### College-level counting

[Computer’s still a few time zones away, bike-without-adapter is still primary means of transportation - and I have an apartment to move to the mainland. And I’ll be away, again, this time south of the border, for part of July, so don’t expect anything interesting or substantial in this space for quite some time.]

In the meantime, a discussion topic: how mathematics education went so horribly awry that we now teach this stuff in *college*. Actually, let me flip that one around: why do we bother teaching this material - integers, fractions, areas of plane figures, basic algebra - in elementary school and junior high in the first place? I know why *I* think students should learn it, but I wonder if educators and curriculum developers at that level can answer that question, given that basic mathematics is so often so poorly retained. I certainly wonder what insight *those* educators would offer when confronted with the fact that more and more colleges are offering remedial classes, especially in math, than ever before; that in many cases, it is unwise for us college math instructors to assume that our students have *any* knowledge of prerequisite material. What sort of subject is grade-school math, that it is absorbed so poorly?

If I were to invent a language with counterintuitive syntax and bizarre vocabulary that bore no relation to that of any Western language, and if I were to teach my invention to a classroom full of schoolchildren, some would excel. Others would do decently. In any event, most, I figure, would pass. But a year later, nearly everyone in my class will have forgotten my crazy language, save a few words that they heard in memorable contexts. Why would they remember it, after all? They have no need for it, and the lessons they took were nowhere reinforced in their day-to-day lives. This is how so many college students see math: as something that they need to learn because their teachers said so, but something that is so poorly connected to the rest of their lives that they have no reason to *remember* (let alone apply, let alone use) any of it.

At the risk of sounding like an obnoxious student, I’m asking those who teach this material the first time: what’s the point of any of this? Why do we have to learn it? What does it have to do with anything?

…and given whatever those answers are…why is math so seldom worked into any aspect of children’s lives outside the mathematics classroom before they graduate from high school?

btw, i got my costume jewelry today

More than once I have noted that some of my students would be no worse off if they had played PlayStation 5 hours a week (+ extra for “homework”) for the past decade instead of having math class.

It makes me appreciate part of the Free School movement — which is silly and unrealistic in any but the most special of circumstances. The kids control the entire curriculm in Free Schools, and they don’t learn any math unless they ask to.

Oh, forgot to mention: Despite it being allegedly useful (and definitely Western), I still resent the four years of having a crazy language inflicted upon me when I was in school. Biggest waste of time ever invented in the history of education. What do I remember? Um, let’s see…

Que veut-dire ça?andComment dit-on …?. That’s about it. Oh, andje ne sais pas.Never say again that french is a crazy language ! That’s MINE !

To answer MS, I’ve to face the same problem with my little sister (she’s completed the year just before the Bac (I don’t know what is the american/canadian equivalent)) who has a really poor level in maths and to whom I give some particular lessons. In front of a problem, I try to make her “think” to the thing, ask herself some question… but to the question “What do you see ?” she always answers “Nothing ! I’ve no prejudices but I can’t see anything in that sequence/function/shape”. I try to put that into perspective in real life, but I think she doesn’t make any link between the intuitive pattern she see all day (the 20% sales in the Gallerie Lafayette) and the ugly things that are written in her math book (about percentage).

English IS a crazy language ! (the only one where you have to put an s to a verb which is singular, isn’t that really abberant ?)

je ne parle pas bien le francais.

(with the squiggly on the c)

Almost NO subjects in school are applicable to one’s day-to-day life as a kid. Literature, history, science… since when do you have to titrate an acid in real life? Reading, writing, and basic arithmetic cover most of day-to-day life stuff (and typing would be helpful, as well as using computers). There was a reason that high school was invented… to keep those pesky adolescents busy since we were banning child labor. And since they couldn’t very well be teaching arithmetic, reading, and writing over and over they had to add a bunch of extra classes.

Why math gets bitched at the most beats me. Moliere doesn’t come up a lot at my job, I can tell you that much. I’ve not had to use my knowledge of when the Battle of Hastings occurred, and who won it. I suppose it’s because math is most obviously cumulative, and that teachers expect you to actually =remember= what you did with it before that sticks in the craw.

Funny you should mention the Free School movement, RH - a few months ago, completely taken aback by my students’ inability to do grade school-level math, I started looking into how math was taught in the earlier grades, and what alternatives people were using. I happened upon some unschooling messageboards and such, and it wasn’t long before I identified a common theme: hardly any of these mothers (always mothers, never fathers - hmm) who were so very devoted to “guiding” their child through learning the subjects the children chose to learn, reported any math lessons. They told stories of brilliant, creative kids who had become veritable experts on dinosaurs, infectious diseases, literature, you name it - but math was virtually absent from the equation. Obviously, it’s not as though, for instance, the dinosaur experts woke up one morning itching to learn about the creatures - presumably they’d been exposed to them in some context before, and got excited about them. But this tended not to happen with math, and a look at the math discussion board quickly provided some insight into why that was: almost to the individual, these moms, who’d shunned the traditional education system, reproted that they never liked math, were never any good at it, etc. I wonder how many of their kids, some of whom were in high school, had ever been exposed to the subject even in passing.

Meep, I know lots of subjects are “irrelevant”, but colleges don’t

reteachMoliere and the Battle of Hastings to all incoming freshmen who never learned about them properly the first time. What especially galls me is that when I went over [fractions | graphing straight lines | computing areas of plane figures | solving simple word problems],which they’d seen before in school, I got blank stares, as opposed to “oh yeah, we did that…I don’t remember much of it, but it’s kinda coming back to me now.” Cognitive psychology has told us that it’s easier to learn something the second time than the first (I was nearly fluent in Hebrew two weeks into a trip to Israel, despite having barely spoken the language in years); it stands to reason that my college students, and RH’s, and so many others,neverlearned math the first time. There’s nothing to “come back” to them.“… rep[or]ted that they never liked math, were never any good at it, etc.”

I can’t remember where I read it, but I remember hearing once how absolutely ridiculous most people would find it if they heard a parent telling their child ‘Oh, I never was very good at reading. I didn’t see much of a point of it’, and yet no one bats an eyelash when the same is said about math. If parents are, from childhood, telling their children that it’s ok not to try or to be good at math is it any surprise that a lot of kids nowdays can’t add fractions?

Simon Rose: I’m pretty sure MS has said it many times. ;)

You can complain that French is complicated. You can talk about the past participle weird rules, and the exceptions on top of that already complicated set of rules. You can also talk about the many plural forms, depending on how a word ends, and, of course, the exceptions to that other rule. You can even mention how they now try to make the language simpler by introducing new ways to write a given word, which confuses us a bit more by giving two “allowed” ways to spell a single word.

You can, I guess, say that French is a crazy language. But please, PLEASE, don’t do it on the very day we celebrate it Quebec! (June 24 is St-Jean-Baptiste day, the “national” day here, celebrating our culture, where French plays a major role.)

The less you do, the less you need to know. Manufacturing is a bit of a mystery to most children and probably also to most adults. Things come from the store and are made in a factory out of chemicals. If there is no need to build anything one wants to use or grow and process anything one wants to eat, then there is no need to muck about with chemicals, plants, or tools. Why not replace school with Playstation? At least Sony’s worlds are fun and coherent.

Math is doubly useless, as it’s something people used to need to use in order to make things AND there are computers to do it. In the unlikely event that anybody was called upon to do anything, the math (whatever it might be) could come from the computer.

It works. It’s a great life. We don’t need those skills. Maybe it means we get taken for a ride now and then, but the flip side is that we get great shit and have no responsibility for any of it. Do people want to know what goes on in that chemical plant? No, they just want it out of their neighborhood. Do they want to know how that chicken taco was made? No way! Knowledge conveys responsibility. Better not to know.

So, math is dangerous, just like all that other learning garbage. If you can do the math, you might have to come to some sort of uncomfortable conclusion, and why spoil a good thing?

Re unlearning, the best part is the conviction that math, science, etc. are things to be avoided because they’re instruments of Evil Inc. and will instantly corrupt all to the dark side. It’s may be mostly true, as Evil Inc. usually has steadier jobs than the temporary gigs posted on FightEvil.org’s website, but it’s still just avoiding power.

So.. watcha gonna do? You want to make math relevant when nothing in school is. My answer is math games. It’s much better than just having a class where kids put math and science together to make or grow things. That would empower them, and then where would they be?

Yeah, I had been thinking that when I posted this that it could easily have been here I read it.

let’s do all remember that there is another side of the coin. i derive heron’s (hero’s?) formula and prove the existence of euler and simson lines to 15-year-olds, and i teach the basics of linear programming and induction with 14-year-olds. most get a basic understanding, some will remember. but most of them appreciate the “real-world-ness” of linear programming and the inherent coolness that we see in euclidean geometry. they even buy into the idea that they may not use this exact stuff in their future lives, but that they will use the problem-solving skills they learn in my class.

i know i’m very lucky to have these kids in class…i don’t take it for granted (or for granite, as my wife’s english student’s write sometimes in all sincerity).

but in addition to being naturally curious, kids want to succeed and please adults. it’s in their nature. even teenagers want our approval as much as they also want to rebel against us. if some adults, even just math teachers, are engaging and clearly LIKE this stuff, they will try to succeed at it, even if they don’t quite buy into its utility for their later lives.

the real killer, IMHO, are the grade-school teachers who aren’t much different from the home-school parents in their approach to and knowledge of math. if your teachers don’t appreciate math, for god’s sake, there’s no reason for you to.

My two cents on the topic..

I don’t particularily believe that math education has been declining. 20+ years ago calculus, factoring quadractics, adding fractions etc. would have been taught in highschool relatively the same way, with same (if not a lower) percentage of the population taking interest in such inane areas of education.

I always imagine what it would have been like to try to teach my grandmother how to do the basic math needed to be an accountant, say, or any sort of remedial work that requires a college education. Then I think, ‘My god, no wonder it’s so hard to get math across to some of the people in my classes’. I don’t particularly see any difference with the times changing except that nowadays someone like my grandmother might actually consider taking a course in accounting because they got themselves believing that there is an 80k/year pot of gold if they can just put up with this boring stuff, like math, for another 3 years. Not that I am complainging about increases in the number of students going to post secondary. It definitely increases the number of academia math jobs out there, but I’m not so sure if the students are getting out of the educaiton what they expecting to.

Another comparison I like to make is having a contractor come into your home to renovate your bathroom, say. You could just imagine what kind of discusion they would be having with themselves if you were to sit there watching over their should pointing out anything you thought wasn’t right. I figure it’s the same feeling when a student tells me ‘but there is now way I’m going to be able to understand that’ to some simple equation manipulation and still expects to do well. Darn those lazy construction workers!! What do they know anyways!!

I asked my students why people found math hard, and I got five different answers:

Huh? I dunno.

I’m a people person, not a quant; plus I was, like, sick last week.

Cause it’s boring and stupid; I mean,

you’renot boring, just the subject.There’s a lot to remember, and it’s confusing. Like here: When it says “of” do I add or multiply?

It’s no harder than anything else, it’s just that everybody has to take harder and harder math classes until they fail. It’s like Dilbert; even if you’re not stupid to start with, they promote you until you are.

Math is useful - it’s just not obviously useful the way reading is (having just returned from Central Europe with no more guidance than a couple Lonely Planet phrasebooks, I can now say definitively that illiteracy

sucks. I haven’t used the quadratic equation, or integration, in years, but the techniques I learned from Algebra and Geometry are essential.Having a computer do the calculations is worthless if you can’t understand the calculations to begin with; I spend a quarter of my time re-writing formulas and macros in Excel, which saves me about three times the time cost by improved productivity. I couldn’t do it without thorough understanding of things like the distributive property, or the multiplicative inverse. I’m just talking about day-to-day stuff - I’ll call a tech person for a large project (with a budget), but at $300/hour, my productivity depends on being able to figure out mathematical shortcuts on my own.

And that’s just on the technical elements of math - even more important is logic and mathematical reasoning. The key to that is not ‘relevance’, but actually its opposite - the able to reduce real-world situations to abstract terms and apply mathematical reasoning to it. This relates directly to your recent posts about those who think of math as a series of formulas to be memorized and copied, and those who think of it as a framework by which you can solve a problem.

The reason we spend so much time on ‘the boring stuff’ is the same reason a basketball player spends hours in the gym dribbling, lifting weights, and running on the treadmill. Success at the fun stuff is accomplished by spending 5x the hours on the boring stuff.

Why are recruits in Boot Camp forced to make their beds so tightly that a quarter can bounce off it? What earthly battlefield purpose is served when our soldiers can make their beds ‘properly’?

Because they learn to pay attention to detail. They develop habits of mind that will serve them well in other capacities.

It is the same with mathematics. When asked to perform difficult mental tasks, their brains are being trained to think abstractly. That they are able to factor polynomial equations is of secondary importance to the fact that they have brains that went from not knowing to knowing how to factor polynomial equations.

We teach higher mathematics to students in the hope that they acquire well-trained minds.

Math is, for some reason, seen as different than other subjects.

All in all, everything can be reduced to math - that’s why it’s so important.

English is about analyzing essays and understanding relationships, as Mobius Stripper has said in previous posts: An equation is a relationship among quantities. In math you have to look at relationships, figure out what you have, what you want and how you get from A to B.

You have to understand, analysis and problem solve.

What other academic area does not benefit from better problem solving? Day to day activities, every day occurences, benefit from problem solving. It’s not about knowing that 2 + 2 is 4, but about understanding that + means putting quantities together.

People are inherently lazy and will continue to be like that. They will live up to your expectations, but because of that, when they fail a math test/exam, quiz or assignment, they will feel like they failed and make themselves feel worse about it.

I tutor TONS of students during the term and time and time again, I think it boils down to the Psychology of the situation more so than the actual mathematics. Given enough examples, anyone can learn about it given enough time.

Mind you, there is no amount of tutoring I could ever give a student to make up for the fact they didn’t do their homework - but it helps to know that the person that no one wants to work with in the office because she doesn’t understand you have to finish reading the book before you can write an essay comparing it, in it’s ENTIRETY (from the prompt), to other things, when SHE can learn Stats… you know the world is a better place.

While education will not get anywhere from placing blame here or there or anywhere, personal responsibility has to begin somewhere. Students have to work for their grades, in all classes not just the ones that the teacher givcs an easy “A”. Teachers/professors have to answer to administrators, and depending on the level of education, parents. Parental involvement = very good (maybe not necessarily on the college-level), but this has to be a consistent thing not just once in a lifetime.

Everyone has to do their part, the question is who failed these kids? Is it correctable? What can a prof. or tutor without sacrificing their own life?

When asked to perform difficult mental tasks, their brains are being trained to think abstractly.…and I’m sure that the general reasoning for teaching math runs somewhere along the above lines. And it’s a perfectly good (partial) answer - good enough, mind you, that it seems that

actually training students to think abstractlyshould be a primary goal. Judging, though, by the staggering proportion of students who emerge from high school completely unable to do above, it seems safe to conclude that educators and students have fallen far short of that goal.My (poorly-made, but I can only use the library computers for half-hour intervals) point was that students’ general mathematical incompetence is utterly at odds with our rationale for teaching math. Students should be able to think abstractly and quantitatively, and that’s why we teach them math - great. So why do we give them A’s and B’s in high school if they can’t even solve the most basic of word problems?

When giving one-on-one help, my students will often complain about the vast amount of memorizing they have to do. (One adult student earnestly gave this example: “For instance, when you need to solve 5x=20, you do 20 divided by 5. But when you want to solve 20/x=4…you have to do 20 divided by 4, even though the 20 and the x are together!”) I generally advise them to not only study

howdo to this step or that, but alsowhywe do those steps in solving various types of problems. Why are we completing the square in this question? To maximize a quantity. Why are we setting up an equation for area and another for perimeter? To reduce the problem to a single equation in one variable.More than one student has been completely surprised at this advice. One in particular told me that it wasn’t just that she didn’t know the reasons for doing the various steps we did - she didn’t even know that there

werereasons. She saw the whole process as an algorithm she had to memorize, that’s all.In over a decade of math classes, she’d never learned otherwise.

“but colleges don’t reteach Moliere and the Battle of Hastings to all incoming freshmen who never learned about them properly the first time.”

And Moliere and the Battle of Hastings are just as irrelevant to the college level student as they are to the high school student.

Hey, I don’t know why half the things that are taught (actually, make that 80%) in high school are taught, except that most are required to be able to take college level courses. Or at least that used to be true. I went to college only because that was what one did after high school, and after switching majors three times, I dropped out and joined the military to keep from getting drafted. Went back 5 years later and concentrated in Computer Engineering and the nicest most wonderful thing about the two years it took me to complete my degree was that I DIDN’T HAVE TO TAKE ANY MORE LIBERAL ARTS COURSES!!! But engineering was fun, lots of fun, but since I was still in the military, I wasn’t able to put it to any direct use.

So, I can still do basic algebra, and even derive the quadratic formula, along with basic integration and derivation, but I have forgotten all the modern algebra and linear algebra and theory of complex variables simply because they are not a part of my world. At least they were interesting at the time, but just as much a “waste” of time as French or Russian in that they never never had any relevency to my life.

So why teach stuff (i.e., math, foreign languages, domestic language(s), history, etc.) at all? Because for some people, an interest will be kindled, and a small portion of those people will go on to college or even higher and learn more about what they are interested in. The vast majority of people will never do so and will never need to know 90% of what they learned in school. And because we are attempting a democracy, we can’t get away with only teaching those who are really capable of learning–that would be classist! Horrors!

I think one of the reasons that math is so difficult for students to reatin from your to year is that it

isn’trelevant to their everyday lives. Math shows them how to do syntactical manipulations on strings of symbols that mean nothing to them. For math to be relevant two conditions would have to be met: First they would have to be taught ways in which math can be applied to their lives and second they would ahve to have faith that math would actually produce the right answer.Attempts to teach students how math is relevant to them are woefully misdirected. Basically, word problems are created to make mock real life situations with everything difficult or complex weeded out. Students don’t even see the word problems as problems that could come up in real life, but rather as more examples of these strange strings of symbols. It is an extra manipulation they have to go through to get the answer, and one that doesn’t even have syntactic rules they can follow to get through it.

More difficult than that, however, is that most people have no faith that math can give them a correct answer. Try to explain to a person at a casino that their roulette betting system doesn’t work. They can hear your premises, understand your arguments, and still not agree with your conclusion. That is because they just don’t

believethat when you translate the problem into the language of math, follow the rules of math, and translate the result back, the answer you get is the truth.As a formalist, I can’t think of a reason why they would believe this, outside of the fact that it seems to work way more often than it doesn’t. As it turns out, we know that even the most basic math is either incomplete or inconsistent, and we have chosen to believe it is the former either because it would make us feel bad otherwise or because it seems to have worked out well so far.

All of that being said, I have an answer to the direct question of why we bother teaching math to students in grade school, even if its not a very good answer to the real question that is being asked. We need to teach kids math because there are lots of kids out there who hate school, who are awkward socially, and who think every subject is a terrible waste of their time, but who excel in math. Through math these kids have an opportunity to come into themselves.

I remember sharing fruitsnacks with two friends in senior kindergarten. N. had split his last 6 pieces with I. so that they each had 3, and I realised we could share them evenly if they each gave me one. I was very excited when I realised this relationship between 6 divided by 2 = 3, and 6 divided by 3 = 2.

Simon Rose, I do not know where you read it, but I first read it here:

http://www.campusi.com/isbn_0809058405.htm

I would like to add a reason to try to teach math to students: to teach them to think by themselves, so that they cannot be easily manipulated.

djfatsostupid said:

most people have no faith that math can give them a correct answerFrom their point of view this may even be rational. After all, they remember doing math problems and getting the wrong answer far more often than the right answer. Having (correctly) no confidence in their own ability to evaluate your math, they see you as just another person telling them something.

It sounds kind of cranky to say so, but I think we lost something when we stopped teaching Euclid. For students who don’t go on to study math post calculus, The Elements can be a great introduction to logic.

Some of math is obviously useful on a regular basis. Let’s see, hmm, okay — adding, subtracting, division, multiplication, percents, fractions, and decimals. All looks like basic arithmetic to me. Geometry to a much lesser degree, in that one doesn’t have to know geometrical proofs to know to make sure a square frame built of wood is not square until the diagonals are equal.

So unless you are in a profession which either uses math (which mine doesn’t) or for which knowing math was a prerequisite (which is true for me), any math of algebra or higher level bears no relation to daily life.

On the other hand, I really really wish that people understood basic statistics so they could understand what a confidence level or standard deviation was. Or even to realize that the law of large numbers is provable mathematically (which I did in my Probability class in college (a technical elective for me). These are all relevant to the numerous political polls which we are cursed with. I scream anytime I see a politician decry a poll as only sampling the opinions of 1,500 people and therefore not being valid. The politician should be attacking the randomness of the sample instead of the sample size.

Just remember, the integral of e to the x equals the function of u to the n.

meep said

Almost NO subjects in school are applicable to one’s day-to-day life as a kid. Literature, history, science… since when do you have to titrate an acid in real life?Yes and no. A basic familiarity with history is essential to daily life. Sure, exact details are unimportant, but being able to identify historical events in the correct general timeframe is necessary to give you a sense of perspective and a sense of time. A basic familiarty with science gives you the ability to recognize absurd claims or conclusions. Again, maybe you don’t need to know how to titrate an acid or use Newton’s laws to solve a 5-body dynamics problem, but being conversant in science lets you recognize the absurdity of “This simple fuel additive can give you 100 mpg in any car!” or such nonsense.

MS said

“Students should be able to think abstractly and quantitatively, and that’s why we teach them math - great. So why do we give them A’s and B’s in high school if they can’t even solve the most basic of word problems”As to this…we shouldn’t be giving those kids As. If I may make a slightly generalized rant here, you’re just pointing at a symptom of the problem. Giving kids who can’t do the work an “A” for effort just to protect their self-esteem is stupid. The phrase “Well, I give you full marks for effort” is supposed to be a joke about doing badly, not literal truth. My HS years aren’t that far behind me, but I don’t remember getting points just for effort or to help me feel better about myself.* It’s hard for me to grasp the mindset that its better for the teacher to tell me I’m good at something when I’m really a moron (or lazy, or lost…). That attitude is built into the curriculum now. School isn’t about education, it’s about validation of your worth as a person.

As to how to fix it? Change the focus of school back to teaching something rather than building self-esteem. Have teachers that hold students to a standard and are willing to flunk students when they don’t measure up. Have administrators willing to back said teachers. Restore a sense of individual responsibility to schooling to accompany teacher accountability. Sure, bad grades might be a sign of bad teachers, but they also might be a sign of someone not doing the necessary work. Yeah, yeah, vague and general terms, but I’m still sort-of ranting here.

————-

*In fact, I got my wrist slapped for putting too much effort into speculating on my final grade.

Chris C.: Can you tell me what specific cases you’re talking about where students got “A”s just to boost their self-esteem? In which schools did this happen?

In general: I find the comments people have made about unschooling and homeschooling to be interesting, because I was an unschooler until college, and my mom was probably about as good at teaching math as your average middle-school math teacher. I was never interested in math until I became interested in computer science. At that point, I knew I would have to learn some math, so I taught myself high-school algebra out of the Saxon books, and ended up minoring in math in college, even though I didn’t really do anything with math between the ages of 8 and 14. There’s nothing wrong with waiting to learn a subject until you have motivation for it.

Jen: Re: the fruit snacks, that is so cute!

MS: Regarding the parental/gender roles: My Mom was perfectly adequate at math though she probably forgot whatever calculus she learned in college. She taught me to count on my finger-lines (20 on each hand! It’s still useful) but she did spend a lot more time teaching me to read and about “content” as we might term the Battle of Hastings and Dinosaurs.

So if we accept that men are generally more interested in math than women, factoring in all the gruesome nurture by the time they become parents, and that they’ve probably had better math experiences, this seems to be indicative of a lack of fathering. The fact is my DAD, the engineer, seemed to think “quality time” consisted of coming home, sitting me on his lap, giving me some kisses and then showing me arithmetic tricks and

not letting me get up until I had done about three pages of problems. He had me doing long division by kindergarten. I’m still sad that my high school calculator killed my previously stunning mental arithmetic skills, and whenever I do manage to do some mental arithmetic quickly and well I find myself feeling a warm glow of filial affection. It sounds kinda stupid and obvious, but if your parents are affectionate and attentive and they also really like doing math with you.This is also sounds kinda dumb, but did anyone watch Square One TV and 3-2-1 Contact on PBS? Are they on Canadian TV? Is there an analog? Cuz I remember in kindgergarten we had a this circle on the carpet that was the alphabet. So everyone sat on a letter, with a couple of gaps. At some point we were thinking of having a party for the other sections of kindergarten and one kid said, how many kids could fit in this circle? And, massive flying dork that I already was, I remember I jumed up and said! oh! that depends on the area! And Paco from 3-2-1 contact had just demonstrated that the area of a rectacle was the base times the width so I wanted to measure the base times the width and suddenlyI was like. .. wah! it’s a circle, how does

thatwork? And the Kindergarten teacher (who I now realize must have been totally freaked) basically gave me a cookie and told me not to worry about it. So I was like, genuinely thrilled to learn (by reading) the formula for the area of a circle even if I didn’t understand why.My points being that a) educational TV is useful b) geometry, attended by arithmetic, can be made quite relevant to children with enough building projects and the like. Another thing that’s useful is some responsibility for momeny and budgeting and debts . . .perhaps organizing some kind of project. Hand them a catalog and and a total budget and a task, and they’ll have to do some arithmetic to figure it out. Student businesses and fundraisers are good for getting people good at addition and subtraction b/c they won’t want to be cheated. Dividing responsibilities equally as well. I mean, these are all things we have to do in real life on a bigger scale, and we often muck them up because we’re bad at math.

This was posted yesterday on another list that I follow:

I have a student who told me his best size for large print, was if regular print was magnified 75%. Which is, well, what exactly. smile.

Math was not one of my strong suits, but I need to know what point size that would be so I can create materials for him. As I don’t photocopy but OCR and then enlarge on the PC.

Is there a mathematical way to figure this out, or does anyone know what size print that would be abouts.

Susan,

I don’t know if font sizes are labeled in a proportional manner or not, but I do know that font size 12 is pretty close, if not exactly, to 1/8 inch tall. 75% larger is 7/32 of an inch which rounds up to 1/4 inch. 75% larger than 12 is 21, which is close to font size 20, which is also close to 1/4 inch. So my recommendation would be to use font size 20 and see how he likes it.

Point sizes are exactly proportional. So to get a 75% increase from 12pt, we find 75% of 12 (0.75*12=9) and add that to 12 to get a type size of 21. With the advent of scalable type, we can have any type size that we want.

For 10 pt type which is the most common size for printed materials. we want 17.5pt.

But in any event, rather than treating this as a strict mathematical problem, a non-mathematical solution is better: Print sample pages at a variety of sizes from 15-25 pt, ask the student which is the smallest size that he can use, then print materials at that size.

Also, it’s worth noting that while point sizes do scale proportionally, the same size of different faces can look different. This is because point size doesn’t actually measure a physical aspect of the printed letters, but rather the amount of space the largest characters take up: It’s a hold-over from the days of type as a physical object arranged on a press. The most significant aspect of the characters that determines apparent size is the x-height (that is the height of lower-case letters without ascenders or descenders: acemnnorsuvwxz). Compare 10pt Helvetica to 10pt Times and you’ll see the difference immediately. The x-height of Helvetica is roughly 10% larger than that of Times. If you wanted to mix the faces, you should use 9pt Helvetica with 10pt Times, a combination which is difficult to effect in most typesetting software.

Rex and Vito,

Thank you for the interesting and useful information. I actually meant this as a “metapost” to support the topic. First, here is a teacher who’s not embarrassed to admit to not being able to do a per cent problem. Second, it is an interesting example to show that the need for a bit of math understanding is not always something one might anticipate.

However, I agree with Vito that an experimental solution probably makes more sense in this situation.

Cheers!

Saheli: I watched Square 1 in Toronto because rabbit ear on our TV could pick up signals from Buffalo’s PBS. I loved Square 1!

“I have a student who told me his best size for large print, was if regular print was magnified 75%. Which is, well, what exactly. smile.”

I don’t think that he did an experiment and came up with the figure 75.000% (or 74.9987%). Newspaper print is about 10-point, and Word offers 10,12,14,16,18,20 points, and seems to allow “.5″ after each. Being a “real-world problem”, I’d just go with “17.5 make it 18″ point. It’s also an exercize in significant figures - 17.4823451 point type is probably way too precise.

Rather than a mathematical approach, I’d take an empirical one, printing out separate pages in 12, 14, 16, 18,… and see which one he picks. Then do the experiment again another day to see if he picks the same one.

Well, this is going to sound very crude, and I already wrote this comment, changed my mind, and deleted it once, but here goes:

The difference is attractive women. I’m a math/econ student (degree in one more semester!) who also speaks Spanish and Russian. My Spanish is fluent; while it isn’t a terribly difficult language to learn, there is lots of work learning and maintaining the language. The payout? I’ve met some really hot women, lived in Buenos Aires, visited Madrid for months at a time, etc. I also am living in CA, so it’s useful here as well.

Russian is a far more difficult proposition than Spanish, but living in Moscow was great and I may end up there again. I met lots of really cool people, spent lots of nights partying, and met some really attractive women because I was studying Russian. Nothing like practicing your Russian in bed over a lazy breakfast.

This experience, unfortunately, has never occurred with mathematics :( If there is somewere that cool math people who like drinking, surfing, martial arts, climbing, or dancing hang out, please share, but I’m convinced there aren’t very many of them.

This has to, in some part, affect how much effort people put into learning any given subject. Languages, at least for me, offered a pretty clear set of rewards while the rewards from mathematics have so far been far more intellectual…

Re self-esteem and A’s for effort - while “I’m giving you an A to make you feel better about yourself” is probably seldom, if ever, the explicit justification for rewarding mediocre work, what we do have is this:

1) Students who know next to nothing in math are getting A’s in the subject.

2) A’s make people feel better than B’s or C’s or D’s.

So the effect is similar to “you get an A because that’ll make you happier”, though the remedy is quite different.

I think that the cause of 1), particularly among the lower grades, has a lot to do with teachers not knowing much math. Rudbeckia Hirta has documented at length the trials of teaching future elementary school teachers who can’t do elementary school-level math. Those teachers are less able to evaluate students’ work; I’m sure that many have students who are quite average who are better at math than they are, and of course you give A’s to students who equal or surpass you. (And, of course, such teachers are largely at the mercy of curricula over which they have no control.)

In any case, we do get a vicious circle: students who know nothing and get A’s get indignant when they have a teacher (me) who doesn’t give them A’s. It’s stressful to deal with that, as I’ve written before; while I want the grades I give to be nothing more or less than an honest reflection of what my students know, it’s emotionally draining to deal with the consequences of that when your students were so ill-educated.

(More later…)

“Why do we have to learn this?”Ah, the question all teachers fear…

The great Moebius Stripper has a nice description of learning math at school:

If I were to invent a language with counterintuitive syntax and bizarre vocabulary that bore no relation to that of any Western lang…

OK, now I want my money back that I paid for French class. Almost five years of frickin’ French class and I did not meet ANY hot women. NONE. I KNEW I should have taken Spanish instead.

Yeah, you sure chose poorly, particularly as I have it on good authority that there are NO good-looking girls in math, either. So said a healthy portion of my classmates - at least when they weren’t lamenting their inability to get laid. I leave it as an exercise to the reader to determine which of these two readings was the accurate one, given a 3:1 M:F ratio in the math department.

Once, some genius even wrote an article for the math humour rag suggesting that we admit female students based not only on grades, but also on their scores on the CGI - the “cute girl index”. Oh, here it is. Money quote: “After all, who wouldn’t want to go to a school where all the girls are super cute?”

Lord,

I can’t imagine!But, anyway. I have a working knowledge of three languages other than English, and no man (or woman) ever fell over me as a result of that. If, indeed, educated and worldly men are merely looking for hot women, then the carnal rewards for the ordinary-looking woman who chooses to educate herself may be hard to come by.

Quelle dommage!Kirsten said: “There’s nothing wrong with waiting to learn a subject until you have motivation for it.”

As a high-unschooler…Hallelujah! If only everyone felt this way.

And it’s not like only academically “smart” people should get the freedom to choose what and when they want to study. My friend, who got terrible grades in school, has found Japanese to be his passion. He sucked learning Spanish in high school, but because he wants to move to Japan someday, he’s spending hours a day with the language and is pretty much fluent, as much as I can tell.

Ah, man.