Life In 19x19

snorri wrote:There are lots of dying skills. Driving a stick shift. Sewing. No one's crying about the decline of these things.

Speak for yourself. As a confirmed Luddite (I have conceded the need for a computer for professional reasons, but have none of the other common devices) I, for one, decry the loss of skill like you mention. Plus a whole load of others. When (and I don't say if) the complete system implodes upon is it is these lost skill which are going to determine the survivors.

Aidoneus wrote:

Bill Spight wrote:I think that it is a mistake to teach arithmetic before 5th grade. It is more sophisticated than it appears. Why waste 4 or 5 years on it (and turn children off of math in the process) instead of waiting until they are more ready and then spend 1 or 2 years on it?

I know that I said I would shut up...but I completely agree with this. With the exception of teaching younger children to count!

I am glad that we agree on that.

After I wrote that note I thought that teaching young children to count would be the exception.

DrStraw wrote:

snorri wrote:There are lots of dying skills. Driving a stick shift. Sewing. No one's crying about the decline of these things.

Speak for yourself. As a confirmed Luddite (I have conceded the need for a computer for professional reasons, but have none of the other common devices) I, for one, decry the loss of skill like you mention. Plus a whole load of others. When (and I don't say if) the complete system implodes upon is it is these lost skill which are going to determine the survivors.

OK, I guess I can't shut up...I drive a manual 5-speed Eclipse, though I never darn my socks. Also, I build computers, fix carburetor engines, manage home repairs, play (poorly) three musical instruments, know how to fish and survive in the woods if necessary, and, most important, keep my wife happy.

"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects."

-Robert A. Heinlein

Aidoneus wrote:"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects."

-Robert A. Heinlein

Well, I am too old to worry about diapers, I am not planning on invading anything, I am vegetarian so don't need to butcher anything, I don't know what conn a ship means, I designed (engineering included) and built my house with my own hands, forget sonnets (I hate poetry), I can balance an account and read a financial statement, build anything I want, I have never set a bone (never even broken one), I have limited experience with the dying, I have been a peon and a manager, I am married so I can cooperate, I can act alone, I am a mathematician so I can solve equations, analysis of problems is one of my biggest strengths, I pitch manure and compost every year in my garden, I was a professional programmer, I am an okay cook (but terrible compared to my wife), I have never had to fight and so far I have not died.

So where does that put me? Above average I hope.

Critical thinking, communication, ability to quickly learn topics, ability to synthesize ideas across fields of knowledge, to develop novel thoughts and opinions, to understand basic facts about the world to reason with, and perhaps a little aesthetics, philosophy and morality. Those are the sorts of thing I think really matter in education.

To address DrStraw's concern about preparing them for the end times: as long as collapse isn't too sudden I'll print off a few thousand pages of practical knowledge when it comes near: canning recipes and manual construction blueprints and how to build a hare trap.

I think the mechanics of mathematics is less important than the ideas conveyed. Is it important that you remember the derivative of 1/x? Or is it important that you understand how infinite infinitesimal approximations converge onto correct solutions? That you see that something like distance traveled is equivalent to area under a curve, that the tangential angle of a 3d shape can correspond to the speed you're traveling in a direction? These isomorphisms let you reason about problems in different domains. By the same token, I memorized sin²(x)+cos²(x)=1, but the most valuable thing I got from trigonometry was the idea that you can switch freely between reasoning with x,y and z to measuring by angles and vectors, and that in euclidean space a few facts about angles can constrain many others. It's another powerful isomorphism.

Which is to say that poor multiplication skills may correspond with poor math skills overall, but that doesn't need to be so. Mathematica can remove the need to understand the interesting connections in Calculus, or it can be a tool to explore and play inside of Calculus, so you develop these insights intuitively. So little of higher math is manually multiplying numbers, I just can't see how lacking that skill would be a big hindrance. I can believe it correlates with poor math skills: that a bright, enthusiastic student will retain his multiplication tables, that a school that doesn't demand mastery of this skill is less likely to demand conceptual mastery of Calculus either. But I definitely believe somebody could go as far as they want into mathematics without knowing 7x7 off the top of their head.

Polama wrote:Mathematica can remove the need to understand the interesting connections in Calculus, or it can be a tool to explore and play inside of Calculus, so you develop these insights intuitively.

I do not think that the importance of play in math education can be overemphasized, especially at the elementary level. Unlike Weather Woman, I want 5th graders to know a lot of fun things that they can do with math.

I often think that society consistently underestimates youth. Our youth may pay lip service to fun but in fact demands relevance. You can try and make education as fun as you want, you will never compete with Grand Theft Auto or whatever new star is on the block. If you make it relevant (and fun) kids will take education seriously.

In Flanders/Belgium, two courses are kids' perennial nightmare: French and math. French used to be important. Nowadays both parts of the country speak English to each other. You can lament it but French has become almost as irrelevant in Flanders as Spanish or Chinese. Stop teaching it, stop trying to make it fun. It's gone.

All kids around the world are told math is relevant to their lives. Sadly, they don't feel it in reality. We're still teaching the math of Euler and Gauss, through an interface resembling Euler's and Gauss'. We replaced pencil and paper with computer screens mimicking pencil and paper. Use computers for what they're good at. Replace arcane symbolic representations with actual simulations. Show linear and non-linear systems. Show singularities. Show 3D objects moving in 3D rendered space. Don't force students to do arkane manipulations like calculations or 2D visualizations of 3D, merely because this was what we needed to do before the computer was there. Don't inflict the solutions of the past on the needing of today.

See Bret Victor's "Kill math".

I have to ask, how many of the people commenting on these education threads have taught at an American state college in the last 20 years? In particular, how many have taught a remedial math class?

The pass rate for remedial math classes at Ivy Tech is 20-30%, depending on course, throughout Indiana. The average for my classes is 40-50%. Before you disparage such rates, let me share some facts. 1) Close to 25% of the students show up for exactly one class in the first two weeks, which means they cannot be dropped and they will get their financial aid check, and they are never seen again. 2) Another 10% or so were "special education" students--I'm not talking about regular disabilities here, but students who are two-and-a-half or even three standard deviations below the mean on IQ tests--but because they get the same high school diploma as regular students (!), they get admitted even though their reading level is no better than 2nd-3rd grade. (Word problems or applications are impossible when a student cannot even figure out the subject and verb in a sentence.) 3) A small, but significant, number of the remaining students have mental health issues requiring medication. Preventing student-student contretemps is a daily issue. (I suspect, but will offer no evidence here, that many American children--especially males, and doubly so African-American males-- have been unnecessarily medicated in order to control the classroom "factory.") 4) For all practical purposes, these are all first-generation college students. We are supposed to teach them appropriate behavior--personally, I don't care how students dress and talk--and I try my hardest to teach them how to study and what it takes to succeed. (I also break my class lessons up with short history segments when I see their eyes are "glazing over." I am continually surprised that no one ever recognizes the name of Euclid or what he is known for doing.) 5) At commuter campuses, such as Ivy Tech, Purdue Calumet, and IUN, students must commute. Sounds easy until one understands that many students have no or unreliable vehicles, and public transportation is inadequate or non-existent in this region. Also, there are issues with jobs and families for them to deal with on a continual basis.

I really try my best to reach all of my students, but I have come here too often to vent my frustration with a common lack of preparation by my students. This clearly is not a forum for teachers! I really will stop here, and only discuss education issues elsewhere with those that have actual experience with teaching.

Back to Go. (Or is that do not collect $200, go straight to jail?! I add this because I hope that I have not offended anyone here with my rants!)

I didn't know the discussion was reserved to Americans. I have taught math in public schools for 3 years and private remedial for my whole life. But only in Belgium, so I cannot really comment on real, American math education.

Regardless, I think all people are entitled to discuss math, and to discuss math education. If we'd reserve any subject only to those that have active experience with it, society would be a lonely place.

Your comment however shows how deeply rooted the problem is. We (society and mathematicians) have alienated the masses from the subject, through excessive abstraction, symbolism and specialism. Before we reform math education for the n-th time, we may need to reform math itself first, so that it becomes an activity in society (which can then be taught with good reason) instead of some esoteric wisdom, preserved to teachers, who hardly practice applied or theoretical math outside their classes in their real lives.

Speaking from a university students' perspective (germany) sitting in any math lecture is a huge waste of time, as in it is not getting you closer to passing the course, with or without a good grade.

Any exam that is not multiple choice tends to be tight on time, so the key to passing is usually not "just" understanding it, but also lots of practice, which (at least in my case) is better done at home alone rather than when a professor is blabbering over what he is doing(no offense). This is probably not applicable to the younger kids, as they might not have as much drive to self study (I sure didn't when I was younger).

Is there any correlation between the attendance and passing? Or is it more about the time invested? I would think it to be the latter, but I'm sure the teachers and professors might have more accurate data in that regard.

Bill Spight wrote:As I tried to indicate, I think that THE problem, if there is only one, lies with the culture, something you pretty much agree with.

That we do, indeed.

snorri wrote:Yes, and kids today cannot even translate simple passages from Latin without using Google. How are they supposed to compete when...oh, right no one cares about that any more.

There are lots of dying skills. Driving a stick shift. Sewing. No one's crying about the decline of these things.

Let's say we revamp the primary education system so that the majority of students are prepared to take, say, the Tripos before they graduate high school. Wonderful. We can congratulate ourselves on our pedagogical genius. The problem is that most of them will just wind up working for the lot that has more charisma despite needing to use a calculator for 6x4. That's a cultural thing, and it may change.

I don't think this is really the problem. Further down the line, in life, more things are important than just education, so it often happens that the person with the most charisma or street smarts, or whatever will get to be your boss. That's how it always was, and this is more "normal" than "cultural". And it is absolutely not an argument for not having to learn anything in school other than stuff like charisma (which school children also don't learn, I have to add.)

snorri wrote:I think the funniest part of the video is her story about how she was better prepared for calculus. Calculus? Who integrates any more? That's what Mathematica is for.

You can say that about anything, not just math. Why learn geography, if you can always use google map? Why learn physics when you can just open wikipedia? Why learn biology if you want to be a car racer? Why learn a foreign language when you never plan to step foot out of Albuquerque? And so on...

Why have schools at all, lets just all be dumb and happy.

I think you miss the point here. Most of the stuff you learn in school you will probably not need in everyday life. Just like most of the stuff you learn in college you will probably not need in your job. However - the stuff you learn teaches you certain things you will need, like abstract thinking, problem solving ability, assimilating and combining new knowledge quickly, extracting an d applying new knowledge, using sources, stuff like that. And true confidence in your own abilities, the knowledge that you have the general skills to tackle almost anything. This is what you learn in school, really, or what you should learn. And you do it by solving hard, abstract problems, in many areas, not just math. This is why I think kids in school should be pushed to learn more and go further, not entertained and amused so they don't complain about having to learn.

THe way things are, we end up with kids who after 12 YEARS OF FORMAL EDUCATION cannot add fractions and cannot write a simple paragraph and don't know where Canada is, but graduated with straight "A"s and think of themselves as geniuses. I know, I have seen it happen. Multiple times. Mind boggles!

And what is REALLY SCARY is not when the guy with more charisma is your boss, but when one of those kids is!

So your argument is , let's teach useless stuff which magically will make kids smarter and let's then be appalled when they neither can do the tricks nor appear to be smarter.

I'll take that as a vote for reform.

paK0 wrote:Is there any correlation between the attendance and passing? Or is it more about the time invested? I would think it to be the latter, but I'm sure the teachers and professors might have more accurate data in that regard.

I have been keeping track of this in my classes for about ten years. There are several things I count, among them attendance and completion of assignments. When I add up all the things I consider important I find that almost all students who complete 90% or more get a grade A or B, and the overwhelming majority of students who complete less than 70% get a D or an F.

Aidoneus wrote:I really try my best to reach all of my students, but I have come here too often to vent my frustration with a common lack of preparation by my students. This clearly is not a forum for teachers! I really will stop here, and only discuss education issues elsewhere with those that have actual experience with teaching.

I gave up trying to reach all my students for the simple reason that *all* of my students rarely attended on a regular basis if at all. My upper division courses were better attended, as you would expect, but I was lucky to get 40% attendance rates for my 100 level gen ed courses. Midterms were always a bit comical. I would preface the midterm by welcoming everyone to the course and introducing myself. My regular attendees would laugh while the newcomers were confused.

I share all of your frustrations and then some. The simple fact is that most students don't want to be there, which is nothing new. Our system is essentially a credentialing system from top to bottom, and when you couple that with faculty tenure and promotion that effectively places teaching at the bottom of the list, you end up with faculty who wax passionately about the importance of teaching while doing everything they can to avoid it, and students who are shocked when you fail them because they genuinely believed that just showing up for the midterm and final was more than enough to pass.

I think it was you, Aidoneus, who posted a link to one of those xtranormal videos featuring a professor/student interaction concerning why the student had failed the course. The sad part is just how close that "parody" is to actual professor/student interactions. The only thing that didn't ring true was when the professor said that most of his students appreciated the value of an education.

Of course, these experiences will vary depending on the type of institution. Smaller liberal-arts colleges and some state colleges are often places where quality teaching (and serious students) takes place. My teaching experiences came from a large, research-one university, where intro-level courses of 400+ students was commonplace. Very little learning takes place within such administrative monstrosities because educating is never the intent of those types of "courses."

Having said all that, I don't blame the students for this mess--they're the victims. They've been trained very well to respond to a system that doesn't value education as an end. And I'll leave it there because I want to enjoy the rest on my evening.