to do it. Well I understand now some of the reasons: it's part of Australian culture, it may be useful and it exposed me to something I may not have ever tried.

All education involves making value judgements as to what's useful.

I use Algebra and Circular Geometry every day but I have yet to need The Calculus to figure out that I can't afford meatloaf for dinner.

But the proper application of Calculus can tell you when you can next expect to be able to afford meatloaf for dinner, through an analysis of the integral and the time derivitive of your cash flow...

As a math major myself (and former prospective teacher), I might be inclined to sing the praises of mathematics. In very rough terms, I wish that average mathematical sophistication were larger. But I would not wish to make a fetish or priesthood over this. There is not much value in torturing students to master too much stuff; it is better to offer appealing topics on a more voluntary or enrichment basis. Math can be quite entertaining if not forced. Mastering concepts and skills can feel very delicious, but not under the crack of a whip.

(On the other hand, when I see CR4 posters that don't know jack about math, physics, or engineering, I am more than eager to crack the whip.)

Simple arithmetic, logics, various shapes in geometry, etc are the basic requirements to solve many day today problems. So one should learn this basic math's in school level rather than complex equations and theorems.

I would say the professor is cover for the educational community.

"our seeming obsession with how poorly U.S. kids perform" ??? If there were an obsession, we wouldn't have a problem...

I say this professor is an idiot! "Most adults" have no contact with math... Here is a source of the problem. People saying things when they obviously are not in touch with the reality of what the daily lives of "most adults" is...

Whether most adults curl up with an algebra book for relaxation or not is, to me, irrelevant. The average person should understand basic math (add, subtract, multiply, divide, fractions and decimals) just to exist in society.

• Don't the vast majority of individuals work for a living?
• Isn't it in the individual's best interest to understand whether or not the wages being paid are what the individual agreed to work for?
• Isn't it in the individual's best interest to be aware of how much they are paying in taxes and understand if they are paying too much (being ripped off) or paying too little (breaking the law)?
• Don't they have to purchase small things (i.e. food, clothing)
• Make decisions such as to whether to purchase 5 for $1.00 or 2 for $0.45?
• Deal in cash where as AH mentioned need to make or receive change?
• Don't many of them (us) have to purchase large things (i.e. car, home)?
• Wouldn't an understanding of simple and compound interest be beneficial?
• Make decision to take a 15 year mortgage at 4% with a monthly payment of $1,479 or 30 year mortgage at 5% and a monthly payment of $1,074?

Sure they can abdicate their fiscal responsibility to someone else (i.e. spouse), but that may prove to be foolish and leaves them open to be take advantage of.

Finally, how are individual's ever going to hold their elected officials fiscally responsible if they themselves don't understand the basics? ^{_{Oops, maybe we are already there.}}

Of course we need basic math. Most high schools used to have a course called general math or something like that for the kids who weren't on the college prep track. Now they are all college prep and algebra is the only option. If your brain is not arranged so you can deal with the abstractions of algebra and geometry then you fail. Forget about college. Go to the bottom of the pile and accept your place in the basement of society.

Perhaps the lesson of Egypt's Tahrir Square will sink in and the idea of college educating an entire generation for jobs that will never be there will lose its appeal. We don't need a millions of minimum wage or unemployed college grads mooching off Mom and Dad, defaulting on their college loans, seething with discontent and arming themselves with 2nd ammendment rights. I say let the multinational companies do their screening of job candidates for the best and the brightest on their own nickel and we focus on training our kids for the actual work we need to get done and the actual lives they will live. And to me a most essential part of life is learning the math that will actually be useful in every day life for both the small decisions in the home and on the job and the big decisions in the voting "booth".

I say that education ought to be about preparing our children for a productive life. It should not be about winnowing out the top students by a hugely expensive and wasteful process for the benefit of some "world business leaders" whose loyalty is to themselves and who would abandon the USA in a moment if they thought some other place would be safer and more comfortable.

Here's a question very relevant to this topic: What specific goals would you make part of a two year high school course on general math requiring only as prerequisites the ability to add, subtract and multiply as well as a comprehension of division if not proficiency in the details of working a long division problem? Let's see your list ..........

Ed Weldon

Basic math is covered in grade school.

Algebra should be a minimum requirement for any student seeking an academic career.

You clearly can't do much of anything in the field of science without algebra. The same goes for fields like psychology, architecture, pharmacy, and a host of other fields.

If their career choice is getting a McJob or Home Invasion, then math is a useless activity. What is more important, Ed, is the student has the choice in high school to select the minimum requirements needed to get out of school. The real issue is complacency for those of us that have been here for generations. Most of us don't appreciate what this country is. Sad.

The problem with Egypt was not so much who they educated, but their lack of a free enterprise system for educated people to take advantage of.

Motivated individuals will make things happen if the environment is ripe. Hell, that is why people have been immigrating to the USA in the first place. It's because this is the land of opportunity.

SPLARF! Math may come in handy if the student is looking toward a career in Home Invasion, so he can figure how much of his life will be spent behind bars...Many of todays kids can't count out change, a job requirement when I was hustling merchandise way back when. Or read...but that's another problem. As for required edumacayshun? In my day (did I just say that?!) algebra was a required high school course. As was P.E., no excuses. These days, some schools don't even have physical education offered...maybe that's part of the problem.

He is just promoting the new buzz word in education. I see that everyday in the public school system in Canada and USA.

It is too difficult to teach math so lets reduce the level required to pass. This way, everybody gets a diploma.

This is what happens when the society eliminates "elite" classes and put everybody together. The slow kids are not happy with the average work load and the gifted ones are bored. They then cause trouble in the class so that even the average kids cannot learn anything.

To improve things:

Split the class as per student capacity as it has always been done.

Forbid calculators until learning trigonometry.

Fire the teachers that complain that it is not fair that their colleague gets all the good kids while they get all the bad ones. The reason they created mixed classes is not to help kids, it is to balance the work load among teachers.

Make sure that the teachers are really qualified and pay them accordingly. Teaching is the easiest program to get into at university. This the way to go when you cannot do anything else. We see the results. The good teachers are now swamped by a majority of incompetents who attack them when they try to do better with their class. I have seen it many times at my kids highschool. The good teacher ended up being fired even when parents objected. Very sad...

How much should they get?

Well everyone should get at least enough to be able to work out for themselves why "their" particular over unity engine won't work.

Anybody who says they don't use math everyday .....lies.

If you don't use some math at work I'm sure you aren't doing a very good job at what ever it may be. Could someone point out a job where zero math is involved? Before you try, think. Verifying that a pay check is correct involves math.

I'm a retired mechanical engineer. I use math virtually every day for something. Some in my head, some with a calculator or a story board in my shop. I'll even use basic algebra on occasion to transcribe the terms of a simple formula. Usually that has to do with a hobby thing or a comment on CR-4 (also a sort of hobby thing). I've rarely dug out an old CRC handbook looking for interest formulas. And rarely go into an engineering text to reread some old proof long forgotten. That's about it. When I worked as a design engineer my work was pretty much the same mix although the math activities were more frequent. There was especially a lot of spreadsheet work.

Still I cannot see why we must put every high school student through detailed study of algebra when no more than a few percent will ever use that knowledge either on the job or in their further education. Even worse is our use of algebra as a talent sorting tool.

Again I will ask all of you to be specific about exactly what math needs to be learned for all the rest of us to use in every day life or future education and jobs. I don't think algebra beyond the use of simple formulas has any real place for most.

Ed Weldon

"Again I will ask all of you to be specific about exactly what math needs to be learned for all the rest of us to use in every day life..."

Scenario. One must go from point A to point B. There are two routes available. On one route, one can average 30 mph. On the other route, one can average 50 mph, but it is twice the distance. Which route will get me to the destination in the minimum amount of time?

More interesting, if you happen to know how your gas consumption varies with speed, which route can be traversed more cheaply?

In either case, you can either use algebra (although some might not recognize this as algebra), or you can flip a coin...Which is a digital solution that may or may not result in the correct answer...

There is a third solution method that most will use for real world situations as opposed to compiling a properly detailed solution to a school problem.

Apply common logic and simple arithmetic to a specific problem. Time in the given example is the issue. So calculate the time for each alternative and compare them to your objective. If the issue is getting there in the least time then your choice is obvious. If your objective is to take more time, rather than sit waiting at either end of the trip (let's say the purpose of the trip is to arrive at a scheduled appointment) then the trip requiring the most time can be chosen along with a clear knowlege of how much time you could either be sitting and waiting or enjoying or hating drive as the case might be.

Note here that the general problem and it's solution for all possible distances is seldom encountered in everyday life. But if you so desire the simplicity of the problem numbers is such that simple logic can solve the general problem quite readily without employing the symbolism of algebra. Just one of several logic paths starts with the observation that the distance in second case is twice that of the first case. Therefore if the time is to be the same then the speed in the second case should be twice that of that of the first case. But the speed is not twice. It is less than twice. Therefore it is obvious from our experience that the speed over the longer route is insufficient and therefore not suitable for an objective of minimum travel time.

So we have solved our real world problem with no need for algebra just some simple arithmetic and logic in the first and most likely commonest case.

For most of what we do in life, such as the example above, simple arithmetic and common logic will do the job quickly and efficiently with little need for the mathematically powerful symbolic (and quite abstract to many people) methodology of algebra and still higher mathematical methods. And note here that the ubiquity of the electronic calculator in our lives usually makes the arithmatic solution more efficient and accurate thereby increasing its preference over algebra, which more often requires writing materials to be at hand.

Ed Weldon

The way you solved the time problem, like it or not, called on basic principles of algebra, whether you chose to call it algebra or not...

Hey, maybe that's the solution! Let's call algebra something like "Virtual Arithmetic" and move on to call calculus "Virtual Virtual Arithmetic"! Then people won't be some intimidated by it! But, what do with do with geometry and trigonometry???

The route without the Cracker Barrel Restaurant is always the quickest.

Ed,

You said, 'Still I cannot see why we must put every high school student through detailed study of algebra when no more than a few percent will ever use that knowledge either on the job or in their further education.'

If we don't require all, or the majority of, high school students to study algebra, how do we determine which ones we will require it of? How many adults are doing what they expected or aspired to be when they were in high school? How many young ones learn algebra enough to get by and then when in college choose a major which requires knowledge of math and they have at least covered the fundamentals. If you don't expose them to algebra, how will any of them know if they like it or want to go into a line of work that might use it.

If we only teach children what we think the majority should know, what would or should we leave out? Can we eliminate music class? What percent become musicians? What about grammar? How many people need good grammar when they are adults? What about biology? Knowing how to 'boink' is instinctual....what more do you really need to know about biology? And how many kids are going to grow up to be lawyers or politicians.....so why don't we do away with civics classes, too?

GA: I agree why stop at not teaching maths. How many jobs require a knowledge of history, geography, modern languages, biology, chemistry, ancient languages, physics or literature.

I think a good question in that case might be also, what percentage of highly talented musicians (those who create the new music) took a substantial number of courses in music while in school relative to what percentage of talented mathematicians spent the same or similar amount of time in math courses in school. Maybe music education are irrelevent to artistic skill, but is mathematics education irrelevent to mathematics/science/engineering skill. Another question might be the long term value to humanity of advanced education in mathematics versus a lesser education?

Those are all valid questions. The point I'm trying to make is that we don't really know what kids are going to be interested in or faced with 10, 20, or 50 years down the road. It makes more sense to me to over educate the young than to under educate them.

Compare two students at two different high schools. Student A goes to High School A where he studies algebra, geometry, trig. Student C goes to High School D where he studies no math....why?...because he wants to be a ditch digger and that's okay at HSD. Student A goes onto college and gets a degree as an engineer, now able to get a job. Student C spends 7 years after HSD digging ditches.

At age 25 Student A decides he would rather dig ditches for a living (if that type of job still exists), that's not difficult to accomplish.

At age 25 Student C decides he wants to become a physicist. He has quite an up hill climb. It's not impossible....but certainly a huge challenge. Had Student C been given the same HS education in math as Student A, he would still have an uphill battle, but nothing compared to what he has to go through now.

JB - Come back to the real world. Student C (on the average) who chose a manual trade but still learned algebra has maybe a 1 in 10 chance of later being admitted to engineering school if he applies.

But if he had taken a general "math for living" course there is a 10 out of 10 chance he would get something useful out of it. He would understand how to measure the ditches he digs, how to figure out his overtime pay and fill out a simple tax return, how to understand the interest he pays on his loans, what the numbers really mean when he hears or reads them in some news report and how to split a recipe when he cooks just for himself since he can't afford to eat out all the time and no woman will marry and cook for him unless he has a college degree.

Ed Weldon

An interesting anecdote regarding "how much math do we need":

A few years back, one of my duties was distributing bi-weekly pay to a workforce consisting of unskilled laborers, many of whom had no formal education at all (not even able to read or sign their names). Very interestingly, they knew TO THE PENNY how much was due them, how much overtime they had worked, etc., even though there was a two-week lag between the work period and payday. No formal exposure to any form of mathematics, no apparent means of keeping personal records...Very impressive.

However, you must consider the cost of education also. It is not free. To over educate them is fine if you can demonstrate a high value to society for increased educational skills in both breadth across society and depth in a few key professions that are highly important. Over-educating people in music is probably not comparable to over-educating them in math. Math has a broad applicability, music is vary narrow, and education in it doesn't tend to show particularly high value to society (nor a substantial advantage in the profession). Maybe an assessment of value to society is important to consider here when considering where to focus resources, how to allocate them, and the amount of resources to devote. Of course math is always important, adn most people don't even realize they are using various forms of math when they do apply it to problems, as they perceive the problems more in the overlying field, such as engineering, accounting, economics, science, medicine, etc..

I agree with you. My use of the term over-educate (in contrast with under-educate) was essentially meant to be the difference between requiring students to have algebra and trig versus not.

While not free, I don't see those classes as being a huge burden as part of the expense could/should be offset by the students not taking other courses (i.e. basket weaving). I believe the potential gains in society far outweigh the potential downside of only providing those courses (algebra and trig) to those who have a strong interest in them.

Over-educate was not intended to require all students to have Calculus and Differential Equations course work.

Somewhere, I have come across studies suggesting that musicians are naturally more adept in mathematics, or was it mathematicians are more adept at music? The affect was hypothesized to be related to the need in music to develop a finesse in timing...

At any rate, there appear to be complimentary mental processes that are poorly understood...And maybe this is one reason why "modern" music is inferior to "ancient" music (or, maybe that is only due to my personal preferences...

According to my piano teacher in college, mathematicians and (hard science majors) are naturally adept at music, particularly reading it (at least with respects to piano). Never met a music major that had any advanced mathematical skills at all (as they usually went into music very early to avoid having to take many classes like math and sciences in high school).

JB -- It's not the exposure to algebra I'm against. It's the mandatory two years of high school course work in algebra I'm against. Such programs are a widely advocated fad this year in California. We have enough reasons why students drop out of high school. We don't need to add motivations like intense course work that is incomprehensible to people whose brains simply are not good at learning abstract concepts.

I know we engineers like to believe that everybody's brains work the way ours do; so obviously they can understand anything we can understand. Not so. It took me a good part of my life and some real world experience to learn that some pretty bright and successful folks, especially ones who are "people" people rather than "thing" people like me, just can't deal with abstractions like maps or algebraic formulas.

There is plenty of room for the algebra challenged right brained heads in this world, especially where leadership is involved. We need to keep them on the train. Teach them algebra in their first year of college if your archaic standards require it. The ones who can't really learn algebra but have plenty of determination will pass the course by simply memorizing enough problem solutions to pass the exam. And like my wife, who did quite well in getting her BA, will promptly forget all they learn about the subject.

Much better we teach our high school students the math they need for life. Things like how to use a calculator; basic financial calculations like compound interest and how to balance a checkbook or fill out a simple tax return; fractions, decimals and percentages; probabilities; orders of magnitude; simple mechanics and trig; the most basic algebra to use and understand simple formulas; how to interpret and draw graphs; physical measurement; simple statistical principles and numbers in the world of science would all be on my list.

BTW, we've pretty much dumped the civics courses here in CA. And if the current condition of our nation is any indication a broad knowledge of civics is a lot more important to our society than how to solve an algebra problem. Or maybe it's better not to teach civics at all and rely on a giant electronic propaganda machine to train people how to vote.

Ed Weldon

Enough to know when somebody is trying to screw you. And not so much, that you conclude the origin of the universe can be explained by it.

Hmm, I would guess they should have sufficient minimum math skills to figure out all the costs involved and the interest on a loan (or mortgage) for such things as house, cars, boats, etc.. Probably enough math to be able to see when some saleman tries to sell something that the cost/benefits aren't adding up or that the thing represents an over unity device that violated physical laws. Plus I suspect most adults have no clue how much math they are actually using in their jobs. I see this out of our admin staff all the time. They don't realize they are using geometry or trigonometry when calculating grades, elevation changes or other such things. They just know that is how someone explained it to them in the past and that is how they do it. On the negative side, since they only are familair with this specific process they apply normally, they do not know when it should not be applied , unless someone explained that to them (which is unlikely since such explanations are usually project specific).

I agree that most adults don't need math skills much above simple addition, subtraction, multiplication, and division. However, . . .

The schools should still (as some would say) torture the students with learning the goemetry, algebra, trigonometry, etc. because we cannot always say who will go on to science or engineering a few years or a few decades down the road.

To ask a child what they plan to do in four or five years is asking a bit much. For most of them will simply pick the path of least resistance and in essence locking them out of the STEM fields.

I'd say it's a bad idea to abandon this track.

Brave Sir Robin -- Costly torture procedures and teaching of statistically low value material are an extravagant way of measuring scholastic aptitudes given our present day knowledge of childhood behavior and how to observe and gauge aptitudes.

To me it is far more efficient to teach children and young adults how to learn and then motivate them in the pursuit of learning. Then they will naturally seek out those occupations they are best at. And even if their chosen occupation does not greatly enrich them at least they will have a better chance at happiness and self fulfillment engaged in work for which they are highly motivated.

We need to get away from the mentality that has schools primarily concerned with the sorting and categorizing young people for the convenience of future oligarchies who will then burn them out and cast them aside for the most trivial of reasons.

Ed Weldon

RCE - You present some good points. Your examples also illuminate another one relevant to this topic: That subjective judgements are a real piece of our endeavors. To the extent that we focus on mathematics skills we weaken our proficiency in areas that do not yield to mathematical or purely logic based building blocks. (eg, Will this piece meet the required code or element of the specs?)

BTW, I don't design bridges; but I have a couple of decent books on how to build model train sized models of them.

Ed Weldon (NJ PE#17571 (mechanical engr))

As a PE I am sure you have had some experience with public inoput process on projects. As a Civil engineer, we get this all the time. Surprisingly, you can achieve consensus on an issue sometimes in public meetings, but when they bring the idea back to the design engineers, the Principals (typically marketing) didn't realize that the proposed idea violates a regulation, code, standard of practice, is just unsafe, is just way more expensive than anyone really thought it would be once you addrsss the related ancillary changes, or even changes other components they wanted in ways that are not acceptable. Just sitting in a meeting where they allow biologists, archeologists, and planners some input, i.e. technical review forums for public agency project proposals, can cause a consensus that is not sound or cost effective. Plus in achieving consensus on a component of a project you can get huge scope drifts from people negotiating with each other to get each interests specific pork belly incorporated into the project design. (I can not tell you how many times we have had to include bird or fish habitat elements into a project where tehy weren't mandated, becasue one of the biologists for a local public agency felt it would be a good bonus to the project and was obviously going to oppose the project unless he got his stuff amended into the project, for the project budget for funding obviously).

studying Math not only teaches a usable skill - it engenders brain connections and formation

The same question can be asked about literature-it is not indefinitely what you learn from math, although algebra IS a very important part of everyday life. The point of learning math is to acquire basic, logical thinking skills that can be applied when tackling any type of problem. You may think that some menial jobs may not have any mathematical problems, such as driving a bus. However, problems arise in every job, some of which you will have to solve. So math encourages the logical part of the brain to develop.

Reminds me of the summer I was out walking with my 4 year old step-grandaughter who asked,

"If I already know how to do everything, why do I need to start going to school?"

I told her, "Because the more you learn about different things, the more you'll realize how much more there is that you need to learn."

To which she replied, "Oh, ok then."

To which I replied, "Don't worry, it will be more fun than you can possibly imagine."

To which she replied, "Ok, I guess I'll go then."